Entangled microwave source based on dual-mode self-oscillation effect

Abstract

The application discloses an entangled microwave source based on a double-mode self-oscillation effect, and has the characteristics of frequency tunability, entanglement robustness and functional diversity. The device comprises input and output ports, a half-coplanar waveguide resonator, a coplanar waveguide transmission line, input and output capacitors, a superconducting quantum interference device formed by two Josephson structures, and alternating and direct current biases. Because the superconducting quantum interference device is embedded in a non-central position of the half-coplanar waveguide resonator, the device has two modes with different frequencies, i.e., a common mode and a differential mode. In a double-mode self-oscillation working mode, the device can generate continuous variable phase entangled microwaves, and the device has the frequency tunable characteristic due to the existence of the superconducting quantum interference device. In addition, the entanglement robustness of the device is due to the stability of the double-mode self-oscillation. The application designs an entangled microwave source based on the double-mode self-oscillation effect, which has the characteristics of frequency tunability and entanglement robustness. The device has important application potential in the fields of quantum computing, quantum lighting and sensing.

Description

Technical Field

[0001] This invention relates to the field of microwave light source design, and more particularly to an entangled microwave source based on a dual-mode self-excited oscillation effect. Background Technology

[0002] Sources capable of generating entangled microwave photon pairs are crucial quantum resources for quantum information technology. Highly robust, frequency-tunable, two-mode continuous-variable entangled microwave sources are the cornerstone of long-range distributed quantum information technology. In recent decades, thanks to mature microfabrication techniques and abundant quantum physics theories, demonstrating the principles of quantum information technology on highly integrated superconducting quantum chips has become increasingly popular. Meanwhile, continuous-variable quantum resources are one of the fundamental technologies of quantum information. In the pursuit of large-scale quantum information processors, research on continuous variables from the optical band to the microwave band is an unstoppable trend. However, preparing continuous-variable entanglement in the microwave domain remains a key focus and challenge in quantum information technology.

[0003] Currently, there are several main approaches to preparing continuous-variable entangled microwave signals on superconducting quantum circuit platforms: The first involves using a superconducting coplanar waveguide resonator with a superconducting quantum interference device (QFID) at its terminal to spontaneously parametrically downconvert a high-energy coherent pump beam into one or more entangled low-energy microwave signals. The second approach involves operating the QFID in the sensitive region of quantum vacuum fluctuations, i.e., the dynamic Casimir effect, to excite entangled microwave photons from the quantum vacuum fluctuation field. The third approach is a four-wave mixing process, which compresses and entangles the signal wave and idle wave; typical devices include Josephson parametric amplifiers and traveling-wave parametric amplifiers. The fourth method utilizes a superconducting Josephson junction to disrupt the Cooper pairs in the quantum circuit, thereby emitting a strongly coherent wave packet signal. In addition, research teams have used Josephson ring modulators to prepare entangled microwave photons. This device is a four-wave mixing four-port nonlinear device that can entangle microwave photons in two different modes of superconducting coplanar waveguide resonators, or strongly interact a superconducting coplanar waveguide resonator with a low-dissipation three-dimensional superconducting resonator.

[0004] However, due to the inherent oscillation frequency limitations of the circuit structure, the second and last schemes mentioned above make it difficult to select and change the frequency of the two-mode entangled microwaves. The third scheme uses an active entanglement generator, which requires a coherent signal with room temperature noise as input. Because the unavoidable Gaussian noise channel is amplified and induces instability in the output signal, it compromises the entanglement stability of the prepared entangled microwaves. For the first type of entangled circuit, the superconducting coplanar wave resonator terminated by a superconducting quantum interference device (SQU) struggles to reduce the frequency difference between adjacent higher-order entangled oscillation modes. For preparing higher-order intermode entangled two-photon pairs using spontaneous parametric downconversion, a novel solution is to replace the traditional non-impedance gradually varying resonator with a variable impedance resonator and add an asymmetric superconducting quantum interference device at the end of the resonator, thereby enhancing the third nonlinearity of the superconducting circuit crystal. However, this entanglement generator also struggles to reduce the spectral bandwidth between different modes within a single resonator. Therefore, designing a continuous-variable entangled microwave source with tunable frequency and stability is crucial for quantum information technology. Summary of the Invention

[0005] The purpose of this invention is to design a frequency-tunable, entanglement-robust continuous variable entangled microwave source.

