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Chinese Journal of Quantum Electronics

Quantization of mesoscopic mutual inductance coupling circuit with superconducting Josephson junctions and their quantum effects

Yanling Li

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The quantization scheme of the mesoscopic mutual inductance circuit with super- conducting Josephson junctions is given.By means of squeezing unitary transformation,the energy level and the ground state vector of the system are obtained.Then,the quantum fluctuations of excess charges and phase difference between the sides of Josephson junction in the ground state are investigated.It is found that the ground state of the system is a rotated two single-mode squeezed vacuum state.

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The quantization scheme of the mesoscopic mutual inductance circuit with super- conducting Josephson junctions is given.By means of squeezing unitary transformation,the energy level and the ground state vector of the system are obtained.Then,the quantum fluctuations of excess charges and phase difference between the sides of Josephson junction in the ground state are investigated.It is found that the ground state of the system is a rotated two single-mode squeezed vacuum state.
The Hamiltonian of the mesoscopic inductance coupling circuits with mutual induc- tance was given by Langrangian function,then it was diagonilized through a unitary operator. The normal ordering form of the unitary operator was obtained by the technique of integration within an ordered product(IWOP),and the quantum fluctuations of charge and its conjugate quantity of this system were discussed.It was found that a rotated two single-mode squeezed vacuum state could be generated by using the system.
A mesoscopic double resonance circuit with mutual inductance and capacitance-inductance coupling was quantized using canonical quantization method.The Hamiltonian of the system was diagonalized by unitary transformation to obtain the eigenenergy spectra of the circuit.The quantum fluctuations of the charge and current in the two loops of the circuit were studied under squeezed vacuum excitation state,squeezed vacuum state and vacuum state,respectively.The results show that quantum fluctuations are dependent not only on circuit parameters,quantum number of excitation,squeezed coefficients and squeezed angle,but also on mutual inductance coefficient,capacitance and inductance.
Mesoscopic double resonance mutual inductance and capacitance coupling circuit is quantized by the method of harmonic oscillator quantization linear transformation.The energy spectra of this circuit are given.The quantum fluctuations of the charge and current of each loop are researched by the method of thermo-field dynamics(TFD) in thermal excited state,thermal squeezed vacuum state,thermal vacuum state and vacuum state.It is show that,the quantum fluctuations of the charge and current are related to not only circuit inherent parameter and coupled magnitude,but also quantum number of excitation,squeezed coefficients,squeezed angle,environmental temperature.And,the quantum fluctuations increase with the increase of temperature.
In order to research quantum effect of a mesoscopic parallel circuit with mutual inductance coupled and damped, we adopt the method of damped harmonic oscillator quantization to quantize the circuit. By using unitary transform, the Hamiltonian of the system is diagonalized. Then we can get the energy levels of the circuit. Our results show that one such circuit can be equivalent to double module coupling harmonic oscillator, the quantum fluctuations of the electrical current and voltage not only relate to the parameters and mutual inductance coupling intensity of the circuit, but also to the quantum states of the circuit. And when the coupling intensity is colse to zero, the quantum fluctuations only relate to the inherence frequency of the circuit. Then we can control the quantum noises of the circuit by adjusting the parameters.