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A multipartite quantum system is entangled when its state cannot be factorized into a product of states or a mixture of such products. Quantum information schemes that exploit this purely quantum mechanical feature have been devised initially for systems with two discrete quantum levels (i.e., qubits), and afterward, extended to continuous-variable (CV) systems characterized by observables with continuous spectra, such as the position and momentum of a particle, or the quadratures of an electromagnetic field. Optomechanical systems, such as a driven optical cavity with vibrating end-mirrors or a classical coherent field scattering sidebands off a freely suspended mirror, hold a promise of being candidates for CV quantum information processing applications. As in most other proposals, light is the information carrier; the difference lies in the choice of a micromirror as a quantum storage device. Desired quantum states can be encoded in acoustic modes. The optomechanical coupling, owing to which quantum state transfer between radiation and mirror is possible, is realized via the radiation pressure effect, which consists in momentum transfer between field and mirror during the scattering process.
The use of the vibrational modes of a micromirror as a quantum state encoder system is somehow unexpected because this is a macroscopic ensemble of atoms expected to behave rather classically. However, there are proposals that show that, in principle, the vibrational occupation number of even such a large collection of atoms in a solid can be reduced close to zero, which signifies a clear transition from the classical to the quantum regime. Remarkable progress has been made to experimentally cool the resonator by a few orders of magnitude to quite low occupation numbers. However, in order to approach the quantum limit, one needs to integrate small, light, and flexible micromechanical elements into high-finesse cavities (which are typically much more rigid and massive), which is technically challenging. Furthermore, the mechanical quality factor has to be quite high, but present microfabrication techniques yield a mechanical quality factor scaling down for smaller and smaller microresonators.
This chapter starts with developing a general framework for treating the dynamics of a driven optical cavity with a vibrating end-mirror system in which two cooling techniques have been recently demonstrated: (i) cold-damping quantum feedback, where the oscillator position is measured through a phase-sensitive detection of the cavity output and the resulting photocurrent is used for a real-time correction of the dynamics, and (ii) backaction or self-cooling, in which the off-resonant operation of the cavity results in a retarded back action on the mechanical system, and hence, in a âselfâ-modification of its dynamics. The two situations are illustrated in Fig. 24.1. Analytical results for the final phonon number are obtained for both schemes and their applicability within today's state-of-the-art laboratory setups is analyzed.
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