NL1044821B1

NL1044821B1 - Josephson travelling wave parametric amplifier and method for obtaining such a josephson travelling wave parametric amplifier

Info

Publication number: NL1044821B1
Application number: NL1044821A
Authority: NL
Inventors: Julian Wesselink Wouter; Boertjes Nils; Jochem Knoll Lennart; Bruno Alessandro; Basili Stefanos; Mykolayovych Dobrovolskiy Sergiy
Original assignee: Quantware Holding B V
Priority date: 2024-02-16
Filing date: 2024-02-16
Publication date: 2025-08-25
Also published as: TW202541418A; WO2025172308A1

Abstract

The present disclosure relates to a Josephson travelling wave parametric amplifier comprising a conductive layer, a dielectric layer, and a plurality of Josephson junctions, wherein each Josephson junction comprises a pair of electrodes that extend towards each other to define an area of overlap, wherein at least one electrode of one or more of the pairs of electrodes comprises a first lengthwise segment comprising the area of overlap, and a second lengthwise segment opposite the first lengthwise segment, wherein the second lengthwise segment of said at least one electrode comprises a diameter extending orthogonal to a lengthwise direction of the electrode and substantially parallel to the conductive layer, said diameter being larger than a diameter of the first lengthwise segment, whereby the second lengthwise segment having the enlarged diameter, in conjunction with the conductive layer and the dielectric layer, defines a capacitive structure that at least partially defines a capacitance of the JTWPA. The present disclosure moreover relates to a method for obtaining such a Josephson travelling wave parametric amplifier and to a system comprising such a Josephson travelling wave parametric amplifier.

Description

Ae

JOSEPHSON TRAVELLING WAVE PARAMETRIC AMPLIFIER AND METHOD FOR

OBTAINING SUCH A JOSEPHSON TRAVELLING WAVE PARAMETRIC AMPLIFIER

TECHNICAL FIELD

& [0001] The present disclosure relates to a Josephson travelling wave parametric amplifier (JTWPA), to a method for obtaining such a JTWPA and to a system comprising such a JTTWPA.

BACKGROUND

[0002] Josephson Iravelling wave parametric amplifiers (JTWPAs) are amplifiers capable of amplifying low amplitude signals with high gain and a minimal amount of introduced noise that approximates the quantum limit,

[0003] JTWPAs comprise a phwality of superconducting Josephson junctions that define a transmission line through which an input signal to be amplified propagates. The Josephson junctions may be connected to one another in series or fo form a plusslity of superconducting quaniun interference devices (SQUIDs) or superconducting non-linear asymmetric inductive elements {SNAILs). Each Josephson junction {or alternatively SQUID or SNAIL) functions as a non-linear inductive element that amplifies the input signal based on non-linear interaction with a pump signal, resulting in a transfer of energy from the pump signal to the signal amplification of the input signal,

The non-linear inductive elements form 4 repeating structure of unit cells, with each urdt cell comprising a capacitance to ground. In the non-linear inductive element the input signal interacts with a pump signal, resulting in a transfer of energy from the pump signal to the input signal. This in ten results in amplification of the input signal and the generation of an additional idler signal. The number of

Josephson junctions comprised by a JTWPA may be selected with respect to a degree of amplification to be achieved.

[0004] JTWPAS are suitable for amplifying particularly weak signals and find application within e.g. the field of quantum computing. In the field of quantum computing, JWTPAs may be utilised to read out superconducting quantum bits (gubits). The number of Josephson junctions comprised by 2 JTWPA may be significant, with hundreds or even thousands of Josephson junctions comprised by 2 transmission Ine.

[0005] State of the art JTWPAs are susceptible to improvements with respect to miniaturisation.

Miniaturisation is an important factor in the design of JTWPAs for various reasons.

[0006] Ow the one hand, an increased degree of miniaturisation decreases the physical diraensions and footprint of a JT WPA. This facilitates integration of JT WPAs into larger systems with Himited space and comprising various additional components. ITWPAs are an essential component Jor high performance quantum compuimg and the miniaturisation of these is on of tbe key challenges for scaling up te the high qubit count systems required for fault tolerant quantum computation,

Se [O007! Onthe other hand, 2 JTWPA with ap increased degree of miniaturisation comprises a reduced amoud of material that makes up the JTWPA. ITWPAs must be cooled to temperatures close to absolute zero, typically in the order of puillikelving, prior to operation. A minlaturised JTWPA having a decreased amount of material may thas be cooled more efficiently and af a faster vate, while using less

H capacity of a cryostat,

[9088] A further important factor in the design of JT WPAs relates to their manofscturing cycle time and manufacturing vield, Mamdacturing cycle time refers to the amount of me reguired to fabricate one or a batch of FEWPAS, whereas manufacturing viekd may refer to the manber of non-defective units that is obiained when x batch of JTWPAsS or alternatively JPWPA components is fabricated. Evidently,

Hr iis desirable to have a short manifacturing Cycle thine and a high manufacturing yield when fabrdeating

STWPAs or JEWPA components. 1 will be appreciated that this 1e particelarly relevant within the Held of gunntum computing, which is currently characterised by a trend towards more complex hardware comprising ever increasing numbers of components. This results it correspondingly Increased manufacturing cycle times and decreased manufacturing yields, H is therefore desirable to provide a 18 ITWPA thet facilitates fabrication techaigues or methods resalifng in ar improved smmdacturing cycle time and/or an improved manufacturing yield,

[0009] The objective of the present disclosure is provide a JDWPA with which one or mre, or possibly even others, of the disadvantages of JTWPAs known from the prior art isfare obviated or abated,

SUMMARY

{00107 The above stated object of the present disclostre is achieved with a Josephson fravelling wave parametric amplifier (IPWPA} in accordance with a first general aspect of the present invention, the

JTWPA comprising a conductive layer, a diclecidde layer, and a plumlity of Jesephson junctisns comprised by a transmission Hine, wherein each Josephson junction comprises £ pairof electrodes that extend towards cach ather to define an area of overlap, wherein at least one electrode of one or more of the pairs of electrodes comprises a first lengthwise segment comprising the area of overlap, and a second lengthwise segment opposite the fiest lengthwise segment, wherein the second lengthwise segment of said at least one electrode comprises a diameter extending orthogonal to a lengthwise direction of the electrode and substantially parallel to the conductive layer, said diameter being larger than a diameter of the first lengthwise segment, whereby the second lengthwise segment having the enlarged diameter, in conjunction with the conductive layer and the dielectrie layer, defines 2 capacitive structure that at ieast partially defines a capacitance of the ITWPA. [DGI] The inventors of the JTWPA according to the present invention realised that by selectively increasing a dimmeter within at feast a certain lengthwise segment of an electrode in a specified direction, a specified capacitance to ground of the transmission Hoe may be achieved for each Josephson junction or unit cell, In this way, 8 characteristic impedance of the JTWPA may be achieved without

3e the inclusion of additional diserste capacitor components, or at Jeast with a reduced amount of such discrete capacitor components.

[0012] The capacitance to ground of consccuiive Josepheon junciions is an important design oriteriog of the ITWPA as a whole. This capacitance to ground must comprise a valire such that satisfies a wave equation describing a signal propagating through the transmission Hoe. In a JTWPA according to the present invention, tbe required capacitance to ground is achieved entirely by leveraging the intrinsic capacitance of electrodes) of one or mare Josephson junctions, by designing the shape of said electrode apcordingly, This renders the inclusion of additional discrete capacitors (e.g. parallel plate capacitors and the like) to be superfluous, which may thus be omitted, The result is that a STWPA is obtained with a decreased physical footprint and increased degree of miniaturisation, which is moreover wel! suited ic be fabrivated In a highly efficient manage with reduced oycle Ume and in increased fabrication yield. 00131 In a preferred eotbodiment of a JTWPA according to the present inventian, the plurality of

Josephson junctions is amranged in a meandering arrangement pattern, wherein toms of the meandering arrangernent pattern are defined hy respective first lengthwise segraents comprising the area of overlap of neighbouring electrode pairs of consecutive Josephson junctions, fO014] The JWTPA according to the present invention having one or more electrodes with an increased diameter may nuecover be advantageously arranged in a space efficient socandering pattern.

