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Backaction-evading measurements of mechanical motion can achieve precisionbelow the zero-point uncertainty and quantum squeezing, which makes them aresource for quantum metrology and quantum information processing. We providean exact expression for the conditional state of an optomechanical system in atwo-tone backaction-evading measurement beyond the standard adiabaticapproximation and perform extensive numerical simulations to go beyond theusual rotating-wave approximation. We predict the simultaneous presence ofconditional mechanical squeezing, intra-cavity squeezing, and optomechanicalentanglement. We further apply an analogous analysis to the multimodeoptomechanical system of two mechanical and one cavity mode and findconditional mechanical Einstein-Podolski-Rosen entanglement and genuinelytripartite optomechanical entanglement. Our analysis is of direct relevance forstate-of-the-art optomechanical experiments that have entered thebackaction-dominated regime.

Conditional dynamics of optomechanical two-tone backaction-evading measurements