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K. Hammerer, K. Stannigel, C. Genes, P. Zoller, P. Treutlein, S. Camerer, D. Hunger, T. W. Hänsch Optical Lattices with Micromechanical Mirrors,
Phys. Rev. A 82 021803(R) (2010-08-25),
http://dx.doi.org/10.1103/PhysRevA.82.021803 doi:10.1103/PhysRevA.82.021803 (ID: 717187)
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We investigate a setup where a cloud of atoms is trapped in an optical lattice potential of a standing-wave laser field which is created by retroreflection on a micromembrane. The membrane vibrations itself realize a quantum mechanical degree of freedom. We show that the center-of-mass mode of atoms can be coupled to the vibrational mode of the membrane in free space. Via laser cooling of atoms a significant sympathetic cooling effect on the membrane vibrations can be achieved. Switching off laser cooling brings the system close to a regime of strong coherent coupling. This setup provides a controllable segregation between the cooling and coherent dynamics regimes, and allows one to keep the membrane in a cryogenic environment and atoms at a distance in a vacuum chamber.
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S. Nimmrichter, K. Hammerer, P. Asenbaum, H. Ritsch, M. Arndt Master Equation for the Motion of a Polarizable Particle in a Multimode Cavity,
New J. Phys. 12 083003 (2010-08-03),
http://dx.doi.org/10.1088/1367-2630/12/8/083003 doi:10.1088/1367-2630/12/8/083003 (ID: 717185)
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We derive a master equation for the motion of a polarizable particle weakly interacting with one or several strongly pumped cavity modes. We focus here on massive particles with a complex internal structure, such as large molecules and clusters, for which we assume a linear scalar polarizability mediating the particle–light interaction. The predicted friction and diffusion coefficients are in good agreement with former semiclassical calculations for atoms and small molecules in weakly pumped cavities, while the current rigorous quantum treatment and numerical assessment sheds light on the feasibility of experiments that aim to optically manipulate beams of massive molecules with multimode cavities.
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M. Ludwig, K. Hammerer, F. Marquardt Entanglement of mechanical oscillators coupled to a nonequilibrium environment,
Phys. Rev. A 82 012333 (2010-07-29),
http://dx.doi.org/10.1103/PhysRevA.82.012333 doi:10.1103/PhysRevA.82.012333 (ID: 716971)
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Recent experiments aim at cooling nanomechanical resonators to the ground state by coupling them to nonequilibrium environments in order to observe quantum effects such as entanglement. This raises the general question of how such environments affect entanglement. Here we show that there is an optimal dissipation strength for which the entanglement between two coupled oscillators is maximized. Our results are established with the help of a general framework of exact quantum Langevin equations valid for arbitrary bath spectra, in and out of equilibrium. We point out why the commonly employed Lindblad approach fails to give even a qualitatively correct picture.
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M. Aspelmeyer, S. Gröblacher, K. Hammerer, N. Kiesel Quantum optomechanics—throwing a glance,
JOSA B 27 197 (2010-05-28),
http://dx.doi.org/10.1364/JOSAB.27.00A189 doi:10.1364/JOSAB.27.00A189 (ID: 717340)
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B. Zhao, K. Hammerer, M. Müller, P. Zoller Efficient quantum repeater based on deterministic Rydberg gates,
Phys. Rev. A 81 052329 (2010-05-21),
http://dx.doi.org/10.1103/PhysRevA.81.052329 doi:10.1103/PhysRevA.81.052329 (ID: 717186)
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We propose an efficient quantum repeater architecture with mesoscopic atomic ensembles, where the Rydberg blockade is employed for deterministic local entanglement generation, entanglement swapping, and entanglement purification. Compared to a conventional atomic-ensemble-based quantum repeater, the entanglement distribution rate is improved by up to two orders of magnitude with the help of the deterministic Rydberg gate. This quantum repeater scheme is robust and fast, and thus opens up a way for practical long-distance quantum communication.
