Nonlinear microwave resonator, josephson device, and method for manufacturing nonlinear microwave resonator

Abstract

A nonlinear microwave resonator (10) comprises an NbN / AlN / NbN structure in which an NbN thin film is used for a lower layer electrode (2) and an upper layer electrode (4), and in which an AlN thin film is used for a dielectric film (3) that is provided between the lower layer electrode and the upper layer electrode. This structure constitutes a Josephson junction that is formed by using the NbN thin film as a superconductor and the AlN thin film as the dielectric film (3), and the structure functions as a Josephson element (10b). In addition, the structure constitutes a capacitor (10a) that has NbN as an electrode and AlN as a dielectric film (insulating layer), and functions as the nonlinear microwave resonator (10).

Description

Nonlinear microwave resonator, Josephson device, and method for manufacturing nonlinear microwave resonator

[0001] The present invention relates to a nonlinear microwave resonator and a method for manufacturing the same.

[0002] A Josephson junction is a nonlinear element with an inductance that depends on the magnitude of the current. Josephson junctions can be fabricated in various ways. In superconducting devices that include a Josephson junction, the Josephson junction can be fabricated by sandwiching a thin dielectric (insulating) film between two superconducting electrodes. Therefore, the Josephson junction can be regarded as a nonlinear LC resonant circuit with a capacitor in parallel with an inductance and a natural resonant frequency.

[0003] A superconducting quantum interference device (SQUID) can be fabricated by connecting two Josephson junctions in parallel to form a loop-shaped device. This device is also a nonlinear device with an inductance that depends on the magnitude of the current. Compared to a single Josephson junction, a SQUID has the advantage that the inductance value can be controlled by the magnetic flux passing through the loop. Therefore, a variable frequency nonlinear LC resonator can be constructed using a SQUID.

[0004] Nonlinear microwave resonators using Josephson junctions are widely used in the field of superconducting quantum computing. For example, a Josephson bifurcation amplifier can be realized by applying a large microwave input to a nonlinear microwave resonator. This allows for quantum bit state measurement (e.g., Non-Patent Document 1). Furthermore, a Josephson parametric amplifier, which amplifies microwave signals with low noise, can be constructed by inputting a microwave pump signal with a frequency twice the resonant frequency of the nonlinear microwave resonator. Josephson parametric amplifiers are used to increase the speed and precision of superconducting quantum bit readout (e.g., Non-Patent Document 2), and are particularly widely used in the S, C, and X bands, around 2-12 GHz.

[0005] Josephson junctions, which are often used in superconducting quantum devices, use aluminum as the superconducting thin film and aluminum oxide as the dielectric. Such Josephson junctions typically have an inductance of about 100 pH and a capacitance of about 10 fF. As a result, the inherent resonant frequency of a Josephson junction is very high, exceeding 100 GHz. Therefore, to fabricate devices that operate in the microwave band, additional circuit elements are required to lower the resonant frequency. Specifically, there are two main types of nonlinear microwave resonators using Josephson junctions:

[0006] The first nonlinear microwave resonator is a distributed constant type linear microwave resonator using a transmission line such as a coplanar line, to which nonlinearity is added by inserting a Josephson junction.

[0007] The second nonlinear microwave resonator is a lumped-element microwave resonator formed by a Josephson junction and a capacitor fabricated on a substrate. This second nonlinear microwave resonator has two further resonator structures.

[0008] The first resonator structure is an interdigital capacitor formed by interdigital electrodes fabricated on a substrate. This structure allows the capacitor to be fabricated by fabricating a single layer of electrodes on the substrate, making it relatively easy to manufacture.

[0009] The second resonator structure is a parallel-plate capacitor formed by stacking metal electrodes and dielectrics. This structure allows for increased capacitance per unit area by using a thin dielectric film with a high dielectric constant. This allows for a relatively small area on the chip (for example, approximately 100 μm × 120 μm in Non-Patent Document 3).

