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Journal of Ningxia University

Quantum effects in inductance-capacitance coupled mesoscopic circuit under excited coherent states

Hua Chen

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

The quantum effects of inductance capacitance coupled circuit under excited coherent states are investigated by quantizing nondissipative mesoscopic circuit. The results show that the mean value and mean square value of charge and current in each circuit are all not zero,the quantum fluctuations in the two circuits are correlated each othr,and the fluctuations are determined by coherent states,particle number states parameter and the circuit parameter.

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Starting from the classical movement equation of a non-dissipative inductance coupled mesoscopic circuit,the circuit is quantized by using linear transformation method,and the quantum fluctuations of currents and charges at excited coherent states are calculated.The results show that the average and square average of current and charge of each loop are not zero without power,i.e.,there exist quantum fluctuations. And the fluctuations are not only determined by the loop parameters,but also related to another loop's parameters and coupled inductance parameters.The quantum fluctuations in two circuits are relevant,and obviously depend on the state parameters of circuits,i.e.,parameters of particle count states and coherent states.
The quantum effect of mesoscopic inductance-capacitance coupled circuit with mutual inductance was investigated by canonical transformation and unitary transformation. The mesoscopic inductance-capacitance coupled circuit was compared with several coupling circuits. It is found that it is convenient to control the quantum fluctuations and squeezed effect by adjusting mutual inductance coupling coefficient in mutual inductance circuit with coupling capacitance. Uncertainty relations of charges and conjugate currents are related to canonical transformation parameter φ and uncertainty relations parameter ξ. When ξ→1 or φ→nπ/2, (n = 0,1,2,…), the uncertainty relations approach minimum value h/2.
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.
The quantum fluctuations of charges and currents of mesoscopic capacitance coupled circuit with mutual inductance and power source were investigated by using canonical transformation and unitary transformation. The results show that the quantum fluctuations of charges and currents are independent of power source. When the components of the circuit are given, if the value of L_1/L_2 is very small or very large, the effect of coupling coefficient on quantum fluctuations of charges and currents are great. From no mutual inductance to having mutual inductance, the quantum fluctuation of charge of loop 2 and the quantum fluctuation of current of loop 1 are obvious. We can conclude that it play a very important role whether the mutual inductance exists or not.
The effects of the difference of circuit parameters or capacitances and inductances on the quantum fluctuations in the non-resonant damped mesoscopic coupled electric circuits were studied. In the calculations, the physical mechanism of the generation of the resistance or the interaction between electrons and phonons was considered. The difference of the circuit parameters in the two component circuits makes the quantum fluctuations in one component circuit smaller and that in the other larger. The results also show that both capacitance coupling and inductance coupling will cause the quantum fluctuations of the electric charge in the coupling part squeezed. But there is no squeezing for the electric current in the coupling part.