In such a meandering pattern, the transmission fine extends in a zig-zagging pattern with pargilelly extending lengthwise segments and turns connecting the lengthwise segments. The above described configuration of electrodes of Josephson junctions facilitates easy and space efficient arangement of the transmission Une in such a meandering pattern. {0013} In further preferred embodiments of a ITWPA according to the present invention, the meandering pattern of the plurality Josephson junctions comprise a first substructure, comprising a first

Josephson jutiction comprising a first electrode and a second electrode, a second fosephson junction comprising the second electrode and a third slecirade, wherein the second electrode is interposed between the first electrode and the third electrode, a third Josephson Junction comprising the third electrode and a fourth electrode, wherein the third electrode is interposed between the second electrode and the fourth electrode, and a fourth Josephson junction comprising the fourth electrode and a fifth electrode, wherein the fourth elecirade is interposed between the between the third electrode and the fifth electrode, wherein the first slectrode, the third electrode and the fifth electrode extend parallel to one another in a frst direction, and the seoond electrode and the fourth electrode extend parallel tc one another in a second dirsclion. {00161 The above described first substructure is particularly suftable for implementing the aforementioned lengthwise segment of the meandering transmission line. Consecutive electrodes are arranged in Usshaped formations exch foroúng two Josephson junctions, wherein sald U-shaped formation are arranged mirrored to one another to achieve a highly space efficient arrangement.

A

JOT In further preferred embodiments of a JTWPA according lc the present invention, the meandering pattern of the phirality Josephson junctions conprises a second substructure, comprising a fifth Josephson function comprising a sixth electrode and a seventh electrode, a sbath Josephson junption comprising the severdh electrode and an eight electrode, a seventh Josepheon junction comprising the eight electrode and a mineth electrode, and an eight Josephson junction comprising the nineth electrode and a teath cleotrade, wherein the sixth electrode, the vight electrode and the tenth slectrode extend substantially parallel to one another in & third direction, and the seventh dectrode and the nineth electrode extend substantially parallel ks one another in fourth divection. 018] The here shove described second sebsineiure is partiodarly suitable to implement bans In 30 the meandering pattern of the transmission Hae, Hiewise In a space efficient manner with an increased nuraber of Josephson junction per unit of length of the transmission ling.

FOR18] In further prefosved embodiments of a JTWPA according fo the prosent invertion, the first fongtiovise segment and the second lengthwise of the al least onc electrode segment are integrally formed. 020) In further preferred embodiments of s JTWPA according to the present invention, the first fonpthwise segment and the second lengthwise segment are formed in a single Heration of 2 fadwivation rochnique, preferably wosingle itendion of an angled evaporation fabrication technique

[0021] The JTWPA according to the present invention and disclosure is not, © eiplained here above, dependent on the inchision of additionn! paraijel plate cupucitors and the Hie. bestead, the entirety of the reguired capaciame 10 ground is achieved by means of the electrodes themselves, which are designed fo achieve the woquired capsctiance to ground to thereby achieve the comesponding sharasteristic impedaner, All electrodes are substantially identical snd dering Rbeication of the JTWPA may be femed bdvgraily using the same fabrication technique (e.g. angled evaporation). This entails that the entire transmission line of the ITWPA may be obiained using only this Rabrication technique, without requiring additional fabeivation techniques to fabricate 2.9. additional capacitors to achieve the required capacitance to groond, As such, in these entbodinents the JTWPA may be fabricated jp a manner that is highly efivient with redeced manofachuring cycling tine and Increased manufacturing yield. 923} in further preferred embodiments of a JTWPA according to the present invention, the second lengthwise segment comprises a shape that is substantially circular or polygons! with a plwrality of equally dimensioned sides. {80231 be further preferred embodiments of a JTWPA acourding to the present inventien, a firs contour of the second lengthwise segment, when viewed in a first deposition divection of the fabrication technique, comespands fe 3 second continue of the second lengthwise segment, when viewed na sevorg! deposition direction of the fabrication technique, and/or the second lengthwise segment exhibits redational symmetry with respect to the first deposition divection and the second deposition direotien of the fabrication technique.

He {00247 In further preferred embodiments of a ITWPA according to the present invention, the second lengthwise segment comprises a substantially square shape. [60251 In embodinents wherein the JTWPA according to present invention is formed using angled evaporation as a fabrication technique, the transmission line of the JTWPA is formed by depositing conduciive material from a crucible from a plurality of different deposition directions. Because angled evaporation Is dependent on shadows cast by a resist to selectively deposit conductive material on specific surfaces, where the conductive material deposited is in principle determined by the orientation of the crucible relative to the work piece. This entails that it is preferable to design the second segment having the enlarged diameter in such a way, that said enlarged diameter remains consistent regardless of the deposition orientation used when performing consgeutive angled evaporation ierations. [00267 The above may be achieved by designing the second lengthwise segment of the af least one electrode to comprise a substantially circular shape, A substantially circular shape comprises the advantage that respective second lengthwise segments comprise similar surface areas regardless of the angled evaporation deposition direction that is used, Similar results may be achieved by designing the second lengthwise segment of the at least one electrode to comprise a polygonal shape having equally dimensioned sides, as loog as said polygonal shape is oriented adequately in consideration of the angled evaporation deposition directions. Both second lengthwise segments comprising a substantially circular shape and second lengthwise segments comprising polygonal shape having equally dimensioned sides oriented in consideration of the angled evaporation deposition directions may be said to exhibit

ZO rotational symmetry with respect to each of these angled evaporation directions, Typically, two different angled evaporation directions are utilised that differ from one another by 90 degrees. {00271 In further preferred embodiments of a JTWPA according to the present invention, the second lengthwise segment having the substantially square shape is oriented such that a diagonal of the second lengthwise segment coincides with a lengthwise direction of the at least one electrode. [D028] In embodiments wherein the JTWPA is fabricated using angled evaporation with two different angled evaporation directions at 90 degrees, it is particularly advantageous to design the second lengthwise segment to comprise the substantially square shape. In these embodiments, second lengthwise segments of consecutive electrodes may be obtained having very consistent physical diraensions, regardless of the deposition direction that is used for that particular angled evaporation iteration. This is because for square shapes, the shadows cast by the resists are particularly well predictable, even more so than for substantially circular shapes and other polygonal shape with equally dimensioned sides.

[0029] In further preferred embodiments of a JTWPA according to the present invention, the diagonal of the second lengthwise segment furthermore coincides with a horizontal vector component of at least one of the first deposition direction and the second deposition direction of the fabrication technique.

Be (00301 In further preferred embodiments of a JTWPA according Io the present invention, the second lengthwise segment comprises a surface area of 3 fun’ to 1000 unt’, more preferably of 6 und to 600 pat, most preferably of 10 wm’ to 130 wn” {00311 in further preferred embodiments of a JTWPBA according to the present invention, one or both of a capacitance and an inductance of the transmission line is periodically modulated, whereby the impedance of the transmission line is periodically modulated, such that a phase matching stopband Is defined in a dispersion relationship of the transmission line. {90321} Ieffpcijls these ernbadirents phase matching between an input signal to be amplified and a purap signal may be achieved by periodically modulating impedance of the lnmsmission fine. In these embodiments, additional phase matching structures otherwise included in the transmission Hine of the

JTWEAL such as discrete phase matching resonators, may be reduced in pumber or even entirely phyiated. Reducing the mumiber of phase matching resonators or excluding them entirely results in a vet further improved degree of minfaturisation. {331 la further preferred ombodinents of a JTWPA acoarding to the present invention, the inductance of the transmission Hae Is periodically modulated by periodic modulation of respective diameters of first lengthwise segments of consecutive slecirades, such that electrode pairs constituting consecutive Josephson junctions comprise periodically modulating areas of overlap.

[6034] In further preferred embodiments of a JTWPA according to the present invention, the capacitance of the transmission fine is periodically modulated by periodic modidation of respective 29 diameters of the second lengthwise segment of consecutive electrodes forming the plurality of

Josephson hunctions constituting the transmission line.

[4935] The above stated object of the present disclose is moreover achieved with a quantum computing system in accordance with a second general aspect of the present invention, said quantum computing system comprising at least a quantum processing unit {QPL comprising al least ane 28 owessurement object, ard at least one JTWPA in accordance with the present disclosure.

[0036] The above stated object of the present disclosure is moreover achieved with a method for abtainiog a JTWPA in accordance with a third general aspect of the present invention, the method comprising: providing a layer stack comprising 2 substrate, a conductive layer, a dielectric layer and a resist, subjecting the layer stack to an exposure process followed by a development progess, to thereby remove the resist af areas corresponding to respective Josephson junctions to be formed, forming a plurality of Josephson junctions each comprising a paly of electrodes that extend towards each other to define an area of pverlap, forming at least one electrode of one or more of the pairs of electrodes ta comprise: á first lengthwise segment comprising an ares of overlap with u neighbouring electrode, and a second lengthwise segraent opposite the first lengthwise segment, wherein said second lengthwise segment is formed to comprise a dienster extending orthogonal to a lengthwise direction of the

Je electrode and substantially paralie] to the conductive layer, said diameter being larger than a diameter of the first lengthwise segment.

