Quantitative analysis method and circuit for superconducting junction arrays used for quantum voltage reference

Abstract

The present invention provides a quantitative analysis method for a superconducting junction array used for a quantum voltage reference. First, m groups of Josephson junction arrays are provided, and discrete parameters corresponding to the m groups of Josephson junction arrays are set. Second, a microwave current and a bias current are applied to any group of Josephson junction arrays to obtain a first correspondence between the bias current and the output voltage. Third, the microwave current amplitude is adjusted to obtain different heights of the a-th Shapiro step corresponding to different microwave current amplitudes, and the maximum height of the a-th Shapiro step in the Josephson junction array is found. Finally, the maximum height of the a-th Shapiro step corresponding to the m groups of Josephson junction arrays is obtained, and a third correspondence between the discrete parameters of each Josephson junction array and the maximum height of the corresponding a-th Shapiro step is established. Furthermore, the circuit structure of the superconducting junction array of the present invention is simple and easy to implement, and can implement the quantitative analysis method for a superconducting junction array used for a quantum voltage reference of the present invention.

Description

Technical Field

[0001] The present invention relates to the field of circuit measurement and analysis, and in particular to a quantitative analysis method of a superconducting junction array for a quantum voltage reference and a circuit of the superconducting junction array. Background Art

[0002] The basic principle of using Josephson junction as voltage standard is the AC Josephson effect: when exposed to microwave radiation, Figure 1 As shown in the figure, the bias current-output voltage characteristic curve of a superconducting Josephson junction exhibits a step structure at specific voltage positions. These characteristic steps are called Shapiro steps. The bias current difference caused by the jump of the Shapiro step on the bias current coordinate axis represents the height of the Shapiro step, and the output voltage corresponding to the Shapiro step on the output voltage coordinate axis represents the position of the Shapiro step. The voltage value corresponding to the Shapiro step is related to the sequence number of the characteristic step, Planck's constant, the frequency of the applied microwave current, and the amount of electron charge.

[0003] Since Planck's constant and electron charge are both internationally recognized benchmark physical constants, the measurement accuracy of the step voltage depends entirely on the accuracy of the microwave current frequency. Modern frequency technology can achieve an uncertainty better than 10 -12 The precise voltage value corresponding to the Shapiro step can be obtained through the precise microwave current frequency, which makes the voltage standard based on the Josephson effect the most accurate quantum voltage reference at present. The precise quantum voltage reference has extremely wide applications in the field of electronic power.

[0004] However, because the output voltage of a single Josephson junction is typically limited to less than 10mV, far from meeting the needs of practical applications, existing technologies typically use a large-scale series structure to increase the output voltage. In this series array structure, the consistency of the parameters between each junction is crucial. This is because the uniformity of the critical current and the uniformity of the normal-state resistance in the Josephson junction directly affect the height of the Shapiro step in the bias current-output voltage characteristic curve of the Josephson junction. The height of the Shapiro step is very important for determining the position of the Shapiro step. Therefore, the consistency of the Josephson junction array can affect the reliability of the voltage standard formed by the Josephson junction array.

[0005] Therefore, how to design a quantitative analysis method to predict the influence of the consistency of the Josephson junction on the height of the Shapiro step has become one of the urgent problems to be solved by those skilled in the art.

[0006] It should be noted that the above technical background is merely provided to provide a clear and complete description of the technical solutions of the present invention and to facilitate understanding by those skilled in the art. Simply because these solutions are described in the technical background section of the present invention, it should not be assumed that the above technical solutions are well known to those skilled in the art. Summary of the Invention

[0007] In view of the shortcomings of the prior art described above, the object of the present invention is to provide a quantitative analysis method for a superconducting junction array for a quantum voltage reference and a circuit for a superconducting junction array, so as to solve the problem in the prior art that it is impossible to quantitatively analyze how the consistency of the Josephson junction affects the Shapiro step height.