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A. Glätzle, K. Hammerer, A. J. Daley, R. Blatt, P. Zoller A single trapped atom in front of an oscillating mirror,
Opt. Com. 283 765 (2010-03-15),
http://dx.doi.org/10.1016/j.optcom.2009.10.063 doi:10.1016/j.optcom.2009.10.063 (ID: 717009)
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We investigate the Wigner–Weisskopf decay of a two-level atom in front of an oscillating mirror. This work builds on and extends previous theoretical and experimental studies of the effects of a static mirror on spontaneous decay and resonance fluorescence. The spontaneously emitted field is inherently non-stationary due to the time-dependent boundary conditions and in order to study its spectral distribution we employ the operational definition of the spectrum of non-stationary light due to the seminal work by Eberly and Wódkiewicz. We find a rich dependence of this spectrum as well as of the effective decay rates and level shifts on the mirror–atom distance and on the amplitude and frequency of the mirror’s oscillations. The results presented here provide the basis for future studies of more complex setups, where the motion of the atom and/or the mirror are included as quantum degrees of freedom.
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K. Hammerer, A. Sorensen, E. Polzik Quantum interface between light and atomic ensembles,
Rev. Mod. Phys. 82 1093 (2010-03-05),
http://dx.doi.org/10.1103/RevModPhys.82.1041 doi:10.1103/RevModPhys.82.1041 (ID: 637865)
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During the past decade the interaction of light with multiatom ensembles has attracted much attention as a basic building block for quantum information processing and quantum state engineering. The field started with the realization that optically thick free space ensembles can be efficiently interfaced with quantum optical fields. By now the atomic ensemble-light interfaces have become a powerful alternative to the cavity-enhanced interaction of light with single atoms. Various mechanisms used for the quantum interface are discussed, including quantum nondemolition or Faraday interaction, quantum measurement and feedback, Raman interaction, photon echo, and electromagnetically induced transparency. This review provides a common theoretical frame for these processes, describes basic experimental techniques and media used for quantum interfaces, and reviews several key experiments on quantum memory for light, quantum entanglement between atomic ensembles and light, and quantum teleportation with atomic ensembles. The two types of quantum measurements which are most important for the interface are discussed: homodyne detection and photon counting. This review concludes with an outlook on the future of atomic ensembles as an enabling technology in quantum information processing.
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M. Wallquist, K. Hammerer, P. Zoller, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, J. Ye, H. Kimble Single-atom cavity QED and optomicromechanics,
Phys. Rev. A 81 023816 (2010-02-18),
http://dx.doi.org/10.1103/PhysRevA.81.023816 doi:10.1103/PhysRevA.81.023816 (ID: 716968)
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In a recent publication [K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, and H. J. Kimble, Phys. Rev. Lett. 103, 063005 (2009)] we have shown the possibility to achieve strong coupling of the quantized motion of a micron-sized mechanical system to the motion of a single trapped atom. In the proposed setup the coherent coupling between a SiN membrane and a single atom is mediated by the field of a high finesse cavity and can be much larger than the relevant decoherence rates. This makes the well-developed tools of cavity quantum electrodynamics with single atoms available in the realm of cavity optomechanics. In this article we elaborate on this scheme and provide detailed derivations and technical comments. Moreover, we give numerical as well as analytical results for a number of possible applications for transfer of squeezed or Fock states from atom to membrane as well as entanglement generation, taking full account of dissipation. In the limit of strong-coupling the preparation and verification of nonclassical states of a mesoscopic mechanical system is within reach.
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P. Zoller, M. Wallquist, K. Hammerer, P. Rabl, M. Lukin Hybrid quantum devices and quantum engineering,
Physica Scripta 014001 (2009-12-14),
http://dx.doi.org/10.1088/0031-8949/2009/T137/014001 doi:10.1088/0031-8949/2009/T137/014001 (ID: 716806)
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We discuss prospects of building hybrid quantum devices involving elements of atomic and molecular physics, quantum optics and solid-state elements with the attempt to combine advantages of the respective systems in compatible experimental setups. In particular, we summarize our recent work on quantum hybrid devices and briefly discuss recent ideas for quantum networks. These include interfacing of molecular quantum memory with circuit QED, and using nanomechanical elements strongly coupled to qubits represented by electronic spins, as well as single atoms or atomic ensembles.