[0037] Ina preferred embodiment of the method in accordance with the present invention, the step of forming the plurality of Josephson junctions comprises: forming the plurality of Josephson junctions ina meandering arrangement pattern, wherein tums of the meandering arrangement pattern are defined by respective first lengthwise segments comprising the area of overlap with a neighbouring electrode of consecutive Josephson junctions, wherein the meandering arrangement patiern is preferably formed to comprise a first substructure, comprising a first Josephson junction comprising a first electrode and a second electrode, and a second Josephson junction comprising the second electrode and a third electrode, wherein the second electrode is interposed between the first electrode and the third electrode, wherein the first and third electrode extend parallel to one another in 2 first meandering direction of the meandering pattern, and the second electrode extends in a second meandering direction of the meandering pattern perpendicular to the first meandering direction, and wherein consecutive first substructures are arranged mirrored along a heartline of the first substructure.

[0038] Iu a further preferred erabodiments of the method in accordance with the present invention, the meandering arrangement pattern is formed to comprise a second substructures, comprising a third

Josephson junction comprising a fourth electrode and a fifth electrode, a fourth Josephson junction camprising the fifth electrode and a sixth electrode, a fifth Josephson junction comprising the sixth electrode and a seventh electrode, and a sixth Josephson junction comprising the seventh electrode and an eight electrode, wherein the fourth electrode, the sixth electrode and the eight electrode extend parallel to one another in the first meandering direction, and wherein the fifth electrode and the seventh electrode extend parallel to one another in the second meandering direction of the meandering pattern, [C039] In a further preferred embodiments of the method in accordance with the present invention, the first lengthwise segment and the second lengthwise of the at least one elecirode segment are integrally formed, preferably in a single iteration of a fabrication technique, more preferably a single iteration of an angled evaporation fabrication technique.

[0040] bua further preferred embodiments of the method in accordance with the present invention, the second lengthwise segment is formed to comprise a substantially square shape, wherein said substantially square shape is preferably oriented such that a diagonal of the second lengthwise segment coincides with a lengthwise direction of the at least one electrode.

BRIEF DESCRIPTION OF THE DRAWING

[6041] The present invention will be elucidated here below with reference to the drawing, in which: [00421 Fig. | schematically depicts an electronic ctrcuit of a JTWPA that may correspond fo some embodiments of the present invention; [00431 Fig. 2 shows a top-down view of an exemplary embadiment of a part of a transmission ling comprised by the JTWPA of Fig. | in accordance with the present disclosure:

Be

[0044] Fig. 3A. Fig. 3B and Fig, 3C illustrate an example of successive steps of a method for obtaining a JTWPA in sceordance with the present disclosure;

[0045] Fra. 4A and Fig. 4B respectively show sectional views of ahtermative embodiments of the sragsmission line of Fig. 2 to Fig. 3C;

[0046] Fie 5A schematically depicts a transmission line of the JDWPA in accordance with prelerred embodiments of fhe present invention; {00477 Fig 5B shows goicroscopic view of a fivst part of the transmission fine of Fig, SA:

[0048] Fig, 50 shows à mieroscogic view of a secord part of the transmission line of Fig. SA: 100491 Fig. 6A shows top-down view of a further exemplary embodiment of a part of a transraission

JO ee comprised by the JTWPA inaceordance with the present disclosure; [D038] Fig. 6B shows a schematic depiction of an electronic ciroult of the embodiment of Fig, 84; asd

[6031] Fie. 7 schematically depicts an exemplary einbodiraent of a system in accordance with cerlant embodiments of the present inventian,

DETAILED DESCRIPTION

10032] Fig. 1 schamativally depicts an electronic circu of 2 Josephson travelling wave parametsic amplifier (JTWEFAY 100 according to an exemplary erabodinment of the present invention, The JTWPA 10G may be cooled te a cryogenic lemperature where it exhibits superconductivity to amplify microwave signals, [00531 The JTWPA 100 comprise a Wansmission Hoe 103 through which an input signal to be amplified propagates. In the exemplary embodiment of Fig, 1, the transmission line 103 comprises a plurality of Josephson junctions 110, 120, 130 connected in series to define the transmission line 103.

It will be appreciated thal the transmission Une 103 may alternalively comprise superconducting goantem interference devices (SQUID) and/or superconducting, non-linear asynmetric inductive eiemenis (SNAILs}, both of which likewise comprise Josephson junctions. Each Josephson junction 110, 126, 130 functions as a non-linear inductive clement capable of amplifying an input signal based on non-linear interacting with a pump signal, to thereby achieve parametric amphification of the input signal, The JTWPA 100 may achieve parametric aoplification based on a four-wave mixing or three- wave mixing principle. fn the case of four-wave mixing, four photons are involved in the amplification process in which two pump signal photons are contbined into a signal having the frequency of the input signal, and an idler signal photon, Similarly, three-wave mixing involves the interaction of three photons.

[0034] In accordance with certain embodiments, the transmission Hne 103 may comprise a microstrip, an iwerted miceostrip or a stripline geemetsy. Possible geometries of the fransmission line 103 in accordance with various embodinents of the present inverdion will be further elucidated here below with reference to Fig, 4A and Fig, 4B.

[DOS5] The transmission fine 103 is pertodically shunted to an electrical ground connection 105 via a plurality of capacitor structures TH, 112, HY to achieve a characteristic impedance JTWPA IQ. To prevent unwanted reflections of signals, the capacitance of cach of the ground capacitors 133 of is selected such that the ITWPA 100 comprises « predefined impedance of eg 30 0. 5 [0036] While the tansmission Une 103 of the SPWPA 100 may be shunted ta the electrival ground conrection 105 at evary Josephson junclion 110, 120, 130 as is depicted in Fig. 1, the present disclosure is not mised thereig.

[0057] Wave mixing-based amplification is a phase dependent process that requires a phase difference between the input signal aad the pump signal to be zero wr at least close lo zere, However, 1D the input signal and the pump signal experience a negative phase shill as they propagate through the transmission fine 103, To counteract this relative phase shifl and coswre phase waiching of the pump signal and the Input signal at each of the Josephson junctions 110, 120, 130, certain embodimenis of the

JTWPA 100 furthermore comprise one or mote phase matching phase matching resonators 107 that ave perindically connected the transmission tne 103 via a capacitor 104, The phase malching resonator 107 in Fig. | comprises a resonalar capacitor 108 and a resonator inductor 106. To enmue adequate phase matching, the phase matching resonator 107 may be configured ic define a phase matching stopband with respect to a specific frequency of the input signal propagating through the transmission line 103.

[0038] It is noted that the phase matching resonator 107 is merely an optional feature that may be excluded from the STWPA 100, in accordance with certain preferred embodiments of the present invention. In these embodiments, phase matching may be achieved by alternative ravans. An example of these embadirpents will be discussed bere below with references to Fig. 64 and Fig. 61% [00591 ht will be appreciated that the JTWPA 100 may comprise additional components other than the components shown in Fig. | and described hereabove. In particular, in certain embodiments the

JTWPA 100 may comprise additional vapacitors and Josephson junctions 110, 120, 130, Tt will moreover be appreciated that the number of capacitors and Josephson junctions 110, 120, 130 comprised JTWBA 100 may vary depending on the required specifications of the JTWPA 160, For example, the namber of Josephson junctions 110, 126, 130 may be selected in consideration of a degree of amplification that is to be achieved. In accordance with certain embodiments, the number of

Josephson junctions 119, 126, 150 comprised by the ITWPA 100 may be several hundred, several thousand or more, (00607 It will also be appreciated that, while all of the Josephson junctions 110, 120, 130 in Fig. 1 are connected in series to define the transmission 103, the present disclosure is not lined thereto. The transmission fine 103 may alternatively comprise e.g. SQUIDs, SNALLs and possibly other devices parnprising Josephson junctions. [00811 The JTWPA 100 may exhibit an enhanced degree of mindatarisation at leest on account of the manner through which the capacitor structures 111, 112, 113 are physically implemented. This is chieldated with reference to Fig. 2 and Fig. 3A to Fig. 3C.Fig. 7 shows a top-down view of a physical

~~ implementation of {a part of) a JTWPA 200, in accordance with the present invention and disclosure.