[0008] To achieve the above-mentioned object and other related objects, the present invention provides a quantitative analysis method for a superconducting junction array used for a quantum voltage reference, wherein the quantitative analysis method for a superconducting junction array used for a quantum voltage reference comprises at least the following steps: S1: providing m groups of Josephson junction arrays, each Josephson junction array including n Josephson junctions, where n and m are both natural numbers greater than or equal to 2; setting discrete parameters possessed by each Josephson junction array; S2: providing a microwave current and a bias current to any group of Josephson junction arrays, obtaining the sum of the output voltages of the n Josephson junctions, and establishing a first corresponding relationship between the bias current and the sum of the output voltages; S3: adjusting the amplitude of the microwave current, and repeating step S2 to obtain different first corresponding relationships under different amplitudes of the microwave current. A corresponding relationship is established, the height of the a-th Shapiro step is different in different first corresponding relationships, a second corresponding relationship between the microwave current amplitude and the corresponding a-th Shapiro step height is established, and the maximum height of the a-th Shapiro step in the Josephson junction array is obtained; wherein a is a natural number greater than or equal to 1; S4: selecting the next group of Josephson junction arrays, returning to step S2, until m groups of Josephson junction arrays are selected, obtaining the maximum height of the a-th Shapiro step corresponding to the m groups of Josephson junction arrays, and establishing a third corresponding relationship between the discrete parameters of each Josephson junction array and the corresponding maximum height of the a-th Shapiro step, and measuring the quantum voltage reference based on the third corresponding relationship.

[0009] Optionally, in step S1 , discrete parameters between critical currents of n Josephson junctions and / or discrete parameters between normal-state resistances of n Josephson junctions are calculated and used as discrete parameters of the Josephson junction array.

[0010] Optionally, in step S2, a first mathematical relationship between the microwave current, the bias current and the output voltage is:

[0011]

[0012] in, Indicates time, represents the bias current, represents the microwave current, , represents the amplitude of the microwave current, represents the frequency of the microwave current, represents the thermal noise current at 77K, represents the critical current of the Josephson junction, represents the phase difference of the wave function between the superconductors inside the Josephson junction, represents the output voltage of the Josephson junction, represents the normal-state resistance of the Josephson junction, represents the charge of the electron, represents the reduced Planck constant; substituting the bias current and the microwave current into the equation, and performing a discrete solution on the first mathematical relationship to obtain the output voltage of each Josephson junction.

[0013] Optionally, in step S2,

[0014]

[0015] in represents the voltage corresponding to each Shapiro step in the first corresponding relationship, represents the frequency of the microwave current, represents Planck's constant, represents the charge of the electron, Represents the ordinal number of the Shapiro step; and verifies the accuracy of the voltage corresponding to each Shapiro step in the first corresponding relationship according to the frequency of the microwave current.

[0016] Optionally, sampling is performed within the target amplitude range of the microwave current to obtain different heights of the ath Shapiro step in the first corresponding relationship under different microwave current amplitudes.

[0017] Optionally, in step S3, the range of a is greater than or equal to 1 and less than or equal to 3.

[0018] Optionally, step S3 further includes: the corresponding relationship between the microwave current amplitude and the height of the a-th Shapiro step is expressed by a second mathematical relationship:

[0019]

[0020] in, represents the height of the a-th Shapiro step, represents the critical current of the Josephson junction, express Bessel function of order, represents the amplitude of the microwave current, represents the normal-state resistance of the Josephson junction, represents the charge of the electron, represents Planck's constant, represents the frequency of the microwave current; and verifies the accuracy of the second corresponding relationship according to the second mathematical relationship.

[0021] Optionally, in step S2, n Josephson junctions in the Josephson junction array are connected in series, and a microwave current and a bias current are provided to the Josephson junction array to obtain the sum of the output voltages of the n Josephson junctions.

[0022] Optionally, in step S2, the same microwave current and bias current are respectively provided to n Josephson junctions in the Josephson junction array to obtain output voltages of the n Josephson junctions, and the output voltages of the n Josephson junctions are added.