[0006] The technical solution for achieving the objective of this invention is: an entangled microwave source based on a dual-mode self-excited oscillation effect, characterized in that it includes an input end, an output end, a coplanar waveguide transmission line, an input capacitor, a half-coplanar waveguide resonator, an output capacitor, a DC bias, an AC bias, a superconducting quantum interference device, a capacitor to ground, and a coupling inductor, wherein:

[0007] The two ends of the coplanar waveguide transmission line are connected to the input end and the output end, respectively. The input end and the output end are connected to the half-coplanar waveguide resonator through the input capacitor and the output capacitor, respectively. One end of the superconducting quantum interference device is embedded in the off-center position of the half-coplanar waveguide resonator, and the other end is grounded through the ground capacitor. The AC bias and DC bias are grounded through the coupling inductor, and the coupling inductor is connected to the superconducting quantum interference device through mutual inductance.

[0008] Furthermore, the superconducting quantum interference device is placed at a non-central position within a half-coplanar waveguide resonator, and the difference between the two segments at this non-central position is Δd = |d1 - d2| < <d w The condition 0 < Δd < 0.01*d is satisfied. w , where d w Let d1 be the length of the half-coplanar waveguide resonator, and d2 be the distances between the non-center position and the two ends of the half-coplanar waveguide resonator, respectively.

[0009] Furthermore, with the aid of a superconducting quantum interference device and a ground-based capacitance, the entangled microwave source exhibits two modes with different frequencies—differential mode and common mode—with frequencies f0 and f1, respectively.d and f w ,in:

[0010] Differential mode frequency satisfies In the formula γ is the initial frequency of the differential-mode signal under zero magnetic field bias, γ is the inductance ratio, i.e., the ratio of the equivalent inductance of the superconducting quantum interference device under zero bias to the equivalent inductance of half the coplanar waveguide resonator, Φ DC The magnetic flux is input into the superconducting quantum interference device via a DC bias through a coupling inductor. Φ0 represents a magnetic flux quantum, and there is a coupling of strength g between the differential and common modes. After coupling, the differential and common modes are denoted as b and a, corresponding to frequencies f. b and f a Satisfy the following relationship

[0011]

[0012]

[0013] In formulas (1) and (2), Δf = |f w -f d | represents the absolute value of the frequency difference between the differential mode and the common mode, where f is the frequency of modes a and b. a with f b The adjustment is achieved by applying a DC bias to the superconducting quantum interference device.

[0014] Furthermore, in order for the entangled microwave source to generate a two-mode entangled microwave signal, the injected pump excitation signal should satisfy the following rule: Suppose a frequency f is applied to the superconducting quantum interference device through an AC bias. p =f a +f b A high-energy, continuous pump excitation signal is injected into the superconducting quantum interference device at a microwave photon velocity of δ. p Let the dissipation rates of entangled microwave source pairs of microwave photons of modes a and b be δ, respectively. a and δ b They should satisfy δ p >max{δ a ,δ b At this point, the entangled microwave source operates in a dual-mode self-excited oscillation mode, emitting two phase-entangled microwave signals from the output terminal, with frequencies f0 and f1 respectively. a and f b .

[0015] Furthermore, the input capacitor, output capacitor, and ground capacitor are all in the form of slot capacitors.

[0016] Furthermore, the coplanar waveguide transmission line is made of aluminum or niobium and has a thickness of 70nm to 120nm.

[0017] Furthermore, the half-coplanar waveguide resonator is made of aluminum or niobium with a thickness of 70nm to 120nm.

