Strong Coupling of a Mechanical Oscillator and a Single Atom

Abstract

We propose and analyze a setup to achieve strong coupling between a single trapped atom and a mechanical oscillator. The interaction between the motion of the atom and the mechanical oscillator is mediated by a quantized light field in a laser driven high-finesse cavity. In particular, we show that high fidelity transfer of quantum states between the atom and the mechanical oscillator is in reach for existing or near future experimental parameters. Our setup provides the basic toolbox for coherent manipulation, preparation and measurement of microand nanomechanical oscillators via the tools of atomic physics.Recent experiments with micro-and nanomechanical oscillators coupled to the optical field in a cavity are approaching the regime where quantum effects dominate [1,2,3]. In light of this progress, the question arises to what extent the quantized motion of a mesoscopic mechanical system can be coherently coupled to a microscopic quantum object [4,5,6,7,8,9], the ultimate challenge being strong coupling to the motion of a single atom. For a direct mechanical coupling the interaction involves scale factors m/M ∼ 10 −7 − 10 −4 depending on the ratio of the mass of the atom m to the mass of the mechanical oscillator M [4]. It is therefore difficult to achieve a coherent coupling for exchange of a single vibrational quantum that is much larger than relevant dissipation rates.In this Letter we show, however, that strong coupling can be realized between a single trapped atom and an optomechanical oscillator. The coupling between the motion of a membrane [10] -representing the mechanical oscillatorand the atom is mediated by the quantized light field in a laser driven high-finesse cavity. Remarkably, in this setup a coherent coupling for single-atom and membrane exceeding the dissipative rates by a factor of ten is within reach for present or near future experimental parameters [11]. Entering the strong coupling regime provides a quantum interface allowing the coherent transfer of quantum states between the mechanical oscillator and atoms, opening the door to coherent manipulation, preparation and measurement of micromechanical objects via the well-developed tools of atomic physics.We propose and analyze a setup which combines the recent advances of micromechanics with membranes in optical cavities [10] and cavity QED with single trapped atoms [11] (see Fig. 1a). We consider a membrane placed in a laser driven high-finesse cavity representing the opto-mechanical system with radiation pressure coupling. In this setup the motion of the membrane manifests itself as a dynamic detuning of cavity modes. For a cavity mode driven by a detuned laser this translates into a variation of the intensity of the intracavity light field. In addition, we assume that this intracavity field provides an optical lattice as a trap for a single atom. Thus for the setup of Fig. 1a the motion of the membrane will be coupled via the dynamics of the optical trap to the motion of the atom, and vice versa. This coupling is strongly enhanced by the...

Entanglement of mechanical oscillators coupled to a nonequilibrium environment

“…As pointed out in this paper, the effects of tunable non-equilibrium environments promise rich physics to be explored in current experimental setups. The optomechanical setup investigated here is in fact just one of a rather large class of setups to which this work applies, and which also extends into the fields of electromechanics [5,6] and cold-atom physics [18]. We also note that completely different systems show similar entanglement production effects under non-equilibrium conditions, as has been explored in the case of coupled, driven qubits [20], atoms [21] and ions [22], or coupled double quantum dots [23].…”

“…The mechanical coupling k between the oscillators (here assumed as given) can itself be implemented via other, strongly driven fardetuned cavity modes [9,18]. Other possible setups include cold-atom or hybrid atom-membrane systems [18]. Elimination of the cavity degrees of freedom generates cavity noise spectra [16] .…”

“…Hereâ ± are the annihilation operators of the cavity modes, m = 1/ √ 2mΩ is the mechanical ground-state width, and g is the oscillator-cavity coupling rate that scales linearly with the laser amplitude (see [18,19] for a derivation of this type of coupling). The mechanical coupling k between the oscillators (here assumed as given) can itself be implemented via other, strongly driven fardetuned cavity modes [9,18]. Other possible setups include cold-atom or hybrid atom-membrane systems [18].…”

Quantum-measurement backaction from a Bose-Einstein condensate coupled to a mechanical oscillator

“…Here φ is the outcome of the F y measurement, P (φ) is the probability of that outcome, W φ is the Kraus operator corresponding to the effects of the measurement on the BEC's quantum state, and ρ sys is the complete system density matrix given in (13). Although Eq.…”

“…The robust and scalable infrastructure provided by micro-and nanoelectromechanical systems, coupled with the high-precision-measurement capability of quantum gases [5][6][7][8], makes them an attractive combination for sensitive force measurements, as well as for a quantitative study of dissipation and decoherence processes at the quantum-classical interface. As a result, there are ongoing experimental [9,10] and theoretical [11][12][13][14][15] efforts toward coupling mechanical systems to atomic ensembles.…”