Fig, 3A to Fig 30 illustrate a method for obtaining or fabricating a ITWPA 300 in accordance with the presen Invention, The JTWPA 300 of Fig, 3A-C and the JTWPA 200 of Fig, Z cach correspond to the

ITWRA Hof Fig. 1 8 DSZ] The JTWPA 200 of Fig. 2 comprises a plurality of Jesephson hmctinns ZIJ, of which one is depicted in Fig, 2. The Josephson junction 218 ds Tormed by a pair of a first electrode ZI and a second electrode 212, The first electrode 211 and a scomd electrodn 212 extend wards ore another fo define an area of overlap indicated by the dashed encirclement in Fig. 2. Elecirode 211 and electrode 212 moreover pack comprise arespective frae aad 2117, 212’ beyond the area of overlap: The area of overlap comprises a weak Hak belween the first electrode 211 and the second electrode 212 of non-conductive oatarigd forming a tunnel junction that {acifitates wave-mixing based soplificatipn, ze described here #hove, {0631 In accordance with certain smbodinwnts of the present fovention, the frst electrode 211 and the seomnd electrode 212 may comprise alumin, In such ambodiments, the weak link interposed

IB between the first dlectrode 217 and the second electrode 212 al the swea of overfap may comprise zhaninium oxide, The skilled person will mavertheless appreviate tha the first and second electrodes 211, 232 may comprise alternative materials thal exhibit superconducting properties al eryogeaic femperatgras. {00641 The Josephson junction 210 formed by the first electrode 211 and the second clecimde 212 are srvanged on a divlectric layer 208 that is comprised by a layer sleek, The layer stick moreover comprises at feast one grounded conductive layer 307 and a substrate 389 {sce Fig, JA), Possible sordigurations of the layer stack within the scope of the present disclose will be elucidated here below with reference lo Fig. 3A be Fig, 30 and Fig, 44 nod Fig. 4B. In Fig. 2, only the disloctric layer 208 ig visible, {DOES} The fest and electrodes 211, 212 constituting the pair of dectrades forming the Josephson

Junction 210 each moreover conmprise a respective frst lengthwise segment 211s, 2122 and a second temthwise segment 2115, 213k. The is lengthwise segment Zia of the first electrode 211 and the

Hirst lengthwise segment 2132 of the seeend electrode 212 exch comprise the aren of overlap defining the fosephson fenation ZE), The size or surface area of the area of overlap is an bnportant characteristic of the Josephson punetion 215, becaose it defines the critical current 1 of the Josephson junction 214, which In tum is selevted in consideration of the input signal (e.g. a signal emitted by a superconducting spb} to be amplified, As suck, the respestive diameters Dh. Daze (In the width direction) of the iest lengthwise segment 2112, 212a are in practice fixed with respect of the application of the ITWPA 206, 308. As van be discerned frome Fig. 2, this siz or surface area of the area of overlap is effectively defined by the respective diameters Da, Dies of the Srst lenpthavise segment 21 Ia, 2122 of the first and seonnd electrodes 211,212.

“A1-

[0066] Each of the first and second electrodes 211, 212 moreover comprises a respective second lengthwise segment 21 Ib, 212b different from the respective first lengthwise segments 21 1a, 212a. The respective second lengthwise segments 21 1b, 212b are each arranged opposite the fust lengthwise segment 21 ta, 2124 on their respective electrodes 211, 212. [D067] As can be discerned from Fig. 2, the second lengthwise segment 211b of the first electrode 211 comprises a diameter Dzn that is larger than the corresponding diameter Dan, of the fist lengthwise segment 21 1a. Likewise, the second lengthwise segment 212b of the second electrode 212 comprises a diameter Da that is larger than the diameter Digs of the first lengthwise segment 2124 of the second electrode 212.

[0068] As can be discemed from Fig. 2 in conjunction with Fig. 3A, the respective enlarged diameters

Daw, Daim, each extend orthogonal tc respective lengthwise direstions of the first and second electrodes 211, 212; and substantially parallel to the conductive layer 307. It is noted that in the top-down view of

Fig. 2, the conductive layer 307 is arranged underneath the dielectric layer 208.

[0069] The first electrode 211 and the second electrode 212 are conductors and therefore exhibit an intrinsic capacitance when arranged in the vicinity of other conductors and separated by a dielectric. In accordance with the present invention, the respective enlarged diameters Dang, Dai of the second lengthwise segments 21 Ib, 212b are dimensioned such that the second lengthwise segments 2115, 2126 form capacitive structures with the conductive layer 307 disposed underneath the dielectric layer 208, 308. In other words, according to the present invention the intrinsic capacitances of the fist electrode 211 and second glectrode 212 are leveraged to implement the capacitor structures 111, 112, 113 shown in the electrical circuit of Fig. 1, by forming the first and second electrodes 211, 212 to comprise said enlarged diameter.

[0070] The here above described configuration of the first and second electrodes 211, 212 renders the inclusion of additional discrete capacitors, such as additional (parallel plate} capacitors and capacitors comprising retum conductors as found in coplanar waveguides, ic be redundant. Such additional discrete capacitors thus do not need to be included for achieving a characteristic impedance of the JTWPA 200, which is typically 30 Q. The JTWPA 200 may therefore be formed with smaller dimensions and with an increased degree of miniaturisation.

[0071] In Fig. 2, the second lengthwise segments 21 1h, 212b of the first and second electrodes 214, 212 have their respective diameters Dei, Deen enlarged and tbe second lengthwise segments 21 1h, 212b each comprise a substantially square shape. kt will be appreciated that the present disclosure is not limited thereto and that the second lengthwise segments 21 ib. 212b may alternatively comprise e.g. circular shapes and polygonal shapes that preferably comprise equally dimensioned sides.

[0072] In embodiments wherein the JTWPA 200 including the at least one Josephson junction 210 is tabricated using angled evaporation or a comparable fabrication technique, certain shapes of the second lengthwise segments 21 1h, 21 2b result in better fabrication results than others. A preferred method for fabricating a JTWPA 100, 200 based on angled evaporation or comparable fabrication techniques is slpcidated here below with reference fo Fig. 3A le 3C. f0073} Regardless of their shape, the second lengthwise segments 21th, 2 126 may comprise enlarged dlameters Dogs. Dhow such that thelr respective surface areas coraprise 3 pat to 1000 pm, more & preferably 6 pm’ to 600 pm’, most preferably 10 um? fo 150 wm’, [00741 Fig 34 shows a perspective view of a workpiece 300 that is subjected to a method in accordance with the present disclosure to thereby obtain the JTWPA 200 of Fig. 2. 0751 The workpiece 300 constitutes {part of) a TWPA and comprises n substrate layer 309, a conductive orelectrieat ground layer 307 armanged on the substrate layer 308 and a dielectric layer 308 arranged on the conductive layer 307 opposite the substrate layer 309. A photoresist 306 is arranged on the dielectric layer 308 opposite the conductive layer 307.

[0076] In a method for obtaining a JTPWPA 100, 209 in accordance with certain embodimenis of the present invention, the photoresist 306 of the workpiece 308 is subjected fo an exposure process followed by a development process to eich a predefined pattern in the photoresist 306, exposing the dielectric layer 308 undameath. From Fig, JA it can be discerned that the etched pattern comprises two elongate patterns that intersect with one another and are formed by selectively removing the material of the photoresist 308, The elongate patterns both comprise a respective narrowed section 31187, 3122" anda respective enlarged section 31107, 32h. {0077} Fig. 38 shows Ine workpiece 300 of Fig. 3A in a state following the state of the workpiece 300 depicted in Fig. 3A.

IDU78] In Fig. 3A, the fist electrode ZH has been formed within the elongate pattern inefuding narrowed section 31 Ia’ and enlarged section 3115’, Here, the first lengthwise segment 31 La of the frst clectrade 311 is formed In the narrowed section 3 11a” and ils second lengthwise segment 3 lib is formed in the enlarged section 3115 of the etched pattern. The first electrode 311 is formed using angled evaporation. Angled evaporation, and substantially similar or comparable fabrication technigues twolving deposition of evaporated metal at an angle, may alse be referred to as the Niemeyer-Dolan technique, shadow evaporation, angelar evaporation and iri-angle deposition. [90791 Angled evaporation involves conductive material {e.g vaporised aluminium) being deposited onto He warkpivee 300 from a crucible {not shown) from a disposition direction at an angle relative tn the workpiece 300, to thereby form the first electrode 311, Ja Fig. 3B, the angled evaporation deposition direction is indicated by the arrow at the righthanded side of the figure.

[0080] When conductive material is deposited onto the workpiece 300 from the deposition direction depicted in Fig. 38, the dielectric layer 308 within the narrowed section 3112” is entirely covered by the deposited conductive material. In contrast, the enlarged section 3115’ is only partially covered by the deposited conductive material, leaving a small area 399 of the dielectric layer 308 along the edge of the enlarged section 311% exposed. At this partial chroundferentisl area 399 of the enlarged seption

311b’, the conductive material is blocked by the photoresist 306 before it can reach the dielectric layer 308, In other words, the photoresists 306 casts a ‘shadow’ in this area 399. [00811 It is noted that in Fig, 3A, no deposited conductive material is present within the second elongate pattern other than within where its narrowed section 3122 overlaps with the narrowed section & 3112" of the elongate pattern, the deposition of conductive material here being blocked by the photoresist 306. 10082] The conductive material deposited onto the workpiece 300 using angled evaporation may be vaporised aluminium or any other suitable material that exhibits superconducting properties al cryogenic temperatures.