[0010] R. Vijay, M. H. Devoret, I. Siddiqi, “Invited Review Article: The Josephson bifurcation amplifier” Review of Scientific Instruments, Vol. 80, No. 11, p. 111101 (2009)T. Yamamoto, K. Inomata, M. Watanabe, K. Matsuba, T. Miyazaki, W. D. Oliver, Y. Nakamura, J. S. Tsai, “Flux-driven Josephson parametric amplifier” Applied Physics Letters, Vol. 93, No. 4, p. 042510 (2008)J. Y. Mutus, T. C. White, E. Jeffrey, D. Sank, R. Barends, J. Bochmann, Yu Chen, Z. Chen, B. Chiaro, A. Dunsworth, J. Kelly, A. Megrant, C. Neill, P. J. J. O’Malley, P. Roushan, A. Vainsencher, J. Wenner, I. Siddiqi, R. Vijay, A. N. Cleland, John M. Martinis, “Design and characterization of a lumped element single-ended superconducting microwave parametric amplifier with on-chip flux bias line” Applied Physics Letters, Vol. 103, No. 12, 122602 (2013)Karl van Bibber, Gianpaolo Carosi, “Status of the ADMX and ADMX-HF experiments” arXiv:1304.7803

[0011] However, when the above-mentioned first nonlinear microwave resonator is adopted, the length of the transmission line on the substrate becomes long, at several mm (for example, about 2.6 mm × 100 μm in Non-Patent Document 2), which in principle poses a problem that the area occupied on the chip becomes large.

[0012] Furthermore, when the first resonator structure in the second nonlinear microwave resonator described above is adopted, a large substrate area (for example, about 100 μm × 300 μm in Non-Patent Document 4) is occupied in order to fabricate a capacitor with a large capacitance of several pF, which is necessary to configure the microwave resonator.

[0013] Furthermore, interdigital capacitors, which are large in size relative to the wavelength used, have large parasitic inductance, which causes a decrease in performance as a microwave nonlinear resonator. Performance degradation due to parasitic inductance is particularly problematic when fabricating Josephson bifurcation amplifiers, and the importance of reducing parasitic inductance has been pointed out in Non-Patent Document 1.

[0014] When the second resonator structure of the second nonlinear microwave resonator described above is adopted, at least three layers of electrodes are required to fabricate a parallel-plate capacitor: a lower electrode film, a dielectric film, and an upper electrode film. Typically, Josephson junctions and parallel-plate capacitors require different dielectric materials and different thicknesses, and therefore must be fabricated using different processes. This increases the number of steps required to fabricate the device, raising concerns about increased manufacturing costs and reduced yields.

[0015] An object of the present invention is to provide a microwave nonlinear resonator having a simpler structure and lower manufacturing costs than conventional ones, and a manufacturing method thereof.

[0016] The present invention is characterized by comprising a first electrode made of a superconductor, a second electrode made of a superconductor, and an insulating layer disposed between the first electrode and the second electrode, and the first electrode, the insulating layer, and the second electrode also function as a Josephson element that constitutes a Josephson junction.

[0017] According to the present invention, a nonlinear microwave resonator including a Josephson device can be made to have a simple configuration, and can therefore be manufactured at low cost.

[0018] Fig. 1 is a cross-sectional view of a microwave resonator according to the present embodiment, and Fig. 2 is a schematic plan view of a variable frequency Josephson parametric amplifier showing an example of the configuration of the present invention.

[0019] [Principle of the microwave resonator according to the present invention] In the present invention, the fabrication conditions of the Josephson junction are devised so that the Josephson junction itself also serves as a capacitor that constitutes the microwave resonator, thereby constructing a microwave resonator using only the Josephson junction. Specifically, a Josephson junction with a three-layer structure consisting of a superconductor, an insulator, and another superconductor is used, and the critical current density Jc of the Josephson junction and the thickness t of the insulator are appropriately adjusted to set the resonant frequency specific to the Josephson junction in the microwave region.

[0020] As mentioned in the Background Art section, up until now, microwave resonators including Josephson junctions could only be fabricated by combining the Josephson junctions with external capacitors, waveguides, and the like.

