We describe a new experimental approach to probabilistic atom-photon (signal) entanglement. Two qubit states are encoded as orthogonal collective spin excitations of an unpolarized atomic ensemble. After a programmable delay, the atomic excitation is converted into a photon (idler). Polarization states of both the signal and the idler are recorded and are found to be in violation of the Bell inequality. Atomic coherence times exceeding several microseconds are achieved by switching off all the trapping fields -including the quadrupole magnetic field of the magneto-optical trap -and zeroing out the residual ambient magnetic field.PACS numbers: 03.65. Ud,03.67.Mn,42.50.Dv Long-distance quantum cryptographic key distribution (QCKD) is an important goal of quantum information science. Extending the reach of quantum cryptography ideally involves the ability to entangle two distant qubits (two level quantum systems) [1,2], using the Bell inequality violation to verify the security of the quantum communication channel. Parametric down conversion is an established technology producing entangled photon pairs. Unfortunately, it is not directly applicable to longdistance QCKD, as the rate scales exponentially with the distance due to probabilistic nature of entangled photon pairs generation. It is necessary to provide a controllable delay between the two photons, that is, to have a means of photon storage. The latter requirement is problematical as photons are difficult to store for an appreciable period of time. By contrast atomic qubits are long lived and easily manipulated by laser fields, they are well suited for long term quantum information storage. Photonic qubits, however, can propagate for relatively long distances in fibers without absorption, making them excellent carriers of quantum information. Entangled systems of a single photon and a long-lived atomic qubit therefore offer an excellent building block for a quantum network.A quantum repeater architecture can overcome the limitations of photons by inserting a quantum memory qubit into the quantum channel every attenuation length or so [2]. The idea is to generate entanglement between two neighboring atomic qubits, which can be done efficiently since light will not be appreciably absorbed within the segment length. After entanglement between each pair of atomic qubits has been established, a joint measurement on each neighboring pair of qubits is performed. The quantum states of all the intermediate qubits are destroyed by the measurement, achieving entanglement swapping such that only the two atomic qubits at the two ends are entangled. These two qubits can be used for QCKD, either with the Ekert protocol, that directly uses the entangled pair of qubits, or the BB84 protocol that performs either remote state preparation or teleportation of a qubit [3,4,5,6,7,8]. The rate of QCKD using a quantum repeater protocol can scale polynomially with distance [2].In the microwave domain, single Rydberg atoms and single photons have been entangled [9]. An entangled st...

We consider the radiative trapping and cooling of a partially transmitting mirror suspended inside an optical cavity, generalizing the case of a perfectly reflecting mirror previously considered [M. Bhattacharya and P. Meystre, Phys. Rev. Lett. 99, 073601 (2007)]. This configuration was recently used in an experiment to cool a nanometers-thick membrane [Thompson et al., arXiv:0707.1724v2, 2007. The self-consistent cavity field modes of this system depend strongly on the position of the middle mirror, leading to important qualitative differences in the radiation pressure effects: in one case, the situation is similar that of a perfectly reflecting middle mirror, with only minor quantitative modifications. In addition, we also identify a range of mirror positions for which the radiation-mirror coupling becomes purely dispersive and the back-action effects that usually lead to cooling are absent, although the mirror can still be optically trapped. The existence of these two regimes leads us to propose a bichromatic scheme that optimizes the cooling and trapping of partially transmissive mirrors.

We propose a technique aimed at cooling a harmonically oscillating mirror to its quantum mechanical ground state starting from room temperature. Our method, which involves the two-sided irradiation of the vibrating mirror inside an optical cavity, combines several advantages over the two-mirror arrangements being used currently. For comparable parameters the three-mirror configuration provides a stiffer trap for the oscillating mirror. Furthermore it prevents bistability from limiting the use of higher laser powers for mirror trapping, and also partially does so for mirror cooling. Lastly, it improves the isolation of the mirror from classical noise so that its dynamics are perturbed mostly by the vacuum fluctuations of the optical fields. These improvements are expected to bring the task of achieving ground state occupation for the mirror closer to completion.PACS numbers: 42.50. Pq, 42.65.Sf, 85.85.+j, 04.80.Nn The observation of quantum dynamics in truly macroscopic objects is a challenging task that, although not yet achieved, has begun to look more and more feasible [1,2,3,4,5] as a result of recent experimental advances that include novel cooling techniques, progress in nanofabrication, and the improved control of decoherence. This is an exciting prospect, as it would enable us to explore the quantum-classical boundary [6] as well as to test quantum mechanics in an entirely new regime [7]. The implementation of characteristically quantum mechanical phenomena such as entanglement and superposition at a macroscopic scale [8] has broad implications, for instance in the impending merger of quantum optics with condensed matter physics [9]. It also signals direct technological benefits for areas like quantum measurement [10] and communication [11]. Additional potential applications include the interferometric detection of gravitational waves [12] and atomic force microscopy [13].A promising route to these objectives seems to be through the use of optomechanical systems, particularly of mirror cavities coupled to laser radiation [14,15,16]. Experimentally two-mirror cavities have been used, with one mirror held fixed and another mounted on a spring of frequency Ω M and damped at a rate Γ M [ Fig.1(a)]. It has been demonstrated that radiation pressure in the cavity can change these quantities to new values Ω eff and Γ eff [17]. To bring the mirror to its quantum mechanical ground state starting from temperature T the number of quanta [17] have to be reduced to < 1. Here k B and are Boltzmann's and Planck's constants. Most progress so far has been achieved by using the technique of cold damping where the thermal Brownian motion heating up the oscillator is countered by the effect of laser radiation, which increases the mirror damping while introducing very little noise [18]. As a result the ratio Γ M /Γ eff can be decreased to about 10 −4 either passively or by using active feedback cooling. This yields n ∼ 10 4 for typical parameters even if the base temperature is cryogenically reduced to T ∼ 4K [19]. We menti...

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.Comment: 4 pages, 2 figure