[0083] Following the deposition of conductive material illustrated in Fig. 3A, an oxidation layer (not shown} may be formed on the deposited conductive material, For example, a layer of aluminium oxide may be formed on the deposited conductive material by briefly introducing oxygen into an enclosure in which the workpiece 300 is contained and which is otherwise kept hermetically sealed from its environment Aluminium oxide may constitute the weak Buk at the area of overlap between the first electrode 211 and the second electrode 212 forming the Josephson junction 210 in Fig. 2.

[0084] Fig. 3C shows the workpiece 300 of Fig, 3A and Fig. 3B in a state following the state of the workpiece depicted in Fig, 3B. The workpiece 300 may have been rotated relative fo a crucible (not shown) prior to the state depicted in Fig. 3C. 0083] In Fig 3C, the workpiece 300 has been subjected to a second iteration of the angled evaporation technique to thereby form the second electrode 312. The deposition direction is indicated by the arrows on the lefthanded side of this figure. The second electrode comprises a first lengthwise segment 3122 formed in the narrowed section 3122 of the elongate pattern and a second lengthwise segment 312b formed in the enlarged section 312° of the elongate pattern,

[0086] Similar to what is described here above with reference to Fig. 3B, the deposited conductive maierial covers the entire surface area of dielectric layer 308 within the narrowed section 312’, and only partially covers dielectric layer 308 within the enlarged section 312b’ due to a shadow being east in a peripheral area of the enlarged section 312b’ by the photoresist 306, The now formed respective first lengthwise segntents 311a and 31th now overlap with one another to form the area of overlap defining the Josephson junction 310. Again, no conductive material is deposited In an area 399° af the periphery of the enlarged section 312b°, duc to the photoresist 306 casting a shadow it this area 399°. [00871 After completion of the fabrication step depicted in Fig. 3C, the photoresist 306 may be removed from the workpiece 300 along with any build-ups of excess deposited conductive material, to : thereafter obtain the JTWPA 200 depicted of Fig. 2.

[0088] Jt will be appreciated that Fig. 34 to Fig, 3C merely depict the fabrication of a single

Josephson junction 310 among a plurality of Josephson junctions comprised by a JTWPA 190, 200 in accordance with the present disclosure and invention. In practica] implementations of the depicted method, multitudes of first electrodes 311 may be formed in a single angled evaporation deposition eration and Rather multitudes of second electrodes 312 may be formed in a single second angled evaporation deposition leration. As such, the many Josephson Junctions 119, 120, 139, 210 comprised by the JTWPA 109, 200 may be fabricated very efficiently In 2 minimal number of fabrication steps and with a reduced manufacturing cycle Hime. With no subsequent fabrication steps required to form further components (e.g. parallel plate capacitors, interdigitated capacitors, and the like) to achieve the characteristic impedance of the transmission Hoe 103, the transmission Hine 183 may be finalised immediately when all the losephson junctions 310 are formed, A JTWPA 100, 200 in accordance with the present disclosure thus not only exhibits a high degree of minlaturisation due to the absence of additional capacitors, but is also particularly well suited to be fabricated using a highly efficient fabrication method, that in principle conducted exclusively using angled evaporation or comparable fabrication techniques, without requiring additional fabrication steps to foro said additional capacitors.

[6089] From Fig, 3B and Fig. 3C, it can be discerned that the formed second lengthwise segments alih, 2170 cach comprise a surface grea that is smaller than a diameter or surface ares of the enlarged sections 31D, 312b° in which they are respectively formed. As is explained here above, this reselts from the casting of shadows by the photoresist 306 within areas 399, 399’, which is inherent to angled evaporation and other comparable fabrication technigues. [00901 The enlarged sections 3110, 3126 etched into the photoresist 306 must therefore be designed and dimensioned to take the casting of shadows by the photoresist 305 Into account, such that the sucoessively formed second lengthwise segments 311k, 312b each comprise a substantially identical diameter Dyn, Diy veselting in respective surface areas matching a desired capacitance, regardless of the angled evaporation direction used to form them. Said desired capactiance in part detenpines the characteristic impedance (typioally 50 OQ) of the IPWPA to prevent reflections of signals entering and teaving the JTWPAL

[0091] One possible shape for the enlarged sections 31 1D, 312b7 that theoretically matches the above stated criteria is a substantially circular shape. A substantially circular shape for the enlarged sections

SHB, 312° comprises the advaniage that the formed enlarged section JI, 312K at ast theoretically always comprises a substantially identical diameter and surface area, regardless of which angled evaporation deposition direction Is used and the angle between them, Substantially circular shapes for the enlarged sections 3110, 212b nwrepver comprise the advantage that, regardless of the angle between the angled evaporation deposition direction, the chtained enlarged sections 31, 312 ave always substantially identical, zi least in theory. {0092} Notwithstanding the above, consistency between second lengthwise segments 311b, 312b of respective electrodes 311, 312 may also be achieved with polygonal shapes having equally dimensioned sides, Such polygonal shapes must, however, be oriented in consideration of both of the angled 38 evaporation deposition directions that are utilised, More specifically, these polygonal shapes must he orfented such that they exhibit rotational syvounetry with respect to the first angled evaporation disposition direction {sce Fig. 38, the arrows on the righthanded side of the figure) and the second angled evaporation disposition direction {see Fig. 3C, the arrows on the lefthanded side of the figure).

[0093] Second leogihwise segmenis 311k, 3126 comprising substantially circular shapes likewise exhibit rotational synumetry with respect to the first angled evaporation disposition divection and the second angled evaporation disposition direction, regardless of the angle between these differant disposition directions. Nevertheless, substantially circular shapes have been found te result in a reduced consistency of the second lengthwise segments 31h, 3180 relative to polygonal shapes {e.g square shapes). Presumably, this results from the fact that circular shapes comprise curved edges, for which it is difficult to predict how shadows will be cast during an angled evaporation fabrication process.

[0094] In accordance with certain embodiments of the present invention, @ first contour of the second lengthwise segment 31 1h, 313k of the at least one sloctmde 311, 312, when viewed In a fest deposition direction (e.g. as indicated the arrows by the arrows at the righthanded side of Fig. 3B) of the angled gvaporation fabrication technique. comesponds to a second contour of the second lengihwise segment 31th, 3124, when viewed in a second deposition direction (e.g. as indicated Isy the arrows af the lefthanded side of Fig. 3B) of the angled evaporation fabrication technique. [00931 In practice, the angle between the first angled evaporation disposition direction and the second angled vvaporation disposition direction is typieally 90 degrees. When said angle is GO degrees, it is particularly advantageous for the lengthwise segments 31 1h, 313h to comprise a substantially square shape, which is the case for the embodiments in the appended drawing. In said depicted embodimends, the substantially square lengthwise segments 31 1b, 312b are moreover oriented such that their diagonal coincides with the lengihwise directions of the at least ong electrode 311, 312, 0096] Ia accordance with more preferred embodiments, the disgonal of the second lengtivedse zcomerds 311k, 312 furthermore coincides with a horizontal vector component of at feast one of the first {angled evaporation) deposition direction and the second {angled evaporation) deposition direction of the {angled evaporation) fabrication technigue. {O097] Fig. 2 and Fig. 3A to Fig, 30 depict an embodiment wherein the JTTWPA 200 or workpiece 300 exhibis what may be referred to as a mmicrestrip geometry, The present disclosure is, however, not

Hmited thereto and Fig, 4A and Fig. 4B respectively depict alternative geometries.

FO0R8] With the method according to the present invention illustrated in Fis 34 to Big. 3B based on angled evaporation, the first lengibwise segment 31a and the second Jengihwise segsoent 311b of the first electrode 311 are preferably integrally formed, Likewise, the first lengthwise segment 3 12a and the second lengthwise segment 212b of the second electrode 312 are preferably integrally formed.

[0099] Fig. 4A depicts a cross section of an alterrative embodinent of the JTWPA 100, 200, 300 of the foregoing figures comprising an altomative geometry, The geometry of the anbodiment depicted in

Fig 48 may be referred to as an inverse mitorosinip geometry that differs frorn the geometry of the foregoing figures in that the conductive layer 407 is arranged on top of the dielectric layer 408 and the substrate 408, In the embodiment of Fig. 4A, the dielectric layer 408 is interposed benween the

~46- conductive layer 407 and the substrate 409, The diclecirde layer 408 moreover encloses an clecirsde 417, which is effectively embedded with the dieleatric ayer 408, The electrode 412 may correspond fr cither the frat electrode 211, 311 or the second elecirade 212, 312 of the forgoing figures. fON1007 Fig 4B depts cross section of a further gltemative enthodiment comprising a stripline peemetry. In Fig dB, a first conductive hyer 407 and a second conductive layer 407 are arranged on either side of the dielectric hayer 408. The conductor 412°, which may correspond to either the electrode 211, 311 or the second electrode 212, 312 of the foregoing figures, is embedded within the sliclectric layer 408.

