Generation of two mode mechanical squeezing induced by nondegenerate parametric amplification

Squeezing light in an optomechanical system involves reducing quantum noise in one of the light's quadratures through the interaction between optical and mechanical modes. However, achieving successful implementation requires careful control of experimental parameters, which can be challenging. Here, we investigate a two-mode squeezed light transfer from optical to mechanical modes induced by a non-degenerate optical parametric amplifier (OPA). The optomechanical system is driven by frequencies nearly resonant with the anti-stokes fields that can realize cooling mechanical oscillators and quantum state transfer within a resolved sideband (good cavity) limit. Our results show that when a non-degenerate OPA is placed inside the optical cavity, the degree of squeezing in both optical and mechanical modes is significantly enhanced. This leads to the two-mode squeezed light being transferred into two-mode mechanical squeezing in the presence of the non-degenerate OPA under weak optomechanical coupling strength. Interestingly, we found that with negligible thermal bath noise, the two-mode squeezed light completely transferred to yield 50% mirror-mirror squeezing. In contrast, at higher thermal noise, the transfer of squeezed light is weak, causing the system to lose its quantum properties and behave more classically. Furthermore, we have shown that the degree of squeezing in the weak coupling regime drastically decreases with increasing mechanical dissipation rates. We believe that our scheme can achieve strong mechanical squeezing in hybrid optomechanical systems and facilitate homodyne detection to measure the quadratures of the squeezed light.