[0021] In the present invention, a microwave resonator is constructed using only a Josephson junction, without using these external elements. This makes it possible to reduce the number of film depositions and lithography steps required for device fabrication compared to conventional devices. Furthermore, since there is no wiring required to connect the Josephson junction, which is a nonlinear inductance, and the capacitor required to construct the resonant circuit, there are no parasitic inductors or capacitors resulting from the wiring. Therefore, there is less degradation in the characteristics of the resonant circuit compared to conventional methods in which the Josephson junction and capacitor are fabricated separately.

[0022] Under the assumption that the current flowing through the Josephson junction is sufficiently smaller than the critical current, the inductance L of the Josephson junction is Ｊ can be expressed by the following equation (1).

[0023] where φ ０is the magnetic flux quantum, Jc is the critical current density of the Josephson junction, and S is the area of ​​the Josephson junction.

[0024] In addition, the capacitance C of the Josephson junction Ｊ can be expressed by the following equation (2).

[0025] where ε ０ is the dielectric constant of a vacuum, ε ｒ is the relative dielectric constant of the insulator, and t is the thickness of the dielectric.

[0026] On the other hand, the inductance L of the Josephson junction Ｊ and capacitance C Ｊ The resonant frequency f of the microwave resonator can be expressed by the following equation (3).

[0027] Combining these, we obtain the following equation (4).

[0028] The parameters other than the physical constants in this equation are Jc, t, and ε ｒ and does not include the area S of the Josephson junction. That is, this has the characteristic that the resonant frequency is unlikely to change even if the area S of the Josephson junction changes due to variations in device fabrication or the like.

[0029] Jc is determined by the conditions of the Josephson junction, i.e., the electrode material, insulator material, and film thickness of these materials that make up the Josephson junction. Under the same conditions, the resonant frequency of the microwave resonator does not change significantly. t is the film thickness of the dielectric material that makes up the Josephson junction, and can be controlled with relatively high precision during fabrication. ε ｒ is the relative dielectric constant of the dielectric film, which may vary somewhat depending on the manufacturing conditions, but is basically a parameter inherent to the material.

[0030] From the above, it is possible to control the resonance frequency, which is important in a nonlinear microwave resonator, with high precision, and the number of parameters that need to be controlled is reduced compared to when the Josephson junction and capacitor are fabricated independently.

[0031] The above derivation of the resonant frequency is for a nonlinear microwave resonator using a single Josephson junction. Ｊ , CＪ By making the following changes to , the resonant frequency of the nonlinear microwave resonator using a SQUID can be obtained as shown in the following equations (5), (6), and (7). By using a SQUID, it is possible to configure a variable frequency nonlinear microwave resonator in which the frequency of the nonlinear microwave resonator can be controlled by an externally applied magnetic flux.

[0032] Here, φ is the magnetic flux passing through the loop that constitutes the SQUID, and by changing this amount, the resonant frequency f of the nonlinear microwave resonator can be changed. Also, it is assumed that the inductance of the SQUID loop is sufficiently smaller than that caused by the Josephson junction. The maximum resonant frequency f ｍａｘ is given by the following equation (8).

[0033] In the microwave resonator according to the present invention, in a fixed frequency device having a single Josephson element, the resonant frequency f is adjusted to be within the range of 2-12 GHz. In a variable frequency device having a nonlinear microwave resonator using a SQUID, the maximum resonant frequency f is adjusted to be within the range of 2-12 GHz. ｍａｘ is adjusted to be in the range of 2-12 GHz.

[0034] Specifically, by selecting a material that can be adjusted by the critical current density Jc of the Josephson junction and the thickness t of the insulating layer, a nonlinear microwave resonator that operates mainly in the microwave band of 2-12 GHz can be realized.

[0035] [Explanation of Microwave Resonator and Device Using the Same] FIG. 1 shows a cross-sectional view of a microwave resonator according to this embodiment.

[0036] The nonlinear microwave resonator 10 has an NbN / AlN / NbN structure in which NbN (niobium nitride) thin films are used for the lower electrode 2 and the upper electrode 4, and an AlN (aluminum nitride) thin film is used for the dielectric film (insulating layer) 3 disposed between the lower and upper electrodes. This structure forms a Josephson junction with the NbN thin film as the superconductor and the AlN thin film as the dielectric film (insulating layer), and functions as a Josephson element 10b. This structure also functions as a capacitor 10a with NbN as the electrode and AlN as the dielectric film (insulating layer), and functions as the nonlinear microwave resonator 10.

