Gaussian Light Modulation of Translational Squeezed Quantum Light Field

It is an important topic of the coupling between quantum and classical light fields. In this paper, a classical Gaussian light field  $${e}^{-\frac{{q}^{2}}{2{\tau }_{1}^{2}}-\frac{{p}^{2}}{2{\tau }_{2}^{2}}}$$  is used to modulate the translational squeezed quantum light field. By using the integral method in the ordered operator, we find that the translational squeezed quantum light field modulated by Gaussian light is still a translational squeezed light, and its quantum properties remain unchanged, but chaotic parameters and compression parameters are changed. We also derive the formula of the Wigner function depending on the modulation parameters. It can be concluded that the integral method in the ordered operator is an effective way to deal with the mixing of classical and quantum light fields.