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P. Rabl, C. Genes, K. Hammerer, M. Aspelmeyer Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems,
DFG - Physik, Math. u. Geowissen. 80 063819 (2009-12-09),
http://dx.doi.org/10.1103/PhysRevA.80.063819 doi:10.1103/PhysRevA.80.063819 (ID: 666215)
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We present a detailed theoretical discussion of the effects of ubiquitous laser noise on cooling and the coherent dynamics in optomechanical systems. Phase fluctuations of the driving laser induce modulations of the linearized optomechanical coupling as well as a fluctuating force on the mirror due to variations of the mean cavity intensity. We first evaluate the influence of both effects on cavity cooling and find that for a small laser linewidth, the dominant heating mechanism arises from intensity fluctuations. The resulting limit on the final occupation number scales linearly with the cavity intensity both under weak- and strong-coupling conditions. For the strong-coupling regime, we also determine the effect of phase noise on the coherent transfer of single excitations between the cavity and the mechanical resonator and obtain a similar conclusion. Our results show that conditions for optical ground-state cooling and coherent operations are experimentally feasible and thus laser phase noise does pose a challenge but not a stringent limitation for optomechanical systems.
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K. Hammerer, M. Wallquist, C. Genes, M. Ludwig, F. Marquardt, P. Treutlein, P. Zoller, J. Ye, H. J. Kimble Strong coupling of a mechanical oscillator and a single atom,
Phys. Rev. Lett. 103 063005 (2009-08-06),
http://dx.doi.org/10.1103/PhysRevLett.103.063005 doi:10.1103/PhysRevLett.103.063005 (ID: 680115)
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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 micro- and nanomechanical oscillators via the tools of atomic physics.
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S. Gröblacher, K. Hammerer, M. Vanner, M. Aspelmeyer Observation of strong coupling between a micromechanical resonator and an optical cavity field,
Nature 460 727 (2009-08-06),
http://dx.doi.org/10.1038/nature08171 doi:10.1038/nature08171 (ID: 669662)
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Current experiments aim to achieve coherent quantum control over massive mechanical resonators. The existing approaches exploit a variety of coupling mechanisms of nano- and micromechanical devices to, for example, single electrons via electrostatic or magnetic coupling and to photons via radiation pressure or optical dipole forces. To date, all such experiments have been operating in a regime of weak coupling, in which reversible energy exchange between the mechanics and its coupled partner is suppressed by fast decoherence of the individual systems to their local environments. Controlled quantum experiments are in principle not possible in such a regime but instead require strong coupling, which has until now only been demonstrated between a variety of microscopic quantum systems such as atoms and photons in the context of cavity quantum electrodynamics (cQED), or between solid state qubits and photons. Strong coupling is an essential requirement for the preparation of mechanical quantum states such as squeezed or entangled states and also for utilizing mechanical resonators in the context of quantum information processing, e.g. as quantum transducers. Here we report the observation of optomechanical normal mode splitting, which is unambiguous evidence for strong coupling of cavity photons to a mechanical resonator. By directly measuring optomechanical correlations we also provide a qualitative analysis of the coupling interaction and show that entering the strong coupling regime is accompanied by a breakdown of the rotating-wave approximation. This paves the way towards full quantum optical control of nano- and micromechanical devices.
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K. Jähne, C. Genes, K. Hammerer, M. Wallquist, E. Polzik, P. Zoller Cavity-assisted squeezing of a mechanical oscillator,
Phys. Rev. A 79 063819 (2009-06-11),
http://dx.doi.org/10.1103/PhysRevA.79.063819 doi:10.1103/PhysRevA.79.063819 (ID: 679748)
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We investigate the creation of squeezed states of a vibrating membrane or a movable mirror in an opto-mechanical system. An optical cavity is driven by squeezed light and couples via radiation pressure to the membrane/mirror, effectively providing a squeezed heat-bath for the mechanical oscillator. Under the conditions of laser cooling to the ground state, we find an efficient transfer of squeezing with roughly 60% of light squeezing conveyed to the membrane/mirror (on a dB scale). We determine the requirements on the carrier frequency and the bandwidth of squeezed light. Beyond the conditions of ground state cooling, we predict mechanical squashing to be observable in current systems.