[0023] To achieve the above-mentioned and other related objectives, the present invention further provides a circuit for a superconducting junction array, and a quantitative analysis method for a superconducting junction array used for a quantum voltage reference. The circuit for the superconducting junction array includes at least: a microwave current source, a bias current source, and n Josephson junctions, wherein the n Josephson junctions are connected in series in sequence; the microwave current source and the bias current source are connected in series and applied to both ends of the n Josephson junctions connected in series.

[0024] As described above, the quantitative analysis method of the superconducting junction array for quantum voltage reference and the circuit of the superconducting junction array of the present invention have the following beneficial effects:

[0025] 1. The present invention first obtains a first correspondence between bias current and output voltage; secondly, by adjusting the amplitude of the microwave current, different Shapiro step heights are obtained, and a second correspondence between the microwave current amplitude and the Shapiro step height is established to confirm the maximum height of the Shapiro step in the Josephson junction array; finally, through m groups of Josephson junction arrays, the present invention can establish a relationship between the discrete parameters of each Josephson junction array and the maximum height of the corresponding Shapiro step, so as to quantitatively analyze the influence of the consistency of the Josephson junction array on the Shapiro step height.

[0026] 3. The present invention can verify whether the voltages corresponding to the various Shapiro steps in the first correspondence actually obtained are accurate by determining the mathematical relationship of the output voltage, thereby verifying whether the first correspondence is accurate, thereby improving the accuracy of the present invention.

[0027] 4. The present invention can verify whether the second corresponding relationship between the microwave current amplitude and the Shapiro step height is accurate through the second mathematical relationship between the microwave current amplitude and the Shapiro step height, thereby improving the accuracy of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Shown is a schematic diagram of the Shapiro steps in the bias current-output voltage characteristic curve.

[0029] Figure 2 It is a schematic flow chart of the quantitative analysis method of the superconducting junction array for quantum voltage reference of the present invention.

[0030] Figure 3 Shown is a schematic diagram of a resistance shunt model of a Josephson junction of the present invention.

[0031] Figure 4 Shown is a circuit schematic diagram of the Josephson junction array of the present invention.

[0032] Figure 5 It is a schematic diagram showing the first corresponding relationship of the present invention under the first microwave current amplitude.

[0033] Figure 6 It is a schematic diagram showing the first corresponding relationship of the present invention under the second microwave current amplitude.

[0034] Figure 7 It is a schematic diagram showing the first corresponding relationship of the present invention under the third microwave current amplitude.

[0035] Figure 8 It is a schematic diagram showing the first corresponding relationship of the present invention under different microwave current amplitudes.

[0036] Figure 9 Shown is a schematic diagram of the first Shapiro step of the present invention at different microwave current amplitudes.

[0037] Figure 10 It is a schematic diagram of function fitting of the second corresponding relationship of the present invention.

[0038] Figure 11 A comparison diagram between actual sample values ​​and ideal values ​​is shown as the second correspondence of the present invention.

[0039] Figure 12 Shown is a schematic structural diagram of a circuit of a superconducting junction array of the present invention.

[0040] Component number description

[0041] 1 Josephson junction array

[0042] 11 Josephson knot

[0043] 1a Ideal Josephson junction

[0044] 1b Normal state resistance DETAILED DESCRIPTION

[0045] The following describes the embodiments of the present invention through specific examples. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. The present invention may also be implemented or applied through various other specific embodiments, and the details in this specification may be modified or altered based on different viewpoints and applications without departing from the spirit of the present invention.

[0046] See also Figures 1-12 It should be noted that the diagrams provided in this embodiment are merely schematic illustrations of the basic concept of the present invention. Therefore, the diagrams only show components related to the present invention and are not drawn according to the number, shape, and size of components in actual implementation. In actual implementation, the type, quantity, and proportion of each component may be changed arbitrarily, and the component layout may also be more complex.