[0037] The area of ​​the dielectric film (insulating layer) 3 in the nonlinear microwave resonator 10 according to the embodiment of the present invention, i.e., the area S of the Josephson junction, does not affect the resonant frequency of the nonlinear microwave resonator 10. The dielectric film (insulating layer) 3 can be fabricated by photolithography, and in a device such as the variable frequency Josephson parametric amplifier 100, it is desirable to make it a square with a side length of 4 μm in order to make the device as small as possible.

[0038] FIG. 2 shows an example of the configuration of a variable frequency Josephson parametric amplifier 100 using the nonlinear microwave resonator 10 shown in FIG. 1, as an embodiment of the present invention.

[0039] Variable frequency Josephson parametric amplifier 100 comprises a first coplanar waveguide line 101 and a second coplanar waveguide line 201. First coplanar waveguide line 101 comprises a ground 102 and a signal microwave input / output line 103 therebetween. Second coplanar waveguide line 201 comprises a ground 202 and a microwave pump input line 203 therebetween.

[0040] The first coplanar line 101 further includes two nonlinear microwave resonators 10 having the function of a Josephson junction between the ground 102 and the signal microwave input / output line 103. The nonlinear microwave resonator 10 simultaneously includes a capacitor 10a that functions as a microwave resonator and a Josephson junction 10b.

[0041] As shown in FIG. 2, in the variable frequency Josephson parametric amplifier 100, a SQUID 104 is formed by arranging two Josephson elements 10b having the same Josephson junction in order to make the frequency of the Josephson parametric amplifier variable.

[0042] According to Reference 1 (W. Qiu, H. Terai, Z. Wang, “Measurement of Epitaxial NbN / AlN / NbN Tunnel Junctions With a Low Critical Current Density,” IEEE Transactions on Applied Superconductivity, Vol. 21, No. 3, pp. 135-138 (2011)), the critical current density of the NbN / AlN / NbN Josephson junction is 2 A / cm. ２ (when the thickness of the AlN film is set to 2.3 nm).

[0043] In addition, Reference 2 (Sunmi Kim, Hirotaka Terai, Taro Yamashita, Wei Qiu, Tomoko Fuse, Fumiki Yoshihara, Sahel Ashhab, Kunihiro Inomata, Kouichi Semba, “Enhanced coherence of all-nitride superconducting qubits epitaxially grown on silicon substrate” Communications Materials, Vol. 2, No. 1, p. 98 (2021)) evaluates the relative dielectric constant of AlN to be around 7.

[0044] From these calculations, the maximum resonant frequency of this variable frequency nonlinear microwave resonator 105 is calculated to be approximately 7.6 GHz, which falls within the 4-8 GHz frequency band often used in superconducting quantum bits and the like.

[0045] In order to operate the variable frequency nonlinear microwave resonator 105 as the variable frequency Josephson parametric amplifier 100, a microwave pump input line 203 is provided. A microwave pump signal having a frequency twice the frequency of the signal to be amplified is applied to the microwave pump input line 203.

[0046] Furthermore, a magnetic field is applied from the outside perpendicular to the substrate, and a magnetic flux is applied to the loop of the SQUID 104, thereby adjusting the resonant frequency of the variable frequency nonlinear microwave resonator 105.

[0047] By appropriately adjusting the frequency and power of the pump microwave signal and the magnitude of the applied magnetic flux, the variable frequency nonlinear microwave resonator 105 can have an amplifying effect and function as a variable frequency Josephson parametric amplifier 100.

[0048] In the embodiment of the present invention, the nonlinear microwave resonator 10, which in the conventional technology was configured by combining a plurality of elements such as a Josephson junction, a waveguide, and an independently fabricated capacitance, is realized by adjusting the critical current density Jc of the NbN / AlN / NbN junction and the film thickness t of the insulating layer. This allows the NbN / AlN / NbN junction that functions as a Josephson junction to also function as the nonlinear microwave resonator 10 at the same time, thereby realizing a simple device structure and reducing the area occupied on the substrate.

