^{1,a)}, A. A. Soroka

^{2}and W. Krech

^{3}

### Abstract

The characteristics of a partially coherent quantum detector based on a charge-phasequbit, coupled with a classical resonant circuit, are analyzed. It is shown that in an electromagnetic field signal characteristics with the maximum coefficient of conversion arise when the effective quantum inductance of the qubit assumes positive and negative values periodically with the frequency of low-frequency oscillations of the occupation probability of the energy levels (Rabi type) . The physical nature of parametric energy conversion (regeneration) in a qubitdetector with a periodic change of the sign of the effective inductance and its possible application in quantum informatics for detecting weak signals is discussed.

This work was financed in part by DFG (code KR 1171/9-2) and the Ministry of Education and Science of Ukraine (“Nanophysics and nanoelectronics”) M/189-07).

We wish to thank D. Born, T. Wagner, U. Hübner, I. Zhilyaev, and S. V. Kuplevakhskiĭ for fruitful discussion and helpful remarks.

I. INTRODUCTION

II. MODEL OF A CHARGE-PHASEQUBIT

III. CHARGE-PHASEQUBIT AND EXPERIMENTAL PROCEDURE

IV. CHARACTERISTICS OF A CHARGE-PHASEQUBIT IN AN ELECTROMAGNETIC FIELD

V. CONCLUSION

### Key Topics

- Qubits
- 111.0
- Inductance
- 20.0
- Quantum measurement theory
- 18.0
- Magnetic flux
- 13.0
- Microwaves
- 12.0

## Figures

Equivalent circuit of a charge-phase qubit with the parameters , , , , , and (a). The image in an electron microscope (SEM) of the region of the “island” with two tunnel contacts and charge gate (b).

Equivalent circuit of a charge-phase qubit with the parameters , , , , , and (a). The image in an electron microscope (SEM) of the region of the “island” with two tunnel contacts and charge gate (b).

Scheme of the dependences of the ground-state |0⟩ and excited-state |1⟩ energy levels of charge-phase qubit versus the external magnetic field. The arrows show Rabi-type oscillations with frequency of the occupation probability of levels near exact resonance with an external microwave field, (a). Curves of the effective quantum inductance in the ground and excited states versus the external magnetic flux (b). It is evident that during part of the period of the low-frequency oscillations of the reactive parameter of the qubit assumes negative values. Computed parameters , , .

Scheme of the dependences of the ground-state |0⟩ and excited-state |1⟩ energy levels of charge-phase qubit versus the external magnetic field. The arrows show Rabi-type oscillations with frequency of the occupation probability of levels near exact resonance with an external microwave field, (a). Curves of the effective quantum inductance in the ground and excited states versus the external magnetic flux (b). It is evident that during part of the period of the low-frequency oscillations of the reactive parameter of the qubit assumes negative values. Computed parameters , , .

Block diagram of the experimental investigations of the characteristics of a charge-phase qubit. The dashed lines enclose temperature regions of the dilution refrigerator and the elements located within them. The polarization charge on the island was produced from a voltage generator coupled with the charge gate of the system of cooled filters. The qubit is enclosed in a lead screen (not shown in the figure), which for microwave frequencies is a cylindrical resonator. The microwave generator excited, through a coaxial cable with large damping and a cooled attenuator, a resonator at the frequency . Excitation of the circuit at the frequency and detuning of the qubit with respect to the magnetic field were performed from rf and constant-current generators. The signal from the resonant circuit, coupled with the qubit by the mutual inductance , was amplified by a cooled amplifier and measured with a vector voltmeter. 1, 2, 3—powder (CuO) filter. 1) Voltage generator 2) Microwave generator, 3) rf generator, 4) Current generator 5) Vector voltmeter 6) Attenuator 7) rf amplifier

Block diagram of the experimental investigations of the characteristics of a charge-phase qubit. The dashed lines enclose temperature regions of the dilution refrigerator and the elements located within them. The polarization charge on the island was produced from a voltage generator coupled with the charge gate of the system of cooled filters. The qubit is enclosed in a lead screen (not shown in the figure), which for microwave frequencies is a cylindrical resonator. The microwave generator excited, through a coaxial cable with large damping and a cooled attenuator, a resonator at the frequency . Excitation of the circuit at the frequency and detuning of the qubit with respect to the magnetic field were performed from rf and constant-current generators. The signal from the resonant circuit, coupled with the qubit by the mutual inductance , was amplified by a cooled amplifier and measured with a vector voltmeter. 1, 2, 3—powder (CuO) filter. 1) Voltage generator 2) Microwave generator, 3) rf generator, 4) Current generator 5) Vector voltmeter 6) Attenuator 7) rf amplifier

Curves of the phase signal on the resonant circuit coupled with a charge-phase qubit versus the external magnetic flux near : 1—no filtering of the measuring channel; 2—with cooling to with a powder filter in the chain of the resonant circuit (a). Curves of the amplitude of the superconducting current circulating in the qubit, constructed on the basis of the characteristics (1) and (2), versus the external flux (b).

Curves of the phase signal on the resonant circuit coupled with a charge-phase qubit versus the external magnetic flux near : 1—no filtering of the measuring channel; 2—with cooling to with a powder filter in the chain of the resonant circuit (a). Curves of the amplitude of the superconducting current circulating in the qubit, constructed on the basis of the characteristics (1) and (2), versus the external flux (b).

Charge-phase qubit with in a microwave resonance field with frequency . Family of curves of the phase signal characteristics coupled with a qubit resonant circuit versus the external magnetic flux . The parameter of the family is the output power of the microwave generator.

Charge-phase qubit with in a microwave resonance field with frequency . Family of curves of the phase signal characteristics coupled with a qubit resonant circuit versus the external magnetic flux . The parameter of the family is the output power of the microwave generator.

Signal characteristics of the charge-phase qubit-detector in a microwave field with frequency at the constant power of the microwave generator . The phase signal in the resonant circuit for the values of the polarization charge and as a function of the external magnetic flux (a). The dependence of the change of the voltage on the resonant circuit and versus the magnetic flux. The family was obtained with the minimum detuning of the generator frequency from the resonance frequency of the circuit and (b). 1) , rad 2) , arb. units

Signal characteristics of the charge-phase qubit-detector in a microwave field with frequency at the constant power of the microwave generator . The phase signal in the resonant circuit for the values of the polarization charge and as a function of the external magnetic flux (a). The dependence of the change of the voltage on the resonant circuit and versus the magnetic flux. The family was obtained with the minimum detuning of the generator frequency from the resonance frequency of the circuit and (b). 1) , rad 2) , arb. units

Phase difference (a) and amplitude difference (b) for the signal characteristics of qubit-detector which are shown in Fig. 6.

Phase difference (a) and amplitude difference (b) for the signal characteristics of qubit-detector which are shown in Fig. 6.

Family of phase signal characteristics charge-phase qubit in a microwave field with frequency with variation of the gate charge by in a neighborhood of (a, b) and (c, d). The input power for all characteristics.

Family of phase signal characteristics charge-phase qubit in a microwave field with frequency with variation of the gate charge by in a neighborhood of (a, b) and (c, d). The input power for all characteristics.

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