Robust mechanical squeezing via interference-enabled Floquet engineering in optomechanical resonators

We propose an interference-assisted scheme to generate mechanical squeezing in the asymptotic Floquet steady state of an optomechanical resonator by combining coherent backscattering suppression with a periodically modulated drive. An auxiliary nanoparticle is introduced to engineer a tunable scattering pathway that destructively interferes with backscattering induced by intrinsic defects, thereby suppressing clockwise–counterclockwise mode mixing and restoring a traveling-wave-dominated intracavity field. Using a Floquet description of the periodic steady state, we show that modulation enhances squeezing primarily through the buildup of phase-sensitive anomalous correlations rather than improved cooling alone. We further develop a compact harmonic characterization of the periodic anomalous correlator, providing a frequency-domain diagnostic of the dominant Floquet harmonic component that carries the squeezing-related correlations. Finally, we demonstrate robustness against finite angular misalignment and thermal noise, underscoring interference-assisted mode control as a practical route to macroscopic continuous-variable quantum resources in optomechanical platforms.