[0018] Furthermore, the superconducting quantum interference device consists of two Josephson junctions connected in parallel, with the Josephson junctions employing Al-AlO4. x -Al three-layer structure.

[0019] Furthermore, the input port, output port, input capacitor, output capacitor, AC bias and DC bias lines are patterned by exposure and etching using ultraviolet lithography, and the superconducting quantum interference device is fabricated using ultraviolet lithography or electron beam lithography and dual-angle electron beam evaporation processes.

[0020] Furthermore, the work process is as follows:

[0021] The DC bias port is connected to an external DC bias voltage source via a lead. Under electromagnetic effects, the DC voltage value is converted into a corresponding magnetic field signal, which is then input into the superconducting quantum interference device through a coupling inductor, effectively changing the natural frequency of the entangled microwave source. Simultaneously, the output of the vector network spectrum analyzer is connected to the input of the entangled microwave source via a lead. The full-band scanning signal emitted by the vector network spectrum analyzer is input from the input to the half-coplanar waveguide resonator and then fed back to the receiving end of the vector network spectrum analyzer via the output lead. When the natural frequency of the entangled microwave source resonates with the applied scanning signal, the resonant signal is absorbed by the entangled microwave source through the input capacitor and the lossy amplitude signal is fed back to the vector network spectrum analyzer through the output capacitor.

[0022] Under a certain DC bias, a coherent microwave source is connected to an AC bias terminal via a lead wire, and a pump excitation signal with a frequency equal to the sum of the differential and common-mode frequencies is applied to the entangled microwave source. When the rate of microwave photons injected into the entangled microwave source by the pump signal is greater than the dissipation rate of the differential and common-mode microwave photons, the entangled microwave source will operate in a dual-mode self-excited oscillation mode. At this time, a pump signal photon will split into a pair of phase-entangled microwave photons, and the sum of their frequencies is equal to the pump signal frequency. After that, the entangled microwave signal will reach the output terminal.

[0023] Compared with existing technologies, the significant advantages of this invention are as follows: 1) Benefiting from the fact that the equivalent inductance of the superconducting quantum interference device changes with the external magnetic flux, the device proposed in this invention can emit entangled microwave signals with adjustable frequencies in the dual-mode self-oscillation mode. 2) The entangled microwave source proposed in this invention operates in the dual-mode self-oscillation mode, requiring no additional input signal, and the emitted dual-mode entangled microwave signal has high robustness. 3) In addition, the device of this invention has rich functionality, can be used in single-mode or dual-mode operation, self-oscillation or parametric amplification mode, and can also realize quantum synchronization function and low-noise microwave source function. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the equivalent circuit of the present invention.

[0025] Figure 2 This is the overall circuit design diagram of an example of the present invention.

[0026] Figure 3 This is the DC bias spectrum of the device in this invention example.

[0027] Figure 4 This invention relates to the frequency tuning characteristics, entanglement, and robustness of the device in the example. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0029] Figure 1 The diagram shows the equivalent circuit of the entangled microwave source based on the dual-mode self-excited oscillation effect of the present invention. It consists of input and output terminals, a coplanar waveguide transmission line, an input capacitor 101, a half-coplanar waveguide resonator 102, an output capacitor 103, a DC bias, an AC bias, a superconducting quantum interference device (SQUID) 104, a ground capacitor 105, and a coupling inductor. The two ends of the coplanar waveguide transmission line are connected to the input and output terminals, respectively. The input and output terminals are connected to the half-coplanar waveguide resonator 102 via the input capacitor 101 and the output capacitor 103, respectively. One end of the superconducting quantum interference device 104 is embedded off-center in the half-coplanar waveguide resonator 102, and the other end is grounded via the ground capacitor 105. Both the AC and DC biases are grounded via the coupling inductor, and the coupling inductor is mutually inductively connected to the superconducting quantum interference device.

