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Strong dispersive coupling of a high finesse cavity to a micromechanical membrane

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 Added by Jack Harris
 Publication date 2007
  fields Physics
and research's language is English




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Macroscopic mechanical objects and electromagnetic degrees of freedom couple to each other via radiation pressure. Optomechanical systems with sufficiently strong coupling are predicted to exhibit quantum effects and are a topic of considerable interest. Devices reaching this regime would offer new types of control of the quantum state of both light and matter and would provide a new arena in which to explore the boundary between quantum and classical physics. Experiments to date have achieved sufficient optomechanical coupling to laser-cool mechanical devices but have not yet reached the quantum regime. The outstanding technical challenge in this field is integrating sensitive micromechanical elements (which must be small, light, and flexible) into high finesse cavities (which are typically much more rigid and massive) without compromising the mechanical or optical properties of either. A second, and more fundamental, challenge is to read out the mechanical elements quantum state: displacement measurements (no matter how sensitive) cannot determine the energy eigenstate of an oscillator, and measurements which couple to quantities other than displacement have been difficult to realize. Here we present a novel optomechanical system which seems to resolve both these challenges. We demonstrate a cavity which is detuned by the motion of a thin dielectric membrane placed between two macroscopic, rigid, high-finesse mirrors. This approach segregates optical and mechanical functionality to physically distinct structures and avoids compromising either. It also allows for direct measurement of the square of the membranes displacement, and thus in principle the membranes energy eigenstate. We estimate it should be practical to use this scheme to observe quantum jumps of a mechanical system.



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We study the quantum dynamics of the cavity optomechanical system formed by a Fabry-Perot cavity with a thin vibrating membrane at its center. We first derive the general multimode Hamiltonian describing the radiation pressure interaction between the cavity modes and the vibrational modes of the membrane. We then restrict the analysis to the standard case of a single cavity mode interacting with a single mechanical resonator and we determine to what extent optical absorption by the membrane hinder reaching a quantum regime for the cavity-membrane system. We show that membrane absorption does not pose serious limitations and that one can simultaneously achieve ground state cooling of a vibrational mode of the membrane and stationary optomechanical entanglement with state-of-the-art apparatuses.
We discuss a hybrid quantum system where a dielectric membrane situated inside an optical cavity is coupled to a distant atomic ensemble trapped in an optical lattice. The coupling is mediated by the exchange of sideband photons of the lattice laser, and is enhanced by the cavity finesse as well as the square root of the number of atoms. In addition to observing coherent dynamics between the two systems, one can also switch on a tailored dissipation by laser cooling the atoms, thereby allowing for sympathetic cooling of the membrane. The resulting cooling scheme does not require resolved sideband conditions for the cavity, which relaxes a constraint present in standard optomechanical cavity cooling. We present a quantum mechanical treatment of this modular open system which takes into account the dominant imperfections, and identify optimal operation points for both coherent dynamics and sympathetic cooling. In particular, we find that ground state cooling of a cryogenically pre-cooled membrane is possible for realistic parameters.
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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.
We present an experimental study of dynamical back-action cooling of the fundamental vibrational mode of a thin semitransparent membrane placed within a high-finesse optical cavity. We study how the radiation pressure interaction modifies the mechanical response of the vibrational mode, and the experimental results are in agreement with a Langevin equation description of the coupled dynamics. The experiments are carried out in the resolved sideband regime, and we have observed cooling by a factor 350 We have also observed the mechanical frequency shift associated with the quadratic term in the expansion of the cavity mode frequency versus the effective membrane position, which is typically negligible in other cavity optomechanical devices.
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