[0049] Conventionally, a Josephson element or a SQUID equipped with two Josephson elements and a capacitor functioning as a resonator had to be arranged separately, so a device such as a Josephson parametric amplifier required an area of ​​approximately 100 μm × 300 μm.

[0050] By using the nonlinear microwave resonator of this embodiment, the area occupied by the device can be reduced to approximately 20 μm×100 μm.

[0051] Furthermore, because the Josephson element and the capacitor had to be formed separately in the past, there were problems with degradation of element and device characteristics due to the occurrence of parasitic inductors, parasitic capacitors, etc. Furthermore, the number of steps in device fabrication increased, raising issues such as increased manufacturing costs and reduced yields due to manufacturing variations.

[0052] According to the embodiment, the number of elements used can be reduced and the configuration can be simplified, which can dramatically reduce the occurrence of parasitic inductors, parasitic capacitors, etc. Furthermore, the reduction in the number of steps in device manufacturing can dramatically improve manufacturing costs and yields due to manufacturing variations, etc.

[0053] Although the variable frequency Josephson parametric amplifier has been described as an example of this embodiment, the Josephson device including the nonlinear microwave resonator according to the present invention is not limited to this.

[0054] In the case of a Josephson device using a single Josephson element, the Josephson device can function as any of a fixed frequency Josephson branch amplifier, a fixed frequency Josephson parametric amplifier, and a fixed frequency Josephson parametric oscillator, depending on the microwaves input to the nonlinear microwave resonator.

[0055] In the case of a Josephson device having a SQUID using two Josephson elements, in addition to the variable frequency Josephson parametric amplifier described in the above embodiment, the Josephson device can be made to function as either a variable frequency Josephson branch amplifier or a variable frequency Josephson parametric oscillator depending on the microwaves input to the Josephson device.

[0056] [Method for Manufacturing Microwave Nonlinear Resonator] The manufacturing process of the nonlinear microwave resonator 10 of this embodiment includes a step of forming the first electrode 2, a step of forming the insulating layer 3, and a step of forming the second electrode 4. A specific manufacturing method will be described below, but the manufacturing method is not limited to this.

[0057] First, in the step of forming the first electrode 2, a first electrode layer made of a superconductor is formed on a substrate 1 made of silicon or the like. In this embodiment, niobium nitride (NbN) is formed by an epitaxial method or the like.

[0058] Next, in the step of forming an insulating layer, an insulating layer is formed on the first electrode 2. In this embodiment, an insulating layer made of aluminum nitride (AlN) is formed by sputtering or the like.

[0059] Next, in the step of forming the second electrode 4, the second electrode layer is formed on the insulating layer 3 and the first electrode 2. In this embodiment, niobium nitride (NbN) is formed by sputtering or the like.

[0060] The method for forming these NbN / AlN / NbN layers is not limited to the above-mentioned method, and may be selected appropriately depending on the formation conditions and materials used, such as epitaxial method, sputtering method, atomic layer deposition (ALD), etc.

[0061] Next, a desired pattern is formed on each of the three layers of NbN / AlN / NbN by photolithography.

[0062] The area of ​​the insulating layer 3 is made as small as possible to minimize changes in characteristics due to variations in the area of ​​the Josephson junctions that occur during the manufacturing process, while still ensuring the function of the nonlinear microwave resonator 10. In this embodiment of the present invention, the insulating layer 3 is formed as a square with a side length of 4 μm.

[0063] In the manufacture of a fixed frequency Josephson device using the Josephson element 10b alone, the thickness t of the insulating layer 3, which functions as a dielectric film, is determined by the above formula (4) so ​​that the resonant frequency is an appropriate value within the range of 2-12 GHz.

[0064] In addition, in manufacturing a device including a SQUID 104 using two Josephson elements 10b, for example, a variable frequency Josephson device, the thickness t of the insulating layer 3 functioning as a dielectric film is determined based on the above equation (8) so that the maximum resonant frequency becomes an appropriate value within the range of 2 to 12 GHz, as shown in FIG. 2.