[0030] The superconducting quantum interference device should be located in a non-central position that satisfies the following rule: assuming a length of d... w A superconducting quantum interference device (QFID) is embedded off-center in half of a superconducting coplanar waveguide resonator. This off-center position divides the circuit of the superconducting coplanar waveguide resonator into two segments with lengths d1 and d2, respectively. The length difference between the two segments, Δd = |d1 - d2|, satisfies 0 < Δd < 0.01 * d w .

[0031] An entangled microwave source based on a dual-mode self-excited oscillation effect, where the two entangled modes have different frequencies and are tunable, should satisfy the following rule: With the support of a superconducting quantum interference device located off-center and a capacitance to ground, this device possesses two modes with different frequencies—a differential mode and a common mode, whose frequencies are f0 and f1, respectively. d and f w Among them, the differential mode frequency satisfies Relationship, in the formula γ is the initial frequency of the differential-mode signal under zero magnetic field bias, γ is the inductance ratio (this inductance ratio refers to the ratio of the equivalent inductance of the superconducting quantum interference device to that of a half-coplanar waveguide resonator under zero magnetic field bias; this value is generally obtained through fitting), Φ DC Φ0 represents the magnetic flux input to the superconducting quantum interference device via a DC bias through a coupling inductor, where Φ0 represents a magnetic flux quantum. Furthermore, there is a coupling of strength g between the differential and common modes, denoted as b and a after coupling, with frequencies f. b and f a Satisfy the following relationship

[0032]

[0033] In formulas (1) and (2), Δf = |f w -f d | represents the absolute value of the frequency difference between two modes. Because the equivalent inductance of a superconducting quantum interference device can be modulated by external magnetic flux, the frequencies f of modes a and b are... a with f b The DC bias can be adjusted by applying a DC bias to the superconducting quantum interference device.

[0034] To enable the entangled microwave source to generate a two-mode entangled microwave signal, the injected pump excitation signal should satisfy the following rule: Assume that a frequency f is applied to the superconducting quantum interference device through an AC bias. p =f a +f b A high-energy, continuous pump excitation signal is injected into the superconducting quantum interference device at a microwave photon velocity of δ. p Meanwhile, assuming that the dissipation rates of microwave photons of modes a and b in this device are δ a and δ b The microwave photon injection rate of the applied pump excitation signal should satisfy the relationship δ p >max{δ a ,δ b At this time, the device operates in dual-mode self-oscillation mode, and will emit two phase-entangled microwave signals from the output terminal with frequencies f0 and f1 respectively. a and f b .

[0035] Furthermore, the input / output capacitors and the capacitors to ground mentioned above are all in the form of slot capacitors.

[0036] Furthermore, the half-wavelength coplanar waveguide resonator and coplanar waveguide transmission line are made of aluminum or niobium material with a thickness of 70nm to 120nm.

[0037] Furthermore, the aforementioned superconducting quantum interference device consists of two parallel superconducting Josephson junctions, and both Josephson junctions are Al-AlO₂. x -Al three-layer structure.

[0038] Furthermore, the input / output ports, input / output capacitors, and AC / DC bias lines are patterned using ultraviolet lithography and etching processes, while the superconducting quantum interference device is fabricated using ultraviolet lithography or electron beam lithography and dual-angle electron beam evaporation processes.

[0039] Example

[0040] To verify the effectiveness of the present invention, the following experiment was conducted.

[0041] Figure 2 This is an example design layout, where the input terminal corresponds to 201, the input capacitor corresponds to 202, the coplanar waveguide transmission line corresponds to 203, the output capacitor corresponds to 204, the output terminal corresponds to 205, the half-coplanar waveguide resonator corresponds to 206, the DC bias corresponds to 207, the capacitance to ground corresponds to 208, and the AC bias corresponds to 209.

