One- and two-mode combination squeezing operator for two harmonic oscillators with coordinate-momentum coupling

By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordinate- 1/2mi + momentum coupling. It turns out that this squeezing operator just diagonalizes the Hamiltonian H = p(1)(2)/2m(1) + m(1)omega(2)(1)x(1)(2)/2 +p(2)(2)/2m(2) + m(2)omega(2)(2)x(2)(2) - lambda x(2)p(1) so its ground state is a one- and two-mode combination squeezed state. Quantum fluctuation in the ground state is calculated.