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Journal of Yanbian University

Quantum fluctuation of a mesoscopic inductance-resistance coupled circuit with power source in squeezed vacuum state

Shou Zhang

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

We investigated the quantum fluctuations of charge and current in mesoscopic inductance-resistance coupled circuit with power source in squeezed vacuum state. The results revealed that the quantum fluctuations of mesoscopic circuit are not related to power source. Furthermore the influence of the squeezed parameter y and the squeezed angle θ on the quantum fluctuations is very important.

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We investigated the quantum fluctuations of charge and current in mesoscopic inductance-resistance coupled circuit with power source in squeezed vacuum state. The results revealed that the quantum fluctuations of mesoscopic circuit are not related to power source. Furthermore the influence of the squeezed parameter y and the squeezed angle θ on the quantum fluctuations is very important.
Starting from the classical motion equation of a non\|dissipative mesoscopic inductance coupled circuit with source, it investigates the fluctuations of the charge and current in the mesoscopic inductance coupled circuit at the squeezed vacuum state, and study especially the influences of the squeezed angle on the fluctuations. The results indicate if the system is in the squeezing vacuum state, the quantum fluctuations of both circuits are related reciprocally but the fluctuations are independent with the source.Also,the squeezed effect of the charge and current is depended on the squeezing parameter γ and the squeezing angle θ as well. Moreover, the fluctuation of the charge and current does not monotonously decrease in an arbitrary squeezed angle θ , instead of has a minimum. [
The quantum fluctuations of the charge and current in a non-dissipative mesoscopic circuit with coupled inductors and capacitors are studied for the squeezed vacuum state. The influence of the phase angle upon the quantum fluctuations is discussed in particular. Our results indicate that when the circuit parameters remain constant and the phases θ of the two circuits are equal, the squeezing of the charge or its conjugate variable increases. When the difference of the two phases equals π, the squeezing will deteriorate. Therefore, if we want to decrease the quantum noise, we should not only control the amplitude r , but also control the phase θ carefully.
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.
We study the quantum fluctuations of the charge and current of two L-C dissipative mesoscopic circuit with the mutual inductance in the vacuum state. Our results show that the system state will evolve to a squeezed coherent state under the effect of external source. We find that the squeezing amplitude parameter is relative to the parameters of circuit and the mutual-inductance coefficient in the existence of dissipation. When the circuit has no dissipation or there is complete coupling between two meshes, the squeezing amplitude parameter only depends on the capacitance's ratio.