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International Journal of Modern Physics B

Quantum disentangling operator and squeezed vacuum state’s noise of a mesoscopic two-loop LC circuit with mutual inductance

Hong-Yi Fan, Xiang‐Guo Meng

Published May 10, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0217979220501210

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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.
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.
Since the birth of quantum mechanics, its classical correspondence (or analogy) has been a hot topic for physicists. In this paper, we first discuss whether there is a classical correspondence of quantum entanglement. We give a positive answer through the following examples: in the framework of quantization of mesoscopic circuits, two mesoscopic capacitance inductance (LC) circuits with mutual inductance are proved to be the source of quantum entanglement by using the integration within an ordered product, and then the formula of their characteristic frequency is obtained, It is found that it is similar to the expression of the small oscillating frequency of a classical system described below. The classical system is shown in Fig. 1 . Two walls are connected with the same spring. And between the two springs a sliding trolley can move on a smooth table. The trolley is hung with a simple pendulum, The small oscillating frequency of the system is calculated by analytical mechanics. It is found that the swing of the simple pendulum will cause the trolley to oscillate back and forth. The mutual restraint effect of the pendulum, the trolley and the spring reflects the “entanglement” between them.