Phonon-mediated squeezing of the cavity field off-resonantly coupled with a coherently driven quantum dot

We theoretically propose a scheme for the quadrature squeezing of the cavity field via dissipative processes. The effects of the electron-phonon interaction (EPI) on the squeezing are investigated, where the cavity is off-resonantly coupled with a coherently driven quantum dot (QD) which is allowed to interact with an acoustic-phonon reservoir. Under certain conditions, the participation of the phonon induced by both the EPI and the off-resonant coupling of the cavity with the QD enables some dissipative processes to occur resonantly in the dressed-state basis of the QD. The cavity-mode photons emitted or absorbed during the phonon-mediated dissipative processes are correlated, thus leading to the squeezing of the cavity field. A squeezed vacuum reservoir for the cavity field is built up due to the EPI plus the off-resonant coupling between the cavity and the QD. The numerical results obtained with an effective polaron master equation derived using second-order perturbation theory indicate that, in low temperature limit, the degree of squeezing is maximal but the increasing temperature of the phonon reservoir could hinder the squeezing and degrade the degree of the squeezing of the cavity field. In addition, the presence of the photonic crystal could enhance the quadrature squeezing of the cavity field.