Coupling ultracold atoms to mechanical oscillators

D. Hunger; S. Camerer; M. Korppi; A. Jöckel; T.W. Hänsch; P. Treutlein

doi:10.1016/j.crhy.2011.04.015

Coupling ultracold atoms to mechanical oscillators
[Coupler des atomes ultrafroids avec des oscillateurs mécaniques]

D. Hunger ^1,² ; S. Camerer ^1,² ; M. Korppi ^1,^2,³ ; A. Jöckel ^1,^2,³ ; T.W. Hänsch ^1,² ; P. Treutlein ^1,^2,³

¹ Ludwig-Maximilians-Universität München, Schellingstr. 4, 80799 München, Germany
² Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
³ Departement Physik, Universität Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

Comptes Rendus. Physique, Volume 12 (2011) no. 9-10, pp. 871-887.

Résumé
Abstract

Dans cet article, nous discutons et comparons différentes méthodes pour réaliser une interface entre des atomes ultrafroids et des oscillateurs micro- ou nanomécaniques. Nous analysons dʼabord le couplage mécanique direct dʼun atome isolé à un oscillateur mécanique, et montrons que la grande différence de masse entre les deux systèmes impose une limite à la constante de couplage réalisable dans ce cas. Nous discutons ensuite plusieurs stratégies prometteuses en vue dʼaugmenter ce couplage : un renforcement collectif par lʼutilisation dʼun grand nombre dʼatomes dans un réseau optique, lʼutilisation de cavités optiques de grande finesse, et un couplage aux états atomiques internes. Nous discutons dans cet article à la fois les propositions théoriques et les premières mises en oeuvre expérimentales.

In this article we discuss and compare different ways to engineer an interface between ultracold atoms and micro- and nanomechanical oscillators. We start by analyzing a direct mechanical coupling of a single atom or ion to a mechanical oscillator and show that the very different masses of the two systems place a limit on the achievable coupling constant in this scheme. We then discuss several promising strategies for enhancing the coupling: collective enhancement by using a large number of atoms in an optical lattice in free space, coupling schemes based on high-finesse optical cavities, and coupling to atomic internal states. Throughout the manuscript we discuss both theoretical proposals and first experimental implementations.

Reçu le : 2010-11-22
Accepté le : 2011-04-29
Publié le : 2011-08-02

DOI : 10.1016/j.crhy.2011.04.015

Keywords: Ultracold atoms, Micro- and nanomechanical oscillators, Hybrid quantum systems, Cavity optomechanics, Bose–Einstein condensate, Ultracold ions
Mot clés : Atomes ultrafroids, Oscillateurs micro- ou nanomécaniques, Systèmes hybrides quantiques, Cavité optomécanique, Condensat de Bose–Einstein, Ions ultrafroids

Affiliations des auteurs :

D. Hunger ^{1, 2} ; S. Camerer ^{1, 2} ; M. Korppi ^{1, 2, 3} ; A. Jöckel ^{1, 2, 3} ; T.W. Hänsch ^{1, 2} ; P. Treutlein ^{1, 2, 3}

@article{CRPHYS_2011__12_9-10_871_0,
     author = {D. Hunger and S. Camerer and M. Korppi and A. J\"ockel and T.W. H\"ansch and P. Treutlein},
     title = {Coupling ultracold atoms to mechanical oscillators},
     journal = {Comptes Rendus. Physique},
     pages = {871--887},
     publisher = {Elsevier},
     volume = {12},
     number = {9-10},
     year = {2011},
     doi = {10.1016/j.crhy.2011.04.015},
     language = {en},
}

TY  - JOUR
AU  - D. Hunger
AU  - S. Camerer
AU  - M. Korppi
AU  - A. Jöckel
AU  - T.W. Hänsch
AU  - P. Treutlein
TI  - Coupling ultracold atoms to mechanical oscillators
JO  - Comptes Rendus. Physique
PY  - 2011
SP  - 871
EP  - 887
VL  - 12
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crhy.2011.04.015
LA  - en
ID  - CRPHYS_2011__12_9-10_871_0
ER  -

