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Chinese Journal of Quantum Electronics

Quantum effects in inductance coupled mesoscopic circuit at excited coherent states

Cai Shao-Hong, Jinping Kang, Zhang Yuqiang

Published Jan 1, 2011• 0 citations
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Abstract

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.

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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 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.
Starting from Kirchhoff's equation for each mesoscopic coupled circuit, we investigated the quantum fluctuations of a dissipative mesoscopic capacitance–resistance–inductance coupled circuit using canonical transformation and unitary transformation. It is shown that the quantum fluctuations of charges and currents are not only related to the parameters of components in the self-circuit and coupled part, but also influenced by the parameters of other circuit. The uncertainty relations of the charges and currents are analyzed briefly.
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.
Using the quantum theory for a mesoscopic circuit based on the discretenes of electric charges, the finite-difference Schrödinger equation of the non-dissipative mesoscopic inductance and capacity coupling circuit is achieved. The Coulomb blockade effect, which is caused by the discreteness of electric charges, is studied. Appropriately choose the components in the circuits, the finite-difference Schrödinger equation can be divided into two Mathieu equations in representation. With the WKBJ method, the currents quantum fluctuations in the ground states of the two circuits are calculated. The results show that the currents quantum zero-point fluctuations of the two circuits are exist and correlated.