A conventional optomechanical system is composed of a mechanical mode and anoptical mode interacting through a linear optomechanical coupling (LOC). Westudy how the presence of quadratic optomechanical coupling (QOC) in theconventional optomechanical system affects the system's stability and opticalquadrature squeezing. We work in the resolved side-band limit with a highquality factor mechanical oscillator. In contrast to the conventionaloptomechanical systems, we find that strong squeezing of the cavity field canbe achieved in presence of QOC along with LOC at lower pump powers and athigher bath temperatures. Using detailed numerical calculations we also findthat there exists an optimal QOC where one can achieve maximum squeezing.
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