%0 Journal Article
%A D. Hunger
%A S. Camerer
%A M. Korppi
%A A. Jöckel
%A T.W. Hänsch
%A P. Treutlein
%T Coupling ultracold atoms to mechanical oscillators
%J Comptes Rendus. Physique
%D 2011
%P 871-887
%V 12
%N 9-10
%I Elsevier
%R 10.1016/j.crhy.2011.04.015
%G en
%F CRPHYS_2011__12_9-10_871_0

D. Hunger; S. Camerer; M. Korppi; A. Jöckel; T.W. Hänsch; P. Treutlein. Coupling ultracold atoms to mechanical oscillators. Comptes Rendus. Physique, Volume 12 (2011) no. 9-10, pp. 871-887. doi : 10.1016/j.crhy.2011.04.015. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2011.04.015/

Bibliographie
Cité par

[1] S.S. Verbridge; H.G. Craighead; J.M. Parpia A megahertz nanomechanical resonator with a room temperature quality factor over a million, Appl. Phys. Lett., Volume 92 (2008), p. 013112

[2] B.M. Zwickl; W.E. Shanks; A.M. Jayich; C. Yang; A.C.B. Jayich; J.D. Thompson; J.G.E. Harris High quality mechanical and optical properties of commercial silicon nitride membranes, Appl. Phys. Lett., Volume 92 (2008), p. 103125

[3] D.J. Wilson; C.A. Regal; S.B. Papp; H.J. Kimble Cavity optomechanics with stoichiometric SiN films, Phys. Rev. Lett., Volume 103 (2009), p. 207204

[4] K.C. Schwab; M.L. Roukes Putting mechanics into quantum mechanics, Phys. Today, Volume 58 (2005), p. 36

[5] T.J. Kippenberg; K. Vahala Cavity optomechanics: Back-action at the mesoscale, Science, Volume 321 (2008), p. 1172

[6] F. Marquardt; S.M. Girvin Optomechanics, Physics, Volume 2 (2009), p. 40

[7] I. Favero; K. Karrai Optomechanics of deformable optical cavities, Nature Photon., Volume 3 (2009), p. 201

[8] J.D. Teufel; Dale Li; M.S. Allman; K. Cicak; A.J. Sirois; J.D. Whittaker; R.W. Simmonds Circuit cavity electromechanics in the strong-coupling regime, Nature, Volume 471 (2011), pp. 204-208

[9] O. Arcizet; P.-F. Cohadon; T. Briant; M. Pinard; A. Heidmann Radiation-pressure cooling and optomechanical instability of a micro-mirror, Nature, Volume 444 (2006), p. 71

[10] B. Abbott; et al.; LIGO Scientific Collaboration Observation of a kilogram-scale oscillator near its quantum ground state, New J. Phys., Volume 11 (2009), p. 073032

[11] T. Rocheleau; T. Ndukum; C. Macklin; J.B. Hertzberg; A.A. Clerk; K.C. Schwab Preparation and detection of a mechanical resonator near the ground state of motion, Nature, Volume 463 (2009), p. 72

[12] J.B. Hertzberg; T. Rocheleau; T. Tdukum; M. Savva; A. Clerk; K.C. Schwab Back-action-evading measurements of nanomechanical motion, Nat. Phys., Volume 6 (2009), p. 213

[13] A. Schliesser; O. Arcizet; R. Riviére; G. Anetsberger; T.J. Kippenberg Resolved-sideband cooling and position measurement of a micromechanical oscillator close to the Heisenberg uncertainty limit, Nat. Phys., Volume 5 (2009), p. 509

[14] S. Gröblacher; J.B. Hertzberg; M.R. Vanner; G.D. Cole; S. Gigan; K.C. Schwab; M. Aspelmeyer Demonstration of an ultracold micro-optomechanical oscillator in a cryogenic cavity, Nat. Phys., Volume 5 (2009), p. 485

[15] J.D. Teufel; T. Donner; M.A. Castellanos-Beltran; J.W. Harlow; K.W. Lehnert Nanomechanical motion measured with an imprecision below that at the standard quantum limit, Nature Nanotech., Volume 4 (2009), p. 820