[0042] One end of the coplanar waveguide transmission line 203 is connected to the input terminal 201, and the other end is connected to the output port 205. One end of the half-coplanar waveguide resonator 206 is connected to the input terminal 201 through the input capacitor 202, and the other end is connected to the output terminal 205 through the output capacitor 204. One end of the superconducting quantum interference device is embedded in the off-center position of the half-coplanar waveguide resonator 206, and the other end is grounded through the ground capacitor 208. One end of the DC bias 207 and AC bias 209 are connected to the external leads, and the other end is mutually inductively connected to the superconducting quantum interference device through the coupling inductor.

[0043] The specific parameters in the device are as follows: the length d of the half-coplanar waveguide resonator w The length difference Δd generated by the location of the superconducting quantum interference device is approximately 9000 μm, and approximately 40 μm. The difference and common-mode frequencies in this embodiment are fd and fd, respectively. w =5.958GHz, The coupling strength g ≈ 35MHz, and the inductance ratio γ = 1.19%. The input and output capacitances are C1 = C2 ≈ 5fF, and the capacitance to ground is approximately C3 ≈ 4.62pF.

[0044] The device of this embodiment is packaged in a sample box with an external lead interface to provide a channel for measurement, and the sample box is placed under a low-temperature platform at 20mK. First, the static spectrum of the device is measured, that is, the frequency transmission characteristics of the device without an additional pump excitation signal applied to the device. The specific process is as follows: different magnetic flux biases are applied to the device through DC bias (207). At the same time, the full-band scanning signal is input from the input terminal (201) to the half-coplanar waveguide resonator (206) and output back to the vector network spectrum analyzer through the output terminal (205). When the natural frequency of the device resonates with the applied scanning signal, the resonant signal in the full frequency band is absorbed by the device through the input capacitor (202) and returned to the vector network spectrum analyzer with a lossy amplitude signal through the output capacitor (204). This process is manifested in the spectrum as the natural frequency of the device forming an absorption peak in the full frequency band of the scanning range. For example, by gradually varying the DC bias from 0Φ0 to 1Φ0, the spectral transfer characteristics of this device in the range of 5.85 GHz to 6.25 GHz were measured and recorded. The measurement results are as follows: Figure 3 As shown in the figure, this spectral transmission characteristic curve lays the foundation for the device's frequency-tunable dual-mode entangled microwave signal transmission.

[0045] from Figure 3 In the static spectrum diagram, it can be observed that both differential mode b and common mode a change with the DC bias. The differential mode b changes drastically, and its curve resembles a downward-opening parabola. The common mode a changes more weakly, only changing drastically when approaching half a flux quantum. Furthermore, there is a significant crossover between the two modes when the DC bias is approximately 0.37Φ0. The two black dashed lines in the spectrum diagram represent the calculation results of formulas (1) and (2), and it can be found that the theoretical calculation results are consistent with the actual measurement results. The white vertical dashed line represents the spectrum under a DC bias of 0.371Φ0. Under this condition, f a =5.95135GHz, f b =6.08256GHz.

[0046] Next, under different DC biases, according to the static frequency transfer characteristic curve of this device, an AC bias of frequency f is applied to this device through the AC bias port (209). p =f a +f b The pump excitation signal. When the pump signal power reaches the dual-mode self-excited oscillation working mode, this device will output a pair of frequencies f through the output port (205). a and f bThe entanglement of microwave signals is characterized by the degree of logarithmic nonnegativity, and the robustness of the device is characterized by the variance of the degree of entanglement. For example, when a power of -6.5 dBm is applied to the device at room temperature with a DC bias of 0.371Φ0, at a frequency of f... p A pump signal of 12.034 GHz is applied. At this time, the device outputs dual-mode microwave signals with frequencies of 5.95135 GHz and 6.08225 GHz from the output port (205). The degree of entanglement of the dual-mode signals is characterized using the non-negativity of logarithm, and the measurement is repeated 200 times. The mean of the degree of entanglement is 1.0723, and the variance of the degree of entanglement is 2.7403 × 10⁻⁶. -5 By gradually varying the DC bias from 0Φ0 to 1Φ0 and applying a pump signal that satisfies the dual-mode self-oscillation mode, the emission spectrum and entanglement degree of the device can be obtained. For example, applying a pump signal that satisfies the dual-mode self-oscillation mode under a DC bias of {0.082, 0.143, 0.213, 0.283, 0.353, 0.371, 0.423, 0.448, 0.476, 0.510}Φ0 will yield the emission spectrum, entanglement degree, and robustness of the device. The results are as follows: Figure 4 As shown.