[0047] The consistency of the physical parameters of the superconducting junction will affect the height of the Shapiro step, and the height of the Shapiro step is very important for the measurement of the quantum voltage reference. Therefore, when preparing superconducting junctions, special attention should be paid to the consistency of the physical properties of the superconducting junctions. In particular, for high-temperature superconducting junctions, the physical properties of the prepared superconducting junctions vary more greatly, making it difficult to measure the quantum voltage reference based on the appropriate Shapiro step height for high-temperature superconducting junctions. Therefore, the present invention proposes a technical solution that quantitatively analyzes the impact of the physical property differences between superconducting junctions on the Shapiro step height, in order to provide a clear optimization parameter direction for the superconducting junction preparation process, so that the superconducting junction array can measure the quantum voltage reference based on the appropriate Shapiro step height. The specific technical solution is as follows:

[0048] Example 1

[0049] like Figure 2 As shown, this embodiment provides a quantitative analysis method for a superconducting junction array for a quantum voltage reference, comprising the following steps:

[0050] like Figure 2 As shown, in step S1, m groups of Josephson junction arrays are provided, each Josephson junction array 1 includes n Josephson junctions 11, and n and m are both natural numbers greater than or equal to 2; discrete parameters of each Josephson junction array 1 are set.

[0051] Specifically, in this embodiment, the discrete parameter of a Josephson junction array 1 refers to the degree of discreteness between the n Josephson junctions 11 in the Josephson junction array 1, that is, the degree of difference between the n Josephson junctions 11. By setting the discrete parameters of m groups of Josephson junction arrays 1 and finding the Shapiro step heights corresponding to the m groups of Josephson junction arrays 1, the relationship between each discrete parameter and each Shapiro step height can be obtained to quantitatively describe the effect of the consistency of the Josephson junction array 1 on the Shapiro step height. Further, as Figure 3 As shown, the resistance shunt model of the Josephson junction 11 includes an ideal Josephson junction 1a and a normal-state resistor 1b connected in parallel. Physical parameters such as the normal-state resistor 1b and the critical current can be used to describe the degree of difference between the Josephson junctions 11. Furthermore, the discrete parameters of the Josephson junction array 1 can be selected from the discrete parameters between n normal-state resistors 1b and / or the discrete parameters between n critical currents. The specific discrete parameters can be selected from any of the standard deviation, variance, or mean deviation. In practical applications, the discrete parameters of the Josephson junction array 1 can be set as needed and are not limited to this embodiment.

[0052] like Figure 2 As shown, in step S2, microwave current and bias current are provided to any group of Josephson junction arrays 1 to obtain the sum of the output voltages of n Josephson junctions 11, and a first corresponding relationship between the bias current and the sum of the output voltages is established.

[0053] Specifically, in this embodiment, any group of Josephson junction arrays between 1 and m is selected, and microwave current and bias current are provided to the group of Josephson junction arrays 1 to obtain the sum of the output voltages of n Josephson junctions 11 in the group of Josephson arrays 1; wherein the microwave current is alternating current and the bias current is direct current. Further, as Figure 4 As shown, n Josephson junctions 11 are connected in series, microwave current and bias current are connected in series and applied to both ends of the n Josephson junctions 11, and the output voltage of the n Josephson junctions 11 connected in series is taken as the sum of the output voltages; alternatively, microwave current and bias current are applied to the n Josephson junctions 11 independently, and the microwave current and bias current applied to the n Josephson junctions 11 are consistent, and the n output voltages obtained by the n Josephson junctions 11 are added together. As an example, Figure 5 As shown, the bias current provided in the first correspondence is sampled within the range of 19.5 mA to 22 mA, with a sampling step of 0.01 mA. The voltage corresponding to the first Shapiro step is 1.034 V, and the height of the first Shapiro step is approximately 1.2 mA. The first correspondence allows for intuitive observation of the relevant characteristics of the Shapiro step. In practical applications, the microwave current and bias current can be set as needed, and are not limited to this embodiment.