[16] C. Höhberger Metzger; K. Karrai Cavity cooling of a microlever, Nature, Volume 432 (2004), p. 1002

[17] J.D. Teufel; J.W. Harlow; C.A. Regal; K.W. Lehnert Dynamical backaction of microwave fields on a nanomechanical resonator, Phys. Rev. Lett., Volume 101 (2008), p. 197203

[18] A.D. OʼConnell; M. Hofheinz; M. Ansmann; R.C. Bialczak; M. Lenander; E. Lucero; M. Neeley; D. Sank; H. Wang; M. Weides; J. Wenner; J.M. Martinis; A.N. Cleland Quantum ground state and single-phonon control of a mechanical resonator, Nature, Volume 464 (2010), p. 697

[19] J.D. Teufel; T. Donner; Dale Li; J.H. Harlow; M.S. Allman; K. Cicak; A.J. Sirois; J.D. Whittaker; K.W. Lehnert; R.W. Simmonds Sideband cooling micromechanical motion to the quantum ground state, 2011 (preprint) | arXiv

[20] K.L. Ekinci; M.L. Roukes Nanoelectromechanical systems, Rev. Sci. Instrum., Volume 76 (2005), p. 061101

[21] C.M. Caves Quantum-mechanical noise in an interferometer, Phys. Rev. D, Volume 23 (1981), p. 1693

[22] C.L. Degen; M. Poggio; H.J. Mamin; C.T. Rettner; D. Rugar Nanoscale magnetic resonance imaging, PNAS, Volume 106 (2009), pp. 1313-1317

[23] G.G. Ghirardi; A. Rimini; T. Weber Unified dynamics for microscopic and macroscopic systems, Phys. Rev. D, Volume 34 (1986), p. 470

[24] R. Penrose Mathematical Physics 2000, International Conference on Mathematical Physics, Imperial College Press, London, 2000

[25] P. Rabl; S.J. Kolkowitz; F.H.L. Koppens; J.G.E. Harris; P. Zoller; M.D. Lukin A quantum spin transducer based on nanoelectromechanical resonator arrays, Nat. Phys., Volume 6 (2010), pp. 602-608

[26] S. Gröblacher; K. Hammerer; M.R. Vanner; M. Aspelmeyer Observation of strong coupling between a micromechanical resonator and an optical cavity field, Nature, Volume 460 (2009), p. 724

[27] C. Fabre; M. Pinard; S. Bourzeix; A. Heidmann; E. Giacobino; S. Reynaud Quantum-noise reduction using a cavity with a movable mirror, Phys. Rev. A, Volume 49 (1994), p. 1337

[28] K. Jähne; C. Genes; K. Hammerer; M. Wallquist; E.S. Polzik; P. Zoller Cavity-assisted squeezing of a mechanical oscillator, Phys. Rev. A, Volume 79 (2009), p. 063819

[29] D.E. Chang; C.A. Regal; S.B. Papp; D.J. Wilson; J. Ye; O. Painter; H.J. Kimble; P. Zoller Cavity opto-mechanics using an optically levitated nanosphere, PNAS, Volume 107 (2010)

[30] M. Pinard; A. Dantan; O. Arcizet; T. Briant; A. Heidmann Entangling movable mirrors in a double-cavity system, Europhys. Lett., Volume 72 (2005), p. 747

[31] D. Vitali; S. Gigan; A. Ferreira; H.R. Böhm; P. Tombesi; A. Guerreiro; V. Vredal; A. Zeilinger; M. Aspelmeyer Optomechanical entanglement between a movable mirror and a cavity field, Phys. Rev. Lett., Volume 98 (2007), p. 030405

[32] S. Mancini; V.I. Manʼko; P. Tombesi Ponderomotive control of quantum macroscopic coherence, Phys. Rev. A, Volume 55 (1997), p. 3042

[33] J.D. Thompson; B.M. Zwickl; A.M. Jayich; F. Marquardt; S.M. Girvin; J.G.E. Harris Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane, Nature, Volume 452 (2008), pp. 72-75

