The evolution and two-mode squeezed states of the time-dependent two coupled harmonic oscillators

A closed solution of the Schrodinger equation for a time-dependent two coupled harmonic oscillators including a driving part and a two-mode coupled part is derived by adopting the Lewis-Riesenfeld invariant theory and properly chosen Hermitian invariant operators. The evolution operator of the system and the condition for generating two-mode squeezed states are obtained. It is shown that the quantum fluctuation of squeezed states of the system is independent of the driving part, but depends on the initial states of the system.