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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...

We theoretically investigate selective coupling of superconducting charge qubits mediated by a superconducting stripline cavity with a tunable resonance frequency. The frequency control is provided by a flux biased dc-SQUID attached to the cavity. Selective entanglement of the qubit states is achieved by sweeping the cavity frequency through the qubit-cavity resonances. The circuit is able to accommodate several qubits and allows to keep the qubits at their optimal points with respect to decoherence during the whole operation. We derive an effective quantum Hamiltonian for the basic, two-qubit-cavity system, and analyze appropriate circuit parameters. We present a protocol for performing Bell inequality measurements, and discuss a composite pulse sequence generating a universal control-phase gate.Coherent coupling of superconducting qubits has been experimentally demonstrated for all major qubit types (charge 1,2 , flux 3,4,5 , and phase 6,7 qubits) using permanent direct qubit-qubit coupling, capacitive or inductive. A major challenge is to implement a tunable coupling of qubits required for any useful gate operation. Numerous suggestions in this direction have been discussed in recent literature together with related quantum gate protocols (for a review see, e.g. Ref. 8).There are two conceptually different approaches to the tunable coupling. The first approach is to employ direct coupling schemes using Josephson junctions in the non-resonant regime as passive controllable elements, either capacitive, 9 or inductive. 10,11,12,13,14 The second approach, which we adopt in this paper, suggests qubit coupling via a dynamic intermediate element, e.g., LCoscillator or Josephson junction, which becomes entangled with a qubit during a two-qubit operation. In this scheme, the entanglement is achieved by tuning the qubit and the mediator in resonance, and then transferring the entanglement to another qubit by tuning the mediator and the second qubit in the resonance. Such coupling method has been first suggested 15 and experimentally tested 16 for the ion trap qubits. For superconducting qubits, qubit-oscillator entanglement has been demonstrated experimentally for a charge qubit coupled to a microwave stripline cavity, 17 and a flux qubit coupled to a SQUID oscillator;18,19 the gate protocols based on controllable qubit-oscillator coupling have been theoretically discussed in Refs. 20,21.The experimental setup with the qubit coupling to a distributed oscillator -stripline cavity 17,22 possesses potential for scalability -several qubits can be coupled to the cavity. In this paper we investigate the possibility to use this setup for implementation of tunable qubit-qubit coupling and simple gate operations. Tunable qubitcavity coupling is achieved by varying the cavity frequency by controlling magnetic flux through a dc-SQUID attached to the cavity (see Fig. 1). An advantage of this method is the possibility to keep the qubits at the optimal points with respect to decoherence during the whole two-qubit operation. The qubi...