[0065] Finally, in the step of forming the second electrode 4, a second electrode layer is formed on the insulating layer 3 and the first electrode 2. In this embodiment, niobium nitride (NbN) is formed by sputtering, atomic layer deposition (ALD), vapor phase epitaxy, or the like. Next, a desired pattern is formed using photolithography or the like, and the desired second electrode 4 is obtained from the second electrode layer.

[0066] The resulting NbN / AlN / NbN structure forms a Josephson junction with the NbN (niobium nitride) thin film as the superconductor and the AlN (aluminum nitride) thin film as the dielectric film (insulating layer), and functions as a Josephson element 10b. This structure also functions as a capacitor 10a with NbN as the electrode and AlN as the dielectric film (insulating layer), and also functions as a microwave resonator.

[0067] Conventionally, in order to manufacture a microwave nonlinear resonator equipped with a Josephson element, the Josephson element and the capacitor had to be formed separately, which increased the number of steps in device fabrication, resulting in issues such as increased manufacturing costs and reduced yields due to manufacturing variations.

[0068] According to the embodiment, the number of elements used can be reduced and the configuration can be simplified, which can dramatically improve the manufacturing cost by reducing the number of steps in device manufacturing and the yield due to manufacturing variations.

[0069] A part or all of the above-described embodiments can be described as follows, but are not limited to the following.

[0070] [Supplementary Note 1] A nonlinear microwave resonator comprising: a first electrode made of a superconductor; a second electrode made of a superconductor; and an insulating layer disposed between the first electrode and the second electrode, wherein the first electrode, the insulating layer, and the second electrode also function as a Josephson element forming a Josephson junction.

[0071] [Supplementary Note 2] The nonlinear microwave resonator according to Supplementary Note 1, characterized in that the film thickness of the insulating layer and the critical current density of the Josephson junction are adjusted by Equation (4) so ​​that the resonant frequency is in the range of 2 to 12 GHz.

[0072] where f is the resonant frequency, Jc is the critical current density of the Josephson junction, t is the thickness of the insulating layer, and φ ０ : magnetic flux quantum, ε ０ : dielectric constant of vacuum, ε ｒ : relative permittivity of the insulating layer.

[0073] [Supplementary Note 3] The nonlinear microwave resonator according to Supplementary Note 1 or 2, wherein the first electrode and the second electrode are made of niobium nitride, and the insulating layer is made of aluminum nitride.

[0074] [Supplementary Note 4] A Josephson device comprising the nonlinear microwave resonator according to Supplementary Note 1.

[0075] [Supplementary Note 5] The Josephson device according to Supplementary Note 4, wherein the Josephson device is any one of a fixed frequency Josephson bifurcation amplifier, a fixed frequency Josephson parametric amplifier, and a fixed frequency Josephson parametric oscillator.

[0076] [Supplementary Note 6] A Josephson device comprising a superconducting quantum interference device (SQUID) configured using two nonlinear microwave resonators according to Supplementary Note 1.

[0077] [Supplementary Note 7] The Josephson device according to Supplementary Note 6, wherein the Josephson device is one of a variable frequency Josephson bifurcation amplifier, a variable frequency Josephson parametric amplifier, and a variable frequency Josephson parametric oscillator.

[0078] [Appendix 8] A method for manufacturing a nonlinear microwave resonator, comprising: a step of forming a first electrode made of a superconductor on a substrate; a step of forming an insulating layer made of an insulating layer on the first electrode; and a step of forming a second electrode made of a superconductor on the insulating layer, wherein the first electrode, the insulating layer, and the second electrode are formed to function as a Josephson junction, and the film thickness of the insulating layer and the critical current density of the Josephson junction are adjusted by the following equation (4) so ​​that the resonant frequency is in the range of 2 to 12 GHz.

[0079] where f is the resonant frequency, Jc is the critical current density of the Josephson junction, t is the thickness of the insulating layer, and φ ０ : magnetic flux quantum, ε ０ : dielectric constant of vacuum, ε ｒ : relative permittivity of the insulating layer.

