介观互感容感耦合双谐振电路的量子涨落

Quantum Fluctuations of Mesoscopic Double Resonance Circuit with Mutual Inductance and Capacitance-Inductance Coupling

用正则量子化方法将介观互感容感耦合双谐振电路量子化.通过幺正变换将系统的哈密顿量对角化,给出体系的本征能谱.研究了压缩真空态的激发态、压缩真空态和真空态下回路中电荷和电流的量子涨落.结果表明,介观互感容感耦合双谐振电路中存在电荷和电流量子涨落,这种量子涨落不仅与电路器件的参数、激发量子数、压缩因子和压缩角有关,还与互感系数、耦合电容和耦合电感有关.

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.