[0047] Figure 4 (a) illustrates the emission spectrum of this device, which is the frequency spectrum of the generated microwave dual-mode entangled signal—that is, the frequency-tunable characteristic of the dual-mode entangled microwave of this device. The white circles and white asterisks in the figure represent the frequencies of a pair of microwave signals emitted by this device after applying a pump excitation signal satisfying dual-mode self-oscillation when the DC bias is {0.082, 0.143, 0.213, 0.283, 0.353, 0.371, 0.423, 0.448, 0.476, 0.510}Φ0. It can be seen that the frequency of the entangled dual-mode microwave signal emitted by this device is strongly correlated with the static spectral characteristics of the device itself, and both show the same trend with the DC bias. Furthermore, the frequency emitted by this device is determined by the inherent frequency of the device itself, and this device has a frequency tuning range of approximately 200MHz.

[0048] Figure 4 (b) This demonstrates the degree of entanglement and robustness of the device. The left axis represents the degree of entanglement—logarithmic nonnegativity—of the device at a DC bias of {0.082, 0.143, 0.213, 0.283, 0.353, 0.371, 0.423, 0.448, 0.476, 0.510} Φ0. The right axis represents the variance of the degree of entanglement at the corresponding DC bias. A positive logarithmic nonnegativity indicates that the dual-mode microwave signals are entangled and correlated, while a negative logarithmic nonnegativity indicates that the dual-mode microwave signals are unentangled. The measurement results show that the device has good robustness, with the variance of the degree of entanglement within 10.-5 Magnitude.

[0049] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. The above embodiments are described in a relatively specific and detailed manner, but this should not be construed as a limitation on the scope of the invention patent. It should be noted that for those skilled in the art, several modifications and improvements can be made without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. An entangled microwave source based on a dual-mode self-excited oscillation effect, characterized in that, This includes the input terminal, output terminal, coplanar waveguide transmission line, input capacitor, half-coplanar waveguide resonator, output capacitor, DC bias, AC bias, superconducting quantum interference device, capacitance to ground, and coupling inductor, among which: The coplanar waveguide transmission line is connected to the input and output ends, respectively. The input and output ends are connected to a half-coplanar waveguide resonator via input and output capacitors, respectively. One end of the superconducting quantum interference device (SQI) is embedded at the off-center position of the half-coplanar waveguide resonator. The difference between the two segments at this off-center position is Δd = |d1 - d2| < <d w The condition 0 < Δd < 0.01*d is satisfied. w , where d w d1 and d2 are the lengths of half of the coplanar waveguide resonator, respectively, and the distances from the non-center position to the two ends of the half-coplanar waveguide resonator. The other end is grounded through a capacitor to ground, and the AC bias and DC bias are grounded through a coupling inductor. The coupling inductor is connected to the superconducting quantum interference device through mutual inductance.

2. The entangled microwave source based on dual-mode self-excited oscillation effect according to claim 1, characterized in that, With the aid of a superconducting quantum interference device and a capacitance to ground, the entangled microwave source exhibits two modes with different frequencies—differential mode and common mode—with frequencies f0 and f1, respectively. d and f w ,in: Differential mode frequency satisfies In the formula γ is the initial frequency of the differential-mode signal under zero magnetic field bias, γ is the inductance ratio, i.e., the ratio of the equivalent inductance of the superconducting quantum interference device under zero bias to the equivalent inductance of half the coplanar waveguide resonator, Φ DC The magnetic flux is input into the superconducting quantum interference device via a DC bias through a coupling inductor. Φ0 represents a magnetic flux quantum, and there is a coupling of strength g between the differential and common modes. After coupling, the differential and common modes are denoted as b and a, corresponding to frequencies f. b and f a Satisfy the following relationship In formulas (1) and (2), Δf = |f w -f d | represents the absolute value of the frequency difference between the differential mode and the common mode, where f is the frequency of modes a and b. a with f b The adjustment is achieved by applying a DC bias to the superconducting quantum interference device.

