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Register a new userMultiple membrane cavity optomechanics
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Added by
Mishkatul Bhattacharya
Publication date
2008
fields
Physics
and research's language is
English
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We investigate theoretically the extension of cavity optomechanics to multiple membrane systems. We describe such a system in terms of the coupling of the collective normal modes of the membrane array to the light fields. We show these modes can be optically addressed individually and be cooled, trapped and characterized, e.g. via quantum nondemolition measurements. Analogies between this system and a linear chain of trapped ions or dipolar molecules imply the possibility of related applications in the quantum regime.
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We present the results of theoretical and experimental studies of dispersively coupled (or membrane in the middle) optomechanical systems. We calculate the linear optical properties of a high finesse cavity containing a thin dielectric membrane. We focus on the cavitys transmission, reflection, and finesse as a function of the membranes position along the cavity axis and as a function of its optical loss. We compare these calculations with measurements and find excellent agreement in cavities with empty-cavity finesses in the range 10^4 to 10^5. The imaginary part of the membranes index of refraction is found to be approximately 10^(-4). We calculate the laser cooling performance of this system, with a particular focus on the less-intuitive regime in which photons tunnel through the membrane on a time scale comparable to the membranes period of oscillation. Lastly, we present calculations of quantum non-demolition measurements of the membranes phonon number in the low signal-to-noise regime where the phonon lifetime is comparable to the QND readout time.
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 study the classical dynamics of a membrane inside a cavity in the situation where this optomechanical system possesses a reflection symmetry. Symmetry breaking occurs through supercritical and subcritical pitchfork bifurcations of the static fixed point solutions. Both bifurcations can be observed through variation of the laser-cavity detuning, which gives rise to a boomerang-like fixed point pattern with hysteresis. The symmetry-breaking fixed points evolve into self-sustained oscillations when the laser intensity is increased. In addition to the analysis of the accompanying Hopf bifurcations we describe these oscillations at finite amplitudes with an ansatz that fully accounts for the frequency shift relative to the natural membrane frequency. We complete our study by following the route to chaos for the membrane dynamics.
The promise of innovative applications has triggered the development of many modern technologies capable of exploiting quantum effects. But in addition to future applications, such quantum technologies have already provided us with the possibility of accessing quantum-mechanical scenarios that seemed unreachable just a few decades ago. With this spirit, in this work we show that modern optomechanical setups are mature enough to implement one of the most elusive models in the field of open system dynamics: degenerate parametric oscillation. The possibility of implementing it in nonlinear optical resonators was the main motivation for introducing such model in the eighties, which rapidly became a paradigm for the study of dissipative phase transitions whose corresponding spontaneously broken symmetry is discrete. However, it was found that the intrinsic multimode nature of optical cavities makes it impossible to experimentally study the model all the way through its phase transition. In contrast, here we show that this long-awaited model can be implemented in the motion of a mechanical object dispersively coupled to the light contained in a cavity, when the latter is properly driven with multi-chromatic laser light. We focus on membranes as the mechanical element, showing that the main signatures of the degenerate parametric oscillation model can be studied in state-of-the-art setups, thus opening the possibility of studying spontaneous symmetry breaking and enhanced metrology in one of the cleanest dissipative phase transitions.
We present a new micromechanical resonator designed for cavity optomechanics. We have used a micropillar geometry to obtain a high-frequency mechanical resonance with a low effective mass and a very high quality factor. We have coated a 60-$mu$m diameter low-loss dielectric mirror on top of the pillar and are planning to use this micromirror as part of a high-finesse Fabry-Perot cavity, to laser cool the resonator down to its quantum ground state and to monitor its quantum position fluctuations by quantum-limited optical interferometry.
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