B03] Fig. % shows a schematic depletion of a transodssion le MG corresponding to the wansmission Hine fn Fig 1. The transmission Une 303 comprises a plurality of Josephson junctions 210 enrresponding to the embodiment depicted In Fig. 2, The number of Josephson jovetions 210 may be sedected in consblamiion of a required degree of aephification of aa put sigeal. As such, the ruber of Josephson junctions included m3 the bansmisston [ins 383 may be several hundred or severst thousand,

[002] The transmission Hoe 303 of Fig ZA is amranged In a patler hat optimises the mumber of

Josephson hmeilons per unit of surface area, As such, the transmission How 503 is armnged in an alternating or zig zegging pattem, comprising foagiiuding] sections 3531 of the wansmission Ine 302 alicrngting with tom sentions 362, after which the tressmission {ine hes made a 159 depres bes, While it fs conceivable that other meandering pattern (e.g. Circular) may be utilised, «transmission Ine 103 comprising Josephson junctions according to fhe present fovention by partivelarly well suited Wo implement the meandering pto of the transadssion Ine 503 of Fig, SA. This will be made apparent with reference to Fig, OB and Fig. SC, which wespectivaly depict microscopic views SST, 5362" of the tongituding! sections 531 und the turn sections 362.

BHD] Fig 3B shows a microscopic view of ene of the longitudinal seotions 338 of the tapsnission 25% line 303 of Fig, SAL From Pig, SR, 11 oan be discerned that consecutive electrodes SIJ, 342, 513, 314,

ZIS form a first substructure 3317 that encompasses corseuutve Josephmon functions S18, 320, 330, 344, fORI04] The first substructure $31 comprises a Íhst Josephson hwetion S10 that with a frst electrode

SU} and asecond electrode S12, that overlap foros the first Josephson junction S ID. The sepond ekeetrode 51% and 2 third electrode 412 overlap to define a zevondt Josephson junetion 328, whh the second electrode $12 being arranged between the frst electrode 311 and the third electrode 312, The died electrode 512 overlaps with a fourth eleutrode 514 to define a third Josephson junction 330. Here, the third slectrode $13 is arranged between the second electrade $12 and the fourth elecivnade $14. The fourth electrode 314 extends towards a fourth Josephson junction 340, which is forped by the Fourth electrode $14 overlapping with a fifth electrode 813,

FOOD] The Gest substructure 3317, comprising the vonseculive electrodes SEY, S12, BIJ, 514, SIS overlapping to form the consecutive Josephson junctions 510, 520, 330, 348, may thus be considered to exhibit a U-like shape; with a plurality of these first substructures 351° arranged sequentially mirrored along opposing sides of the dashed heartline 588 in Fig. 38, forming the longitudinal sections 531 of the transmission line 503. {001061 In certain embodiments, the first electrode, the third electrode $13 and the fifth electrode 515 all extend lengihwise parallel to one another in a single first meandering direction ceinciding with a diagonal direction of the substantially square shaped second lengthwise segments of each of the first, third and fifth electrodes STI, 513, 515. In these embodiments, said first direction meandering may moreover coincide with a horizontal vector component of a first deposition direction of the angled svaporation fabrication technique.

[00107] Likewise, it can be discerned from Fig, 5B that the second electrode 512 and the fourth electrode 514 also extend parallel to one another in a second meandering direction. In embodiments wherein the deposition directions of the angled evaporation fabrication technique intersect one another at 90 degrees, the second meandering direction may be perpendicular ie the aforementioned first meandering direction. This second meandering direction preferably coincides with a horizontal vector component of a second deposition direction of the angled evaporation fabrication technique, and with diagonal directions of the respective substantially square shaped second lengthwise segments of both of the second electrode 512 and the fourth electrode 514, Consequently, the first substructure 5517 of

Fig, SA is easily fabricated using the fabrication method described here above with reference to Fig. 3A to Fig. 3C.

[00108] The first slectrode 511 and the fifth electrode may be arranged at an offset in the first meandering direction, The first electrode 511 and the third electrode 513 may be arranged at an offset in the second meandering direction, The third electrode and the fifth electrode 515 may be arranged at an offset in the second meandering direction, The second electrode 312 and the fourth electrode 514 may be arranged at an offset in the first meandering direction.

[00109] The longitudinal sections 551 of Fig. SA are preferably connected fo one another via tum sections 562. Fig. 5C shows 2 microscopic view of a tum section 362, which will be referred to as a second substructare 562° of the transmission line 503. 0118] Fig. 5C shows that said second substruciure 560° comprises a fifth Josephson junction 550 with a sixth electrode 516 and a seventh electrode S17 that overlap one another to define the fifth

Josephson junction 550, The seventh electrode 517 moreover overlaps with an eight electrode 518 to form the sixth Josephson junction 560. The second substructure 360° moreover comprises a seventh

Josephson 570 junction having the eight electrode 518 overlapping with a nineth electrode 519. Lastly, the second substructure 560° comprises an eight Josephson junction 580 where the nineth electrode 519 overlaps with a tenth electrode 521.

[00111] InFig. SC, the seventh electrode 517 and the nineth electrode 519 extend substantially parallel to one another in a third direction. In embodiments wherein the transmission line 503 comprises both the here ahove described first substructure 331° and the second substructire 562°, this third direction may be the first direction referred to ís relation te Fig. SB. 99112] Likewise, in Fig, SC the sixth electrode 515, the eight electrode 518 and the tenth electrode 521 extend substantially parallel to one another in a fourth direction, The fourth direction may be § substantially perpendicular to the third direction of Fig. 5B. In embodiments wherein the transmission {ine 503 comprises both the first substructure 35817 and the second substruchee 3607, the fourth direction may correspond io the second direction of referred to in relation to Fig, 5B. {001137 Fig. 6A and Fig. 68 show a transmission line 803 of a JTWPA in accordance with additional embodiments of the present invention, The embodiment depicted In Fig. 6A and Fig. 68 comprises additional measures for achieving phase matching between the input signal to be amplified and the pomp signal, As such, in these embedisents the one or more phase matching resonators 107 {see Fix. 1) may be reduced or even omitted entirely. {001141 As explained here above with reference Ie Fig. 1, the impedance of the transmission ling 163 is predefined to prevent unwanted reflections, and typically comprises 30 £2, In the embodiment of Fig. 6A and oR, the npedance of the transmission line 603 is periodically modulated, e.g. from 48 {to 52 £3, to thereby engineer a phase matching stopband in the dispersion relation of the {ransmission line, As such, phase matching between the input signal to be amplified and the pump signal may be achieved without using a discrele phase matching resonator 107, as is the case inthe embodiment of Fig. 1.

[60115] The impedance of the transmission Hne 603 may be perindisally modulated by peripdically modolating one or both of the vapachance and inductange {or critical current) of cach Josephson lunction 610, 620, 638. In the exeraplary embodiment of Fig. 0A and Fig. 68, both of the capacitance and the inductance are periodically modulated. {001161 In Fig. 68, the capacitance of the second lengthwise segraems 6115, 612b, 613b of the consecutive electrodes £11, 612, 613 is represented by the respective symbol sizes of capacitors Cam,

Dan, Can, From Fig. 6B, it van be discerned that the second lengthwise segments 6115 of sleetrode 611 comprises a capacitance Ca that is larger than a capacitance Caz of second lengthwise segments 8121 of electrode 612. Similarly, the second lengthwise segments 6120 of electrode 612 comprises 2 capacitance Cun that is larger than a capacitance Cue of second lengthwise segments 613b of electrode 613. In other words, in the embodiment of Fig, 6B the capacitance of consecutive electrodes 611, 612, 613, 814 periodicaliy modulated by periodic modulation of respective diameters Dan, Den, Dent,

Bae of the second lengthwise segments 61th, 612b, 613b, 6145 of consecutive electrodes 611, 612, 613, 614 forming the plurality of Josephson junctions 616, 628, 630 constituting the iransmission line 603.

IB01173 The inductance of Josephson junctions 610, 620, 630 is Inversely proportional io their respective areas of overlap and their respective critical currents, In Fig, GB, the symbol size of the

Josephson junctions 610, 620, 630 represents their respeciive critical cerrents, Thus, from Fig. 68 itean be discerned that Josephson junction 610 comprises a larger critical current than neighbouring

Josephson junction 620 and a correspondingly smaller inductance than neighbouring Josephson

Jonction 620, Josephson junction 620 in tum comprises a larger critical current and smaller inductance than neighbouring Josephson junction 630.

[00118] Referring now to Fig. 6A, the partially shown transmission line 603 comprises a phurality of electrodes 611, 612, 613, 614 that collectively form three Josephson junctions 619, 620, 630 among additional Josephson junctions of the transmission line 603. Each electrode 611, 612, 613, 614 comprises a respective second lengthwise segment 61 1b, 612b, 613b, 614b with a respective enlarged diameter Ds, Beinn, Do, Dein.