[34] A.M. Jayich; J.C. Sankey; B.M. Zwickl; C. Yang; J.D. Thompson; S.M. Girvin; A.A. Clerk; F. Marquardt; J.G.E. Harris Dispersive optomechanics: a membrane inside a cavity, New J. Phys., Volume 10 (2008), p. 095008

[35] S. Bose; K. Jacobs; P.L. Knight Scheme to probe the decoherence of a macroscopic object, Phys. Rev. A, Volume 59 (1999), p. 3204

[36] W. Marshall; C. Simon; R. Penrose; D. Bouwmeester Towards quantum superpositions of a mechanical resonator, Phys. Rev. Lett., Volume 91 (2003), p. 130401

[37] O. Romero-Isart; M.L. Juan; R. Quidant; J.I. Cirac Toward quantum superposition of living organisms, New J. Phys., Volume 12 (2010), pp. 1-16

[38] O. Romero-Isart; A.C. Pflanzer; M.L. Juan; R. Quidant; N. Kiesel; M. Aspelmeyer; J.I. Cirac Optically levitating dielectrics in the quantum regime: Theory and protocols, 2010 (preprint) | arXiv

[39] U. Akram; N. Kiesel; M. Aspelmeyer; G.J. Milburn Single-photon opto-mechanics in the strong coupling regime, New J. Phys., Volume 12 (2010), p. 083030

[40] A.D. Armour; M.P. Blencowe; K.C. Schwab Entanglement and decoherence of a micromechanical resonator via coupling to a cooper-pair box, Phys. Rev. Lett., Volume 88 (2002), p. 148301

[41] I. Bargatin; M.L. Roukes Nanomechanical analog of a laser: Amplification of mechanical oscillations by stimulated Zeeman transitions, Phys. Rev. Lett., Volume 91 (2003), p. 138302

[42] A.N. Cleland; M.R. Geller Superconducting qubit storage and entanglement with nanomechanical resonators, Phys. Rev. Lett., Volume 93 (2004)

[43] D. Rugar; R. Budakian; H.J. Mamin; B.W. Chui Single spin detection by magnetic resonance force microscopy, Nature, Volume 430 (2004), p. 329

[44] L. Tian Entanglement from a nanomechanical resonator weakly coupled to a single cooper-pair box, Phys. Rev. B, Volume 72 (2005), p. 195411

[45] P. Rabl; P. Cappellaro; M.V. Gurudev Dutt; L. Jiang; J.R. Maze; M.D. Lukin Strong magnetic coupling between an electronic spin qubit and a mechanical resonator, Phys. Rev. B, Volume 79 (2009), p. 041302(R)

[46] M.D. LaHaye; J. Suh; P.M. Echternach; K.C. Schwab; M.L. Roukes Nanomechanical measurements of a superconducting qubit, Nature, Volume 459 (2009), p. 960

[47] S. Chu Cold atoms and quantum control, Nature, Volume 416 (2002), p. 206

[48] D.M. Harber; H.J. Lewandowski; J.M. McGuirk; E.A. Cornell Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas, Phys. Rev. A, Volume 66 (2002), p. 053616

[49] P. Treutlein; P. Hommelhoff; T. Steinmetz; T.W. Hänsch; J. Reichel Coherence in microchip traps, Phys. Rev. Lett., Volume 92 (2004), p. 203005

[50] C. Langer; R. Ozeri; J.D. Jost; J. Chiaverini; B. DeMarco; A. Ben-Kish; R.B. Blakestad; J. Britton; D.B. Hume; W.M. Itano; D. Leibfried; R. Reichle; T. Rosenband; T. Schaetz; P.O. Schmidt; D.J. Wineland Long-lived qubit memory using atomic ions, Phys. Rev. Lett., Volume 95 (2005), p. 060502

[51] C. Deutsch; F. Ramirez-Martinez; C. Lacroûte; F. Reinhard; T. Schneider; J.N. Fuchs; F. Piéchon; F. Laloë; J. Reichel; P. Rosenbusch Spin self-rephasing and very long coherence times in a trapped atomic ensemble, Phys. Rev. Lett., Volume 105 (2010), p. 020401