[0054] Specifically, in this embodiment, the first mathematical relationship between the microwave current, the bias current and the output voltage is:

[0055]

[0056] in, Indicates time, represents the bias current, represents the microwave current, , represents the amplitude of the microwave current, represents the frequency of the microwave current, represents the thermal noise current at 77K, represents the critical current of the Josephson junction 11, represents the phase difference of the wave function between the superconductors inside the Josephson junction 11, represents the output voltage of the Josephson junction 11, represents the normal-state resistance of the Josephson junction 11, represents the charge of the electron, represents the reduced Planck constant. Furthermore, by substituting the microwave current and bias current actually used in step S2 and performing a discrete solution to the first mathematical relationship using a numerical calculation method, the output voltages of the n Josephson junctions in the Josephson junction array 1 can be obtained. The numerical calculation method can be any of the Euler method, the Runge-Kutta method, or the trapezoidal method. In practical applications, the solution method for the first mathematical relationship can be set as needed, and is not limited to this embodiment.

[0057] Specifically, in this embodiment, the frequency of the microwave current determines the voltage corresponding to each Shapiro step, that is, , Indicates the voltage corresponding to each Shapiro step in the first correspondence, represents the ordinal number of the Shapiro step, which is a natural number greater than or equal to 1. represents the frequency of the microwave current, represents Planck's constant, represents the amount of electron charge. Furthermore, the theoretical voltage value corresponding to each Shapiro step in the first correspondence can be calculated based on the actual microwave current frequency used, and used to verify the accuracy of the voltage value corresponding to the Shapiro step in the first correspondence obtained in step S2, thereby verifying the correctness of the first correspondence. In actual applications, the verification method for the first correspondence can be set as needed, and is not limited to this embodiment.

[0058] like Figure 2As shown, in step S3, the amplitude of the microwave current is adjusted, and step S2 is repeated to obtain different first corresponding relationships under different microwave current amplitudes. The height of the a-th Shapiro step is different in different first corresponding relationships. A second corresponding relationship between the microwave current amplitude and the corresponding a-th Shapiro step height is established, and the maximum height of the a-th Shapiro step in the Josephson junction array is obtained; wherein a is a natural number greater than or equal to 1.

[0059] Specifically, in this embodiment, the amplitude of the microwave current is adjusted, and the process returns to step S2. The height of the ath Shapiro step in the first corresponding relationship will change. The amplitude of the microwave current is related to the power of the microwave current, and the amplitude of the microwave current can be adjusted by adjusting the power of the microwave current. Figure 5 、 Figure 6 and Figure 7 As shown, different microwave current amplitudes will produce different first correspondences, and the height of the ath Shapiro step in different first correspondences changes, and as shown in Figure 8 As shown, by expanding the range of microwave current amplitude, it can be seen that each microwave current amplitude corresponds to the output characteristic curve of the first corresponding relationship. Figure 8 Analyze the height of the first Shapiro step: Figure 9 As shown, the lines from bottom to top on the left side of the first Shapiro step correspond one-to-one to the lines from top to bottom on the right side of the first Shapiro step, and each line represents a first correspondence relationship in different microwave current amplitudes. It can be seen that the height of the first Shapiro step is different in different microwave current amplitudes in the first correspondence relationship, so a second correspondence relationship between the microwave current amplitude and the height of the a-th Shapiro step can be established; wherein, since the smaller the ordinal number a is, the higher the height of the Shapiro step is, the 1st, 2nd or 3rd Shapiro step can be selected as the a-th Shapiro step in this embodiment. As an example, Figure 10 As shown in FIG, the microwave current amplitude is set to sample within 0 mA ~ 200 mA, the sampling step is 4 mA, and the height of the corresponding first Shapiro step is observed to obtain the different heights of the first Shapiro step of the Josephson junction array 1 under different microwave current amplitudes, thereby fitting to obtain the following: Figure 10 The second corresponding relationship is shown, and the maximum height of the first Shapiro step is obtained from the second corresponding relationship, which is the first peak of the second corresponding relationship. In practical applications, the value range of the microwave current amplitude is set according to actual needs and is not limited to this embodiment.