[0080] [Supplementary Note 9] A superconducting quantum interference device (SQUID) configured using two nonlinear microwave resonators according to Supplementary Note 1, characterized in that the film thickness of the insulating layer and the critical current density of the Josephson junction are adjusted by Equation (8) so that the maximum value of the resonant frequency is in the range of 2 to 12 GHz.

[0081] where f ｍａｘ : maximum value of resonance frequency, Jc: critical current density of Josephson junction, t: film thickness of insulating layer, φ ０ : magnetic flux quantum, ε ０ : dielectric constant of vacuum, ε ｒ : relative permittivity of the insulating layer.

[0082] [Supplementary Note 10] A method for manufacturing a nonlinear microwave resonator, comprising the steps of: forming a first electrode made of a superconductor on a substrate; forming an insulating layer made of an insulating layer on the first electrode; and forming a second electrode made of a superconductor on the insulating layer, wherein the first electrode, the insulating layer, and the second electrode are formed to function as a Josephson junction, and the film thickness of the insulating layer and the critical current density of the Josephson junction are adjusted by the following formula (8) so that the maximum value of the resonant frequency is in the range of 2 to 12 GHz when the nonlinear microwave resonator is manufactured as a superconducting quantum interference device (SQUID) configured using two of the nonlinear microwave resonators.

[0083] where f ｍａｘ : maximum value of resonance frequency, Jc: critical current density of Josephson junction, t: film thickness of insulating layer, φ ０ : magnetic flux quantum, ε ０ : dielectric constant of vacuum, ε ｒ : relative permittivity of the insulating layer.

[0084] 1...substrate, 2...first electrode (layer), 3...dielectric film (insulating layer), 4...second electrode, 10...nonlinear microwave resonator having the function of a Josephson element.

Claims

1. A nonlinear microwave resonator comprising: a first electrode made of a superconductor; a second electrode made of a superconductor; and an insulating layer disposed between the first electrode and the second electrode, wherein the first electrode, the insulating layer, and the second electrode also function as a Josephson element forming a Josephson junction.

2. A nonlinear microwave resonator according to claim 1, characterized in that the thickness of the insulating layer and the critical current density of the Josephson junction are set according to formula (1) so that the resonant frequency is in the range of 2 to 12 GHz. where f is the resonant frequency, Jc is the critical current density of the Josephson junction, t is the thickness of the insulating layer, and φ ０ : magnetic flux quantum, ε ０ : dielectric constant of vacuum, ε ｒ : relative permittivity of the insulating layer.

3. A nonlinear microwave resonator according to claim 1 or 2, characterized in that the first electrode and the second electrode are made of niobium nitride, and the insulating layer is made of aluminum nitride.

4. A Josephson device comprising the nonlinear microwave resonator according to claim 1.

5. The Josephson device according to claim 4, wherein the Josephson device is one of a fixed frequency Josephson bifurcation amplifier, a fixed frequency Josephson parametric amplifier, and a fixed frequency Josephson parametric oscillator.

6. A Josephson device comprising a superconducting quantum interference device (SQUID) constructed using two nonlinear microwave resonators according to claim 1.

7. The Josephson device of claim 6, wherein the Josephson device is one of a variable frequency Josephson bifurcation amplifier, a variable frequency Josephson parametric amplifier, and a variable frequency Josephson parametric oscillator.

8. A method for manufacturing a nonlinear microwave resonator, comprising the steps of: forming a first electrode made of a superconductor on a substrate; forming an insulating layer made of an insulator on the first electrode; and forming a second electrode made of a superconductor on the insulating layer, wherein the first electrode, the insulating layer, and the second electrode are formed to function as a Josephson junction, and the film thickness of the insulating layer and the critical current density of the Josephson junction are set so that the resonant frequency is in the range of 2 to 12 GHz according to the following formula (1): where f is the resonant frequency, Jc is the critical current density of the Josephson junction, t is the thickness of the insulating layer, and φ ０ : magnetic flux quantum, ε ０ : dielectric constant of vacuum, ε ｒ : relative permittivity of the insulating layer.

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