[00119] The embodiment of Fig. 6A differs from e.g. the embodiment depicted in Fig. 2 with respect to the relative dimensions of the respective diameters Dain, Dein, Dea, Dea of the second lengthwise segments 6116, §12b, 613h, 614b of consecutive electrodes 611, 612, 613, 614. From Fig, 6A, it can be discerned that the diameter Dein of the second lengthwise segment 611b of electrode 611 is larger than the diameter Dam of the second lengthwise segment 612b of electrode 612. Similarly, said diameter

Dep of the second lengthwise segment 612b of electrode 612 is larger than the diameter Dei of the second lengthwise segment 613b of electrode 613. The second lengthwise segment 614b of electrode 614 comprises a diameter Deus larger than the diameter Dee of the second lengthwise segment 613b of the electrode 613. The second lengthwise segments 61 1b, 6126, 613b, 614b of consecutive electrodes 611, 612, 613, 614 thus exhibit variance with respect to thelr respective enlarged diameters Dein, Dern,

Dan, Dow. The varying diameters Dan. Dam, Dae, Deus of consecutive electrodes 611, 612, 613, 614 modulate periodically, wherein the respective diameters Don, Dax, Dan. Daan of second lengthwise segments 611b, 612b, 613b, 614b of consecutive electrodes 613, 612, 613, 614 incrementally increase and incremendally decrease along the length of the transmission line 603. As depicted in Fig, 6B, this results in the period modulation of the respective capacitances Cs, Cen,

Ceus of the second lengthwise segments 61 1h, 612b, 813b. The periodic modulation of the respective diameters Da, Dente Demn, Dent of the second lengthwise segments 611b, 612b, 613%, 6146, and consequently the capacitances Cen, Cene, Coin, follow a sinusoidal course having a first period.

[00120] Referring again to Fig. 6A, the consecutive first lengthwise segments 61 1a, 612a, 6129, 6134, 5132’, 614a of consecutive electrodes 611, 612, 613, 614 likewise exhibit variance with respect to their diameters Doi. Dein, Daas Darga. Specifically, electrode 611 comprises a first lengthwise segment 611a having a diameter Den, equal fo the diameter Dan. of the first lengthwise segment 612a of electrode 612; and larger than the respective diameters Deine and Dea of the respective first lengthwise segments 6122’, 6134 of electrodes 612 and 613. Similarly, the respective diameters Deus and Den of the first lengthwise segments 6122" and 613a may be equal to one another and each larger than the respective diameters Dasa and Deu, of the first lengthwise segments 6139’, 6144.

[00121] Hence, the respeciive areas of overlap of the consecutive Josephson junctions 610, 620, 630 likewise exhibit variance with respect to their respective sizes. Specifically, Josephson junction 610 comprises a larger area of overlap than Josephson junction 620, which in turn comprises a favger area of overlap than Josephson junction 630. The variance in respective areas of overlap of consecutive

Josephson hmctions 610, 620, 630 may likewise follow a sinusoidal course, having a second period. fG01227 Because the critical current of pach Josephson junction 610,620, 630 is inversely proportional & io their respective area of overlap, Josephson junction 610 comprises a critical current larger than

Josephson junction 828, which in turn comprises a critical current larger than Josephson junction 630,

Because the inductance of Josephson junctions 610, 520, 630 is inversely related io thelr respective areas of overlap and oritical currents, Josephson junction 610 comprises 3 smaller inductance than

Josephson junction 620, which in tum comprises a smaller inductance to Josephson junction 634.

JO [00123] The respective overlaps (see the dashed encirclements in Fig. 8A) of consecutive Josephson junetiens 610, 620, 630 are defined by the respective first lengthwise segments 61 1a, 6123, 61227, 6134, 6139’, 614a constituting said overlaps, 100124 In ather words, in the embodiment of Fig, 6A and Fig. 6B the inductance of the transmission fine 603 is periodically modidated by periodic modalation of respective diameters Der, Dean, Doze

Parser Den, Danae of fest lengthwise segments 61 la, 6124, 6122’, 6134, 6139, 61de of the consecutive electrodes 611, 612, 613, 614, such that electrode pairs constituting consecutive Josephson junctions 610, 620, 63¢ comprise periodically modulating areas of overlap {indicated by the dashed line sncirclements in Fig, 6B [001257 Periodic modulation of the impedance of the trarmission line 603 may thas be achieved hy periodically modulating the capacitance, the inductance, or both the capacitance and the inductance of electrodes 611, 612, 613, that form the Josephson junstions 818, 628, 630 constituting the transmission tire 603. The impedance of the transmission line is periodically modulated to define a phase matching stopband in the dispersion relationship of the transmission Hne 603, ie. a Hoquensy band af which signals are absorbed and dissipation of energy occurs, This phase matching stopband matches a

Bequency of the pump signal used in the parametric amplification of the input signal to be amplified, causing the pump signal to aoguire a positive phase shift. Carefid control of the pump sigral frequency and pump power results in this positive phase shift cancelling out the aforementioned negative phase shift, thereby achieving the phase matching required for amplification of the signal tone.

[00126] It will be appreciated that in the embodiment of Fig. 6A and Fig. 6B, the inclusion of discrete phase matching resonators 107 {see Fig, 1} may be redundant. Instead, adequate phase matching may be achieved with the incrementally varying diameters of the first lengthwise segments 61 Ia, 6324, 613a and the second lengthwise segnenis 61h, 612b, H13b of the consceutive electrodes 611, 612, 613, A

JEWPA in apcordance with the embodiment of Fig. 6A and Fig. 68 may therefore exhibit an enhanced degree of miniaturization and can moreover be fabricated using the efficient fabrication process as described here above with reference to Fig. 3A to Fig. 3B. This efficient fabrication process may not include additional steps for fabricating discrete phase matching resonators 107.

[00127] With no subsequent fabrication steps required to form further components (e.g. the phase marching resonator 107 of Fig. 1, and the like) to achieve the characteristic impedance of the JTWPA, the transmission line 603 may be finalised inmediately when all the Josephson junctions 610, 620, 630 are formed. A JTWPA in accordance with the embodiment of Fig. 6 therefore not only exhibits a high degree of miniaturisatien due to the absence of additional phase matching resonators, but is morzover particularly well suited to be fabricated using a highly efficient fabrication method, that may in principle be conducted exclusively using angled evaporation or comparable fabrication techniques, without requiring additional fabrication steps to form said additional phase niatching resonators.

[00128] The aforementioned first and second periods may be determined with respect to various other parameters of the of the JTWPA and/or the input signal to be amplified. The skilled person is aware that these periods may be determined by solving the relevant wave equations, e.g. using specialised simulation software, or the like,

[00129] Fig. 7 schematically depicts an exemplary embodimerd of a system 780 in accordance with a further aspect of the present disclosure and invention. In the exemplary embodiment of Fig, 7. the system 780 is (part of) a quantum computing system, However, the present disclosure is not limited thereto and it will be appreciated that it is entirely conceivable that the system 780 is of an alternative nature. The system 780 may, for exaraple, constitute an astronomical measurement system for measuring weak astronomical signals.

[00130] Notwithstanding the above, the system 780 of Fig. 7 comprises a measurement object 710 embodied by a qubit 710. More than one gubit 710 may be present within the system 789, of which only one is shown in Fig. 7. In embodiments of the system 780 that are not quantum computing systems, the measurement object 710 may be constituted by eg. 3 detector configured to detect cosmic microwave background, or the like.

[00131] The qubit 710 may emit a signal representing a quantum state of the qubit 780 and is connected twa JTWPA 700 via an isolator 740 and a divectional coupler 760, Said signal emitted by the gubit 710 constitutes the input signal in the description here above with reference to the foregoing figures. The isolator 740 is included to prevent any back-action stemming from additional components from reaching the qubit 710, which is extremely sensitive and is therefore preferably protected,

[00132] The pump signal is generated by a wave generator 720 connected to the directional coupler 760 via a plurality of attenuators 730, 730°, 7307". The directional coupler 760 feeds the input signal from the gubit 710 to the JTWPA 700 together with a pump signal vig an input {not shown).

Alternatively, two inputs may be present for separately feeding the input signal and the pump signal into the JTWPA 700. In such embodiments, the directional coupler 760 may be integrated within a housing of the JTWPA 700.

[00133] Upon reaching the JTWPA 760, the input signal is aroplified based on the pump signal as described here above with reference to the foregoing figures. The JTWPA 700 of Fig. 7 is equivalent to the JPWPA 200 of Fig. 2.