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K. Hammerer, M. Aspelmeyer, E. Polzik, P. Zoller Establishing Einstein-Poldosky-Rosen Channels between Nanomechanics and Atomic Ensembles,
Phys. Rev. Lett. 102 020501 (2009-01-12),
http://dx.doi.org/10.1103/PhysRevLett.102.020501 doi:10.1103/PhysRevLett.102.020501 (ID: 637866)
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We suggest interfacing nanomechanical systems via an optical quantum bus to atomic ensembles, for which means of high precision state preparation, manipulation, and measurement are available. This allows, in particular, for a quantum nondemolition Bell measurement, projecting the coupled system, atomic-ensemble–nanomechanical resonator, into an entangled EPR state. The entanglement is observable even for nanoresonators initially well above their ground states and can be utilized for teleportation of states from an atomic ensemble to the mechanical system.
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K. Hammerer, E. Polzik, J. I. Cirac High-fidelity teleportation between light and atoms,
Phys. Rev. A 74 064301 (2006-12-01),
http://dx.doi.org/10.1103/PhysRevA.74.064301 doi:10.1103/PhysRevA.74.064301 (ID: 433792)
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We show how high-fidelity quantum teleportation of light to atoms can be achieved in the same setup as was used in the recent experiment [J. Sherson et al., Nature 443, 557, 2006], where such an interspecies quantum state transfer was demonstrated for the first time. Our improved protocol takes advantage of the rich multimode entangled structure of the state of atoms and scattered light and requires simple postprocessing of homodyne detection signals and squeezed light in order to achieve fidelities up to 90% (85%) for teleportation of coherent (qubit) states under realistic experimental conditions. The remaining limitation is due to atomic decoherence and light losses.
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J. F. Sherson, H. Krauter, R. K. Olsson, B. Julsgaard, K. Hammerer, J. I. Cirac, E. Polzik Quantum teleportation between light and matter,
Nature 443 557 (2006-10-05),
http://dx.doi.org/10.1038/nature05136 doi:10.1038/nature05136 (ID: 433800)
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Quantum teleportation is an important ingredient in distributed quantum networks, and can also serve as an elementary operation in quantum computers. Teleportation was first demonstrated as a transfer of a quantum state of light onto another light beam; later developments used optical relays and demonstrated entanglement swapping for continuous variables. The teleportation of a quantum state between two single material particles (trapped ions) has now also been achieved. Here we demonstrate teleportation between objects of a different nature—light and matter, which respectively represent 'flying' and 'stationary' media. A quantum state encoded in a light pulse is teleported onto a macroscopic object (an atomic ensemble containing 10^12 caesium atoms). Deterministic teleportation is achieved for sets of coherent states with mean photon number (n) up to a few hundred. The fidelities are 0.58 plusminus 0.02 for n = 20 and 0.60 plusminus 0.02 for n = 5—higher than any classical state transfer can possibly achieve. Besides being of fundamental interest, teleportation using a macroscopic atomic ensemble is relevant for the practical implementation of a quantum repeater. An important factor for the implementation of quantum networks is the teleportation distance between transmitter and receiver; this is 0.5 metres in the present experiment. As our experiment uses propagating light to achieve the entanglement of light and atoms required for teleportation, the present approach should be scalable to longer distances.
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C. A. Muschik, K. Hammerer, E. Polzik, J. I. Cirac Efficient quantum memory and entanglement between light and an atomic ensemble using magnetic fields,
Phys. Rev. A 73 062329 (2006-06-21),
http://dx.doi.org/10.1103/PhysRevA.73.062329 doi:10.1103/PhysRevA.73.062329 (ID: 433791)
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We present two protocols, one for the storage of light in an atomic ensemble and the subsequent retrieval, and another one for the generation of entanglement between light and atoms. They rely on two passes of a single pulse through the ensemble, Larmor precessing in an external field. Both protocols work deterministically and the relevant figures of merit—such as the fidelity or the EPR variance—scale exponentially in the coupling strength. We solve the corresponding Maxwell-Bloch equations describing the scattering process and determine the resulting input-output relations which only involve one relevant light mode that, in turn, can be easily accessed experimentally.