[0060] Specifically, in this embodiment, the amplitude of the microwave current and the height of the a-th Shapiro step can be described by the second mathematical relationship, namely: ,in, represents the height of the a-th Shapiro step, represents the critical current of the Josephson junction 11, express Bessel function of order, represents the normal-state resistance of the Josephson junction 11, represents the charge of the electron, represents the amplitude of the microwave current, represents Planck's constant, Furthermore, the accuracy of the second corresponding relationship actually obtained can be verified by the second mathematical relationship. For example, Figure 11 As shown, the actual second correspondence (actual sampled values) is very consistent with the theoretical second correspondence (ideal values), and the functional characteristics between the ideal values ​​and the actual sampled values ​​are also consistent. Therefore, it can be determined that the actual second correspondence is accurate. In actual applications, the verification method of the second correspondence can be set as needed, and is not limited to this embodiment.

[0061] like Figure 2 As shown, in step S4, the next group of Josephson junction arrays is selected, and the process returns to step S2 until m groups of Josephson junction arrays are selected, the maximum height of the a-th Shapiro step corresponding to the m groups of Josephson junction arrays 1 is obtained, and a third corresponding relationship between the discrete parameters of each Josephson junction array 1 and the maximum height of the corresponding a-th Shapiro step is established, and the quantum voltage reference is measured based on the third corresponding relationship.

[0062] Specifically, in this embodiment, m groups of Josephson junction arrays are subjected to steps S2 and S3, ultimately obtaining the maximum height of the a-th Shapiro step corresponding to the m groups of Josephson junction arrays 1. A third correspondence is established between the discrete parameters of each Josephson junction array and the maximum height of the corresponding a-th Shapiro step using the discrete parameters corresponding to the m groups of Josephson junction arrays 1, thereby quantitatively describing the effect of the consistency of the Josephson junction array 1 on the maximum height of the a-th Shapiro step. Furthermore, by understanding the effect of the consistency of the Josephson junction array 1 on the maximum height of the a-th Shapiro step, the consistency of the Josephson junction array 1 can be adjusted to maximize the maximum height of the a-th Shapiro step. The quantum voltage reference is then measured based on the increased maximum height of the a-th Shapiro step (with the first Shapiro step being optimal), thereby improving the measurement accuracy of the quantum voltage reference and providing a clear parameter optimization direction for the superconducting junction fabrication process. As an example, a Josephson junction array 1 includes 10,000 Josephson junctions 11. The critical current of the Josephson junction array 1 is normally distributed, with a mean of 2 mA and a standard deviation of 5%. The normal-state resistance is uniformly set to 0.005 Ω. The frequency of the microwave current is 50 GHz. The maximum height of the first Shapiro step in the Josephson junction array 1 is approximately 2 mA. Since the higher the dispersion of the Josephson junction array 1, the smaller the height of the Shapiro step. Therefore, when the height of the first Shapiro step in the Josephson junction array 1 needs to be no less than 2 mA for measuring a quantum voltage reference, the standard deviation of each critical current of the Josephson junction array 1 should be no greater than 5%. The maximum height of the first Shapiro step can be found for measuring the quantum voltage reference, thereby achieving measurement of the quantum voltage reference. In practical applications, the Josephson junction array 1 can be configured as needed, and is not limited to this embodiment.

[0063] Example 2

[0064] like Figure 12 As shown, this embodiment provides a circuit of a superconducting junction array, including a microwave current source, a bias current source and n Josephson junctions 11, and the n Josephson junctions 11 are connected in series in sequence; the microwave current source and the bias current source are connected in series and applied to both ends of the n Josephson junctions 11 in series.

