Quantization and squeezed state of two L-C circuits with mutual-inductance

It is pointed out that the quantum mechanical Hamiltonian of two L-C circuits with mutual-inductance is equivalent to a pair of harmonic oscillators with a kinetic coupling term. We then diagonalize the Hamiltonian. It is shown that instantaneously switching on the external sources may result in a two-mode squeezed state of the system, which actually arises from the effect of mutual-inductance. The quantum fluctuation for the case of l(1)c(1) = l(2)c(2) is analysed and it is found that the current fluctuation in the circuits increases with the increment of the mutual-inductance.