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Chinese Journal of Quantum Electronics

Quantum effects in a mesoscopic nonlinear electronic circuit

Xiao Kai-xuan

Published Jan 1, 2005• 0 citations
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Abstract

Considering the bidirection diode in a mesoscopic circuit, we studied the quantum effect of the nonlinear circuit. The results indicate that the quantum Kerr state will been prepared in the nonlinear electronic circuit and the time evolution of the quantum squeezing effects appear periodically in the circuit according to the nonlinear device.

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Communications in Theoretical Physics•Nov 15, 2002•3 citations
Considering the bidirection diode in a mesoscopic circuit, we studied the quantum effect of the nonlinear circuit. The results indicate that the quantum Kerr state will been prepared in the nonlinear electronic circuit and the time evolution of the quantum squeezing effects appear periodically in the circuit according to the nonlinear device.
The mesoscopic nonlinear inductance-capacitance circuit is a typical anharmonic oscillator, due to diodes included in the circuit. In this paper, using the advanced quantum theory of mesoscopic circuits, which based on the fundamental fact that the electric charge takes discrete value, the diode included mesoscopic circuit is firstly studied. Schrödinger equation of the system is a four-order difference equation in representation. Using the extended perturbative method, the detail energy spectrum and wave functions are obtained and verified, as an application of the results, the current quantum fluctuation in the ground state is calculated. Diode is a basis component in a circuit, its quantization would popularize the quantum theory of mesoscopic circuits. The methods to solve the high order difference equation are helpful to the application of mesoscopic quantum theory.
Using the path integral method we derive quantum wave function and quantum fluctuations of charge and current in the mesoscopic RLC circuit. We find that the quantum fluctuation of charge decreases with time, oppositely, the quantum fluctuation of current increases with time monotonously. Therefore there is a squeezing effect in the circuit. If some more charge devices are used in the mesoscopic-damped circuit, the quantum noise can be reduced. We also find that uncertainty relation of charge and current periodically varies with the period π/2 in the under-damped case.