[52] I. Bloch Ultracold quantum gases in optical lattices, Nat. Phys., Volume 1 (2005), p. 23

[53] S. Hofferberth; I. Lesanovsky; B. Fischer; J. Verdú; J. Schmiedmayer Radiofrequency-dressed-state potentials for neutral atoms, Nat. Phys., Volume 2 (2006), p. 710

[54] P. Böhi; M. Riedel; J. Hoffrogge; J. Reichel; T.W. Hänsch; P. Treutlein Coherent manipulation of Bose–Einstein condensates with state-dependent microwave potentials on an atom chip, Nat. Phys., Volume 5 (2009), p. 592

[55] S. Gupta; K.L. Moore; K.W. Murch; D.M. Stamper-Kurn Cavity nonlinear optics at low photon numbers from collective atomic motion, Phys. Rev. Lett., Volume 99 (2007), p. 213601

[56] F. Brennecke; S. Ritter; T. Donner; T. Esslinger Cavity optomechanics with a Bose–Einstein condensate, Science, Volume 322 (2008), p. 235

[57] K.W. Murch; K. Moore; S. Gupta; D.M. Stamper-Kurn Observation of quantum-measurement backaction with an ultracold atomic gas, Nat. Phys., Volume 4 (2008), p. 561

[58] T.P. Purdy; D.W.C. Brooks; T. Botter; N. Brahms; Z.-Y. Ma; D.M. Stamper-Kurn Tunable cavity optomechanics with ultracold atoms, Phys. Rev. Lett., Volume 105 (2010), p. 133602

[59] N. Brahms; D.M. Stamper-Kurn Spin optodynamics analog of cavity optomechanics, Phys. Rev. A, Volume 82 (2010), p. 041804

[60] R. Kanamoto; P. Meystre Optomechanics of ultracold atomic gases, Physica Scripta, Volume 82 (2010), p. 038111

[61] C. Gross; T. Zibold; E. Nicklas; J. Estève; M.K. Oberthaler Nonlinear atom interferometer surpasses classical precision limit, Nature, Volume 464 (2010), p. 1165

[62] M.F. Riedel; P. Böhi; Y. Li; T.W. Hänsch; A. Sinatra; P. Treutlein Atom-chip-based generation of entanglement for quantum metrology, Nature, Volume 464 (2010), pp. 1170-1173

[63] D.J. Wineland; C. Monroe; W.M. Itano; D. Leibfried; B.E. King; D.M. Meekhof Experimental issues in coherent quantum-state manipulation of trapped atomic ions, J. Res. Natl. Inst. Stand. Technol., Volume 103 (1998), p. 259

[64] W.K. Hensinger; D.W. Utami; H.-S. Goan; K. Schwab; C. Monroe; G.J. Milburn Ion trap transducers for quantum electromechanical oscillators, Phys. Rev. A, Volume 72 (2005), p. 041405(R)

[65] S. Singh; M. Bhattacharya; O. Dutta; P. Meystre Coupling nanomechanical cantilevers to dipolar molecules, Phys. Rev. Lett., Volume 101 (2008), p. 263603

[66] M. Bhattacharya; S. Singh; P.-L. Giscard; P. Meystre Optomechanical control of atoms and molecules, Laser Physics, Volume 20 (2010), p. 57

[67] D. Hunger; S. Camerer; T.W. Hänsch; D. König; J.P. Kotthaus; J. Reichel; P. Treutlein Resonant coupling of a Bose–Einstein condensate to a micromechanical oscillator, Phys. Rev. Lett., Volume 104 (2010), p. 143002

[68] L. Tian; P. Zoller Coupled ion–nanomechanical systems, Phys. Rev. Lett., Volume 93 (2004), p. 266403

[69] V. Peano; M. Thorwart; A. Kasper; R. Egger Nanoscale atomic waveguides with suspended carbon nanotubes, Appl. Phys. B, Volume 81 (2005), p. 1075

