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Communications in Theoretical Physics

Quantum Effects of a Dissipative Mesoscopic Circuit with Mutual Inductance

Yinghua Ji, Yi-you Nie, Le Jian-Xin, Lei Min-Sheng

Published Mar 15, 2002• 3 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/37/3/346

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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.
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.
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 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 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.