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Journal of Zhengzhou University

The Quantum Fluctuations of Mesoscopic Double Resonance Mutual Inductance and Capacitance Coupling Circuit in Squeezed Vacuum State

Xing-Lei Xu

Published Jan 1, 2006• 0 citations
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Abstract

Mesoscopic double resonance mutual inductance and capacitance coupling circuit is quantized by the method of harmonic oscillator quantization.Hamiltonian is diagonalized by unitary transformation.The energy spectra of this circuit are given.The quantum fluctuations of the charge and current of each loop in squeezed vacuum state are researched.

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Mesoscopic double resonance mutual inductance and capacitance coupling circuit is quantized by the method of harmonic oscillator quantization.Hamiltonian is diagonalized by unitary transformation.The energy spectra of this circuit are given.The quantum fluctuations of the charge and current of each loop in squeezed vacuum state are researched.
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.
Based on the scheme of damped harmonic oscillator quantization and thermo-field dynamics (TFD), the quantization of mesoscopic damped double resonance RLC circuit with mutual capacitance-inductance coupling is proposed. The quantum fluctuations of charge and current of each loop in a squeezed vacuum state are studied in the thermal excitation case. It is shown that the fluctuations not only depend on circuit inherent parameters, but also rely on excitation quantum number and squeezing parameter. Moreover, due to the finite environmental temperature and damped resistance, the fluctuations increase with the temperature rising, and decay with time.
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.