We investigate the behaviour of two non-linearly coupled flexural modes of adoubly-clamped suspended beam (nanomechanical resonator). One of the modes isexternally driven. We demonstrate that classically, the behavior of thenon-driven mode is reminiscent of that of a parametrically driven linearoscillator: It exhibits a threshold behavior, with the amplitude of this modebelow the threshold being exactly zero. Quantum-mechanically, we were able toaccess the dynamics of this mode below the classical parametric threshold. Weshow that whereas the mean displacement of this mode is still zero, the meansquared displacement is finite and at the threshold corresponds to theoccupation number of 1/2. This finite displacement of the non-driven mode canserve as an experimentally verifiable quantum signature of quantum motion.
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