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While quantum mechanics imposes a fundamental limit on the precision ofinterferometric measurements of mechanical motion due to measurementbackaction, the nonlinear nature of the coupling also leads to parametricinstabilities that place practical limits on the sensitivity by limiting thepower in the interferometer. Such instabilities have been extensively studiedin the context of gravitational wave detectors, and their presence has recentlybeen reported in Advanced LIGO. Here, we observe experimentally and describetheoretically a new type of optomechanical instability that arises in two-tonebackaction-evading (BAE) measurements, designed to overcome the standardquantum limit, and demonstrate the effect in the optical domain with a photoniccrystal nanobeam, and in the microwave domain with a micromechanical oscillatorcoupled to a microwave resonator. In contrast to the well-known oscillatoryparametric instability that occurs in single-tone, blue-detuned pumping, whichis characterized by a vanishing effective mechanical damping, the parametricinstability in balanced two-tone optomechanics is exponential, and is a resultof small detuning errors in the two pump frequencies. Its origin can beunderstood in a rotating frame as the vanishing of the effective mechanicalfrequency due to an optical spring effect. Counterintuitively, the instabilityoccurs even in the presence of perfectly balanced intracavity fields, and canoccur for both signs of detuning. We find excellent quantitative agreement withour theoretical predictions. Since the constraints on tuning accuracy becomestricter with increasing probe power, it imposes a fundamental limitation onBAE measurements, as well as other two-tone schemes. In addition to introducinga new limitation in two-tone BAE measurements, the results also introduce a newtype of nonlinear dynamics in cavity optomechanics.

Two-Tone Optomechanical Instability and Its Fundamental Implications for Backaction-Evading Measurements