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Chinese Journal of Quantum Electronics

Quantization and quantum effects of mesoscopic inductance coupling circuits with mutual inductance

Xiang‐Guo Meng

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

The Hamiltonian of the mesoscopic inductance coupling circuits with mutual induc- tance was given by Langrangian function,then it was diagonilized through a unitary operator. The normal ordering form of the unitary operator was obtained by the technique of integration within an ordered product(IWOP),and the quantum fluctuations of charge and its conjugate quantity of this system were discussed.It was found that a rotated two single-mode squeezed vacuum state could be generated by using the system.

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The Hamiltonian of the mesoscopic inductance coupling circuits with mutual induc- tance was given by Langrangian function,then it was diagonilized through a unitary operator. The normal ordering form of the unitary operator was obtained by the technique of integration within an ordered product(IWOP),and the quantum fluctuations of charge and its conjugate quantity of this system were discussed.It was found that a rotated two single-mode squeezed vacuum state could be generated by using the system.
Employing a special unitary operator and the virtue of the technique of integration within an ordered product (IWOP), we research on the quantum effects for an inductance–capacitance coupling double L–C circuit. It is found that it is convenient to research on the mesoscopic circuit with such an operator. First, eliminating the coupling term of Hamiltonian becomes easier than other methods. Second, the system’s ground state can be easily generalized into a two-mode squeezed state. Thus, the quantum fluctuations of the circuit and the variances of current in each loop are calculated, the charge-current uncertainty relation is revealed. As a result, both the uncertainty relation and fluctuation of the current in each loop become larger when [Formula: see text] is larger or [Formula: see text] is smaller.
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 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.
Quantum disentanglement refers to the transformation of entangled quantum system into disentangled system via some physical processes. In this paper, we search for quantum disentangling operator for the mesoscopic two-loop [Formula: see text] circuit with mutual inductance [Formula: see text]. It is this mutual inductance that causes quantum entanglement. By virtue of the method of integration within ordered product (IWOP) of operators, we find the disentangling operator and deduce the energy level (characteristic frequency). The quantum noise expression of squeezed vacuum state is also derived based on which we see that the large number of quantum entanglement engendered by the mutual inductance is, the more quantum noise produces in the mesoscopic circuit.