ZR

[001341 At iis other end, the JT WPA 700 is connected to an output 720 via first and second high- elecivon-mebility transistors 782, 784, a high/low pass filter 770, and first and second isolators 742, 744. The output 790 may be constituted by a digitiser ov the like. The first high-electron-mobiity transistors (HEMT) 782 and second HEMT 784 are included in the system 780 10 further amplify the

Input signal, because the STWPA 700 by self may not produce sufficient gain to facilitate a readmit of the amplified input signal. First and second isolators 742, 744 are included to prevent noise generated bv the first and second HEMT 782, 784 from reaching the JTWPA 700 andfor the qubit 710. The low/high pass filter 770 hers out the pump signal, which may simplify readout of the amplified input signal by means of digitiser 790, 80135] With reference to Fig. 2, in certain embodiments of 2 JITWPA in accordance with the present disclosure the second lengthwise segments 21 Eb, 212b having the relatively enlarged diameter Dang, hin may aliernatively or additionally be arranged at the free ends 2117, 212° of thelr respective electrodes ZH, 212.

[00126] In certain embodiments of a JTWEA in accordance with the present disclosure, the JTWPA may comprise at least one electrode having 2 second lengthwise segment with a diameter extending orthogonal to a lengthwise direction of the electrode and substantially paralie! to a conductive laver, said diameter being larger than a diameter of a first lengthnwise segment of said at least one electrode,

In these embodiments, the at least one electrode may comprise two first lengthwise sections, each comprising an area of overlap with a neighbouring electrode, Moreover, in these embodiments the second lengthwise segment having the erdarged diameter may be aranped at or near a midpoint of said at electrode, when considered in its lengthwise divection, {D137} HH will be appreciated that the scope of the sought after projection is not limited to any one of the above described embodiments of the disclosed method and quantum computing circuitry apparatus.

The skilled person will acknowledge thet various coraponents and features of the described embodiments can be combined with one another or otherwise modified, The scope of the sought after protection is therefore not Hmited to any one of the above Hsted practical applications or embodiments, but is defined solely by the features stated in the claims and, at east in certain jurisdictions, their equivalents.

Claims

CONCLUSIONS

A Josephson travelling wave parametric amplifier (JTWPA), comprising: a conductive layer; a dielectric layer; and a plurality of Josephson junctions encompassed by a transmission line, each Josephson junction comprising a pair of electrodes extending toward each other to define an overlap region, at least one electrode of one or more of the electrode pairs comprising: a first length segment encompassing at least the overlap region; and a second length segment disposed opposite the first length segment, the second length segment of said at least one electrode having a diameter orthogonal to a length direction. of the electrode and substantially parallel to the conductive layer (wuitstreki), said diameter being larger than a diameter of the first length segment, whereby the second length segment with the enlarged diameter, in combination with the conductive layer and the dielectric layer, defines a capacitive structure which at least partly defines a characteristic impedance of the JTWPA.

The JTWPA of claim 1, wherein the plurality of Josephson junctions are arranged in a serpentine arrangement pattern, wherein turns of the serpentine arrangement pattern are defined by respective first length segments of adjacent electrode pairs of successive Josephson junctions. The JTWPA of claim 2, wherein the serpentine arrangement pattern of the plurality of Josephson junctions comprises a first substructure comprising: a first Josephson junction comprising a first electrode and a second electrode; a second Josephson junction comprising a second electrode and a third electrode, the second electrode disposed between the first electrode and the third electrode; a third Josephson junction comprising the third electrode and a fourth electrode, the third electrode disposed between the second electrode and the fourth electrode; and a fourth Josephson junction comprising the fourth electrode and a fifth electrode, the fourth electrode being disposed between the third electrode and the fifth electrode; the first electrode, the third electrode and the fifth electrode extending parallel to each other in a first direction; and the second electrode and the fourth electrode extending parallel to each other in a second direction.

QA. 4. The ITWPA according to claim 2 or 3, wherein the meandering pattern of the plurality of Josephson junctions comprises a second substructure comprising: a fifth Josephson junction comprising a sixth electrode and a seventh electrode; a sixth Josephson junction comprising the seventh electrode and an eighth electrode; a seventh Josephson junction comprising the eighth electrode and a ninth electrode; and an eighth Josephson junction comprising the ninth electrode and a tenth electrode, wherein the sixth electrode, the eighth electrode, and the tenth electrode extend substantially parallel to each other in a third direction, and the seventh electrode and the ninth electrode extend substantially parallel to each other in a third direction.

5. The JTWPA of any preceding claim, wherein the first length segment and the second length segment of the at least one electrode are integrally formed,

6. The ITWPA of claim 3, wherein the first length segment and the second length segment are formed using a single manufacturing technique, preferably a single manufacturing technique based on angle vapor deposition,

7. The JTWPA of claim 6, wherein the second length segment comprises a shape that is substantially circular or angular with equal-sized convex sides. The JTWPA of claim 6 or 7, wherein a first contour of the second length segment, when viewed in a semi-deposition direction of the manufacturing technique, corresponds to a second contour of the second length segment when viewed in a second deposition direction of the manufacturing technique; and wherein the second length segment exhibits rotational symmetry with respect to the first deposition direction and the second deposition direction of the manufacturing technique. 9. The JTWPA of claim §, wherein the second length segment comprises a substantially square shape,

The JTWPA of claim 9, wherein the second length segment having the square shape is oriented such that a diagonal of the second length segment coincides with a length direction of the at least one electrode.

11. The JTWPA of claim 10, wherein the diagonal of the second length segment further coincides with a horizontal vector component of at least one of the first deposition direction and the second deposition direction of the manufacturing technique.

The JTWPA according to any of the preceding claims, wherein the second length segment comprises a surface area of from 3 µm to 1000 µm, more preferably from 6 µm to 600 µm, most preferably from 10 µm to 150 µm,

The JTWPA of any preceding claim, wherein one or both of a capacitance and an inductance of the transmission line is periodically modulated, thereby periodically modulating the impedance of the transmission line so that a stop band for phase matching is defined in a dispersion relationship of the transmission line. The TWP of claim 13, wherein the inductance of the transmission line is periodically modulated by periodic modulation of respective diameters of first length segments of successive electrodes, so that electrode pairs forming successive Josephson junctions include periodically modulating overlap regions.

15. The JTWPA of claim 13 or 14, wherein the capacitance of the transmission line is periodically modulated by periodically modulating respective diameters of the second length segments of successive electrodes forming the transmission line.

16. A quantum computing system comprising at least: - at least one measurement object, such as a quantum bit, gubit; and - at least one JTWPA according to any of the preceding claims.

A method for obtaining a JTWPA, comprising providing a multi-layered stack comprising a substrate, a conductive layer, a dielectric layer, and a photoresist layer; subjecting the multi-layered stack to an exposure process followed by a development process, thereby removing the photoresist layer in areas corresponding to respective Josephson junctions to be formed; forming a plurality of Josephson junctions, each comprising a pair of electrodes extending toward each other and defining an overlap region; the method further comprising:

forming at least one electrode of one or more of the plurality of electrode pairs to include: a first length segment including a region of overlap with an adjacent electrode; and a second length segment disposed opposite the first length segment, said second length segment being formed to include a diameter extending orthogonally to a lengthwise direction of the electrode and substantially parallel to the conductive layer, said diameter being greater than a diameter of the first length segment.

18. The method of claim 17, wherein the step of forming the plurality of Josephson junctions comprises: forming the plurality of Josephson junctions in a serpentine placement pattern, wherein turns of the serpentine placement pattern are defined by respective first electrode segments comprising the region of overlap with an adjacent electrode of successive Josephson junctions, the serpentine placement pattern preferably being formed to form a substructure comprising: a first Josephson junction comprising a first electrode and a second electrode; and a second Josephson junction comprising the second electrode and a third electrode, the second electrode being disposed between the furthest electrode and the third electrode, the first and third electrodes extending parallel to each other in a first meandering direction of the meandering placement pattern, and the second electrode extending in a second meandering direction of the meandering placement pattern perpendicular to the first meandering direction, wherein successive first substructures are disposed in mirror image along a line of the first substructure.

19. The method of claim 18, wherein the meandering placement pattern is formed to include a second substructure comprising: a third Josephson junction comprising a fourth electrode and a fifth electrode; a fourth Josephson junction comprising the fifth electrode and a sixth electrode; a fifth Josephson junction comprising the sixth electrode and a seventh electrode; and a sixth Josephson junction comprising the seventh electrode and a seventh electrode, wherein the fourth electrode, the sixth electrode, and the seventh electrode extend parallel to each other in the first meandering direction, and wherein the fifth electrode and the seventh electrode extend parallel to each other in the second meandering direction of the meandering placement pattern.

20. The method of any of the preceding claims 17 to 19, wherein the first length segment and the second length segments of the at least one electrode are integrally formed, preferably in a single iteration of a manufacturing technique, more preferably a single iteration of an angle vapor deposition based manufacturing technique.

The method of claim 20, wherein the second length segment is formed to include a shape that is substantially circular or polygonal with a plurality of sides of equal size, the second length segment being formed to exhibit rotational symmetry with respect to a first deposition direction and a second deposition direction of an angle vapor deposition manufacturing technique,