[70] K. Hammerer; K. Stannigel; C. Genes; M. Wallquist; P. Zoller; P. Treutlein; S. Camerer; D. Hunger; T.W. Hänsch Optical lattices with micromechanical mirrors, Phys. Rev. A, Volume 82 (2010), p. 021803(R)

[71] D. Meiser; P. Meystre Coupled dynamics of atoms and radiation-pressure-driven interferometers, Phys. Rev. A, Volume 73 (2006), p. 033417

[72] A.B. Bhattacherjee Cavity quantum optomechanics of ultracold atoms in an optical lattice: Normal-mode splitting, Phys. Rev. A, Volume 80 (2009), p. 043607

[73] 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., Volume 103 (2009), p. 063005

[74] M. Wallquist; K. Hammerer; P. Zoller; C. Genes; M. Ludwig; F. Marquardt; P. Treutlein; J. Ye; H.J. Kimble Single-atom cavity QED and opto-micromechanics, Phys. Rev. A, Volume 81 (2010), p. 023816

[75] K. Zhang; W. Chen; M. Bhattacharya; P. Meystre Hamiltonian chaos in a coupled BEC-optomechanical-cavity system, Phys. Rev. A, Volume 81 (2010), p. 013802

[76] M. Paternostro; G. De Chiara; G.M. Palma Cold-atom-induced control of an optomechanical device, Phys. Rev. Lett., Volume 104 (2010), p. 243602

[77] G. De Chiara; M. Paternostro; G.M. Palma Entanglement detection in hybrid optomechanical systems, Phys. Rev. A, Volume 83 (2011), p. 052324

[78] C. Genes; D. Vitali; P. Tombesi Emergence of atom-light-mirror entanglement inside an optical cavity, Phys. Rev. A, Volume 77 (2008), p. 050307

[79] H. Ian; Z.R. Gong; Y. Liu; C.P. Sun; F. Nori Cavity optomechanical coupling assisted by an atomic gas, Phys. Rev. A, Volume 78 (2008), p. 013824

[80] Y. Chang; T. Shi; Y. Liu; C.P. Sun; F. Nori Multi-stability of electromagnetically induced transparency in atom-assisted optomechanical cavities, 2009 (preprint) | arXiv

[81] P. Treutlein; D. Hunger; S. Camerer; T.W. Hänsch; J. Reichel Bose–Einstein condensate coupled to a nanomechanical resonator on an atom chip, Phys. Rev. Lett., Volume 99 (2007), p. 140403

[82] S. Singh; P. Meystre Atomic probe Wigner tomography of a nanomechanical system, Phys. Rev. A, Volume 81 (2010), p. 041804(R)

[83] C. Joshi; A.H.F. Zimmer; M. Johnson; E. Andersson; P. Öhberg Quantum entanglement of nanocantilevers, Phys. Rev. A, Volume 82 (2010), p. 043846

[84] A.A. Geraci; J. Kitching Ultracold mechanical resonators coupled to atoms in an optical lattice, Phys. Rev. A, Volume 80 (2009), p. 032317

[85] Y.-J. Wang; M. Eardley; S. Knappe; J. Moreland; L. Hollberg; J. Kitching Magnetic resonance in an atomic vapor excited by a mechanical resonator, Phys. Rev. Lett., Volume 97 (2006), p. 227602

[86] K. Hammerer; M. Aspelmeyer; E.S. Polzik; P. Zoller Establishing Einstein–Podolsky–Rosen channels between nanomechanics and atomic ensembles, Phys. Rev. Lett., Volume 102 (2009), p. 020501

[87] M. Antezza; L.P. Pitaevskii; S. Stringari Effect of the Casimir–Polder force on the collective oscillations of a trapped Bose–Einstein condensate, Phys. Rev. A, Volume 70 (2004), p. 053619

[88] H. Ott; J. Fortágh; S. Kraft; A. Günther; D. Komma; C. Zimmermann Nonlinear dynamics of a Bose–Einstein condensate in a magnetic waveguide, Phys. Rev. Lett., Volume 91 (2003), p. 040402

[89] I. Favero; C. Metzger; S. Camerer; D. König; H. Lorