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Quantum squeezing is an important resource in modern quantum technologies,such as quantum precision measurement and continuous-variable quantuminformation processing. The generation of squeezed states of mechanical modesis a significant task in cavity optomechanics. Motivated by recent interest inmultimode optomechanics, it becomes an interesting topic to create quadraturesqueezing in multiple mechanical resonators. However, in themultiple-degenerate-mechanical-mode optomechanical systems, the dark-modeeffect strongly suppresses the quantum effects in mechanical modes. Here westudy the generation of mechanical squeezing in a two-mechanical-modeoptomechanical system by breaking the dark-mode effect with thesynthetic-gauge-field method. We find that when the mechanical modes work at afinite temperature, the mechanical squeezing is weak or even disappeared due tothe dark-mode effect, while the strong mechanical squeezing can be generatedonce the dark-mode effect is broken. In particular, thethermal-phonon-occupation tolerance of the mechanical squeezing isapproximately three orders of magnitude larger than that without breaking thedark-mode effect. We also generalize this method to break the dark modes and tocreate the mechanical squeezing in a multiple-mechanical-mode optomechanicalsystem. Our results describe a general physical mechanism and pave the waytowards the generation of noise-resistant quantum resources.

Controllable generation of mechanical quadrature squeezing via dark-mode engineering in cavity optomechanics