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Register a new userCavity mode dephasing via the optomechanical interaction with an acoustic environment
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We consider an optomechanical system comprising a single cavity mode and a dense spectrum of acoustic modes and solve for the quantum dynamics of initial cavity mode Fock (i.e., photon number) superposition states and thermal acoustic states. The optomechanical interaction results in dephasing without damping and bears some analogy to gravitational decoherence. For a cavity mode locally coupled to a one-dimensional (1D) elastic string-like environment or two-dimensional (2D) elastic membrane-like environment, we find that the dephasing dynamics depends respectively on the string length and membrane area--a consequence of an infrared divergence in the limit of an infinite-sized string or membrane. On the other hand, for a cavity mode locally coupled to a three-dimensional (3D) bulk elastic solid, the dephasing dynamics is independent of the solid volume (i.e., is infrared finite), but dependent on the local geometry of the coupled cavity--a consequence of an ultraviolet divergence in the limit of a pointlike coupled cavity. We consider as possible respective realizations for the cavity-coupled-1D and 2D acoustic environments, an LC oscillator capacitively coupled to a partially metallized strip and a cavity light mode interacting via light pressure with a membrane.
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We study the cavity mode frequencies of a Fabry-Perot cavity containing two vibrating dielectric membranes. We derive the equations for the mode resonances and provide approximate analytical solutions for them as a function of the membrane positions, which act as an excellent approximation when the relative and center-of-mass position of the two membranes are much smaller than the cavity length. With these analytical solutions, one finds that extremely large optomechanical coupling of the membrane relative motion can be achieved in the limit of highly reflective membranes when the two membranes are placed very close to a resonance of the inner cavity formed by them. We also study the cavity finesse of the system and verify that, under the conditions of large coupling, it is not appreciably affected by the presence of the two membranes. The achievable large values of the ratio between the optomechanical coupling and the cavity decay rate, $g/kappa$, make this two-membrane system the simplest promising platform for implementing cavity optomechanics in the strong coupling regime.
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