3. The entangled microwave source based on dual-mode self-excited oscillation effect according to claim 1, characterized in that, To enable the entangled microwave source to generate a two-mode entangled microwave signal, the injected pump excitation signal should satisfy the following rule: Suppose a frequency f is applied to the superconducting quantum interference device through an AC bias. p =f a +f b A high-energy, continuous pump excitation signal is injected into the superconducting quantum interference device at a microwave photon velocity of δ. p Let the dissipation rates of entangled microwave source pairs of microwave photons of modes a and b be δ, respectively. a and δ b They should satisfy δ p >max{δ a ,δ b At this point, the entangled microwave source operates in a dual-mode self-excited oscillation mode, emitting two phase-entangled microwave signals from the output terminal, with frequencies f0 and f1 respectively. a and f b .

4. The entangled microwave source based on dual-mode self-excited oscillation effect according to claim 1, characterized in that, The input capacitor, output capacitor, and ground capacitor are all in the form of slot capacitors.

5. The entangled microwave source based on dual-mode self-excited oscillation effect according to claim 1, characterized in that, The coplanar waveguide transmission line is made of aluminum or niobium and has a thickness of 70nm to 120nm.

6. The entangled microwave source based on dual-mode self-excited oscillation effect according to claim 1, characterized in that, Half-coplanar waveguide resonators are made of aluminum or niobium with a thickness of 70nm to 120nm.

7. The entangled microwave source based on dual-mode self-excited oscillation effect according to claim 1, characterized in that, The superconducting quantum interference device consists of two Josephson junctions connected in parallel. The Josephson junctions are Al-AlO3. x -Al three-layer structure.

8. The entangled microwave source based on dual-mode self-excited oscillation effect according to claim 1, characterized in that, The input ports, output ports, input capacitors, output capacitors, AC bias lines, and DC bias lines are patterned using ultraviolet lithography. The superconducting quantum interference device is fabricated using ultraviolet lithography or electron beam lithography and dual-angle electron beam evaporation.

9. The entangled microwave source based on dual-mode self-excited oscillation effect according to claim 1, characterized in that, The work process is as follows: The DC bias port is connected to an external DC bias voltage source via a lead. Under electromagnetic effects, the DC voltage value is converted into a corresponding magnetic field signal, which is then input into the superconducting quantum interference device through a coupling inductor, effectively changing the natural frequency of the entangled microwave source. Simultaneously, the output of the vector network spectrum analyzer is connected to the input of the entangled microwave source via a lead. The full-band scanning signal emitted by the vector network spectrum analyzer is input from the input to the half-coplanar waveguide resonator and then fed back to the receiving end of the vector network spectrum analyzer via the output lead. When the natural frequency of the entangled microwave source resonates with the applied scanning signal, the resonant signal is absorbed by the entangled microwave source through the input capacitor and the lossy amplitude signal is fed back to the vector network spectrum analyzer through the output capacitor. Under a certain DC bias, a coherent microwave source is connected to an AC bias terminal via a lead wire, and a pump excitation signal with a frequency equal to the sum of the differential and common-mode frequencies is applied to the entangled microwave source. When the rate of microwave photons injected into the entangled microwave source by the pump signal is greater than the dissipation rate of the differential and common-mode microwave photons, the entangled microwave source will operate in a dual-mode self-excited oscillation mode. At this time, a pump signal photon will split into a pair of phase-entangled microwave photons, and the sum of their frequencies is equal to the pump signal frequency. After that, the entangled microwave signal will reach the output terminal.

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