[0065] Specifically, in this embodiment, n Josephson junctions 11 are connected in series. A microwave current source and a bias current source are applied to the two ends of the n Josephson junctions 11. This generates the output voltage of the n Josephson junctions 11, and a first correspondence between the bias current and the output voltage is obtained. Furthermore, by adjusting the amplitude of the microwave current and observing the different heights of the a-th Shapiro step, a second correspondence between the microwave current amplitude and the height of the a-th Shapiro step is obtained, and the maximum height of the a-th Shapiro step corresponding to the circuit of the superconducting junction array is found; where a is a natural number greater than or equal to 1. Furthermore, by replacing the n Josephson junctions in the circuit of the superconducting junction array and changing the discrete parameters between the n Josephson junctions 11, a third correspondence between the discrete parameters of the circuit of the superconducting junction array and the maximum height of the corresponding a-th Shapiro step is obtained, ultimately quantitatively describing the impact of the discrete parameters of the circuit of the superconducting junction array on the height of the a-th Shapiro step.

[0066] It should be noted that the circuit of the superconducting junction array of Example 2 can be used to implement the quantitative analysis method of the superconducting junction array for quantum voltage reference of Example 1, and can also be used to implement other quantitative analysis methods of superconducting junction arrays for quantum voltage reference, without specific limitation here.

[0067] In summary, the present invention provides a quantitative analysis method for a superconducting junction array for a quantum voltage reference. First, m groups of Josephson junction arrays are provided, and discrete parameters corresponding to the m groups of Josephson junction arrays are set. Second, a microwave current and a bias current are applied to any group of Josephson junction arrays to obtain the sum of the output voltages of the n Josephson junctions, and a first correspondence between the bias current and the sum of the output voltages is obtained. Third, the microwave current amplitude is adjusted to obtain different heights of the a-th Shapiro step corresponding to different microwave current amplitudes, a second correspondence between the microwave current amplitude and the height of the a-th Shapiro step is established, and the maximum height of the a-th Shapiro step in the Josephson junction array is found. Finally, the maximum height of the a-th Shapiro step corresponding to the m groups of Josephson junction arrays is obtained, and a third correspondence between the discrete parameters of each Josephson junction array and the maximum height of the corresponding a-th Shapiro step is established to quantitatively describe the influence of the discrete parameters of the Josephson junction array on the maximum height of the Shapiro step. Furthermore, the circuit structure of the superconducting junction array of the present invention is simple and easy to implement, and can implement the quantitative analysis method for a superconducting junction array for a quantum voltage reference of the present invention. Therefore, the present invention effectively overcomes various shortcomings of the prior art and has high industrial utilization value.

[0068] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Anyone skilled in the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by one of ordinary skill in the art without departing from the spirit and technical principles disclosed herein are intended to be covered by the claims of the present invention.

Claims

1. A quantitative analysis method for a superconducting junction array for a quantum voltage reference, characterized in that: The quantitative analysis method of the superconducting junction array for quantum voltage reference comprises at least the following steps: S1: providing m groups of Josephson junction arrays, each of which includes n Josephson junctions, where n and m are both natural numbers greater than or equal to 2; and setting discrete parameters of each Josephson junction array; S2: providing microwave current and bias current to any group of Josephson junction arrays, obtaining the sum of the output voltages of n Josephson junctions, and establishing a first correspondence between the bias current and the sum of the output voltages; S3: adjusting the amplitude of the microwave current and repeating step S2 to obtain different first corresponding relationships under different microwave current amplitudes, wherein the height of the a-th Shapiro step is different in different first corresponding relationships, establishing a second corresponding relationship between the microwave current amplitude and the corresponding a-th Shapiro step height, and obtaining the maximum height of the a-th Shapiro step in the Josephson junction array; wherein a is a natural number greater than or equal to 1; S4: Select the next group of Josephson junction arrays and return to step S2 until m groups of Josephson junction arrays are selected, obtain the maximum height of the a-th Shapiro step corresponding to the m groups of Josephson junction arrays, and establish a third corresponding relationship between the discrete parameters of each Josephson junction array and the maximum height of the corresponding a-th Shapiro step, and measure the quantum voltage reference based on the third corresponding relationship.

2. The quantitative analysis method for a superconducting junction array for a quantum voltage reference according to claim 1, characterized in that: In step S1 , discrete parameters between critical currents of n Josephson junctions and / or discrete parameters between normal-state resistances of n Josephson junctions are calculated and used as discrete parameters of the Josephson junction array.

3. The quantitative analysis method for a superconducting junction array for a quantum voltage reference according to claim 1, characterized in that: In step S2, a first mathematical relationship between the microwave current, the bias current, and the output voltage is: in, Indicates time, represents the bias current, represents the microwave current, , represents the amplitude of the microwave current, represents the frequency of the microwave current, represents the thermal noise current at 77K, represents the critical current of the Josephson junction, represents the phase difference of the wave function between the superconductors inside the Josephson junction, represents the output voltage of the Josephson junction, represents the normal-state resistance of the Josephson junction, represents the charge of the electron, represents the reduced Planck constant; The bias current and the microwave current are substituted into the first mathematical relationship, and a discrete solution is performed on the first mathematical relationship to obtain the output voltage of each Josephson junction.

4. The quantitative analysis method for a superconducting junction array for a quantum voltage reference according to claim 1, characterized in that: In step S2, in represents the voltage corresponding to each Shapiro step in the first corresponding relationship, represents the frequency of the microwave current, represents Planck's constant, represents the charge of the electron, Indicates the ordinal number of the Shapiro step; The accuracy of the voltage corresponding to each Shapiro step in the first corresponding relationship is verified according to the frequency of the microwave current.

5. The quantitative analysis method for a superconducting junction array for a quantum voltage reference according to claim 1, characterized in that: In step S3, sampling is performed within the target amplitude range of the microwave current to obtain different heights of the ath Shapiro step in the first corresponding relationship under different microwave current amplitudes.

6. The quantitative analysis method for a superconducting junction array for a quantum voltage reference according to claim 1, characterized in that: In step S3 , the range of a is greater than or equal to 1 and less than or equal to 3.

7. The quantitative analysis method for a superconducting junction array for a quantum voltage reference according to claim 1, characterized in that: Step S3 also includes: the corresponding relationship between the microwave current amplitude and the height of the a-th Shapiro step is expressed by a second mathematical relationship: in, represents the height of the a-th Shapiro step, represents the critical current of the Josephson junction, express Bessel function of order, represents the amplitude of the microwave current, represents the normal-state resistance of the Josephson junction, represents the charge of the electron, represents Planck's constant, represents the frequency of the microwave current; According to the second mathematical relationship, the accuracy of the second corresponding relationship is verified.

8. The quantitative analysis method for a superconducting junction array for a quantum voltage reference according to claim 1, characterized in that: In step S2, n Josephson junctions in the Josephson junction array are connected in series, and microwave current and bias current are provided to the Josephson junction array to obtain the sum of output voltages of the n Josephson junctions.

9. The quantitative analysis method for a superconducting junction array for a quantum voltage reference according to claim 1, characterized in that: In step S2, the same microwave current and bias current are respectively provided to n Josephson junctions in the Josephson junction array to obtain output voltages of the n Josephson junctions, and the output voltages of the n Josephson junctions are added.

10. A circuit of a superconducting junction array, used to implement the quantitative analysis method of a superconducting junction array for a quantum voltage reference according to any one of claims 1 to 8, characterized in that: The circuit of the superconducting junction array comprises at least: a microwave current source, a bias current source and n Josephson junctions, wherein the n Josephson junctions are connected in series in sequence; the microwave current source and the bias current source are connected in series and applied to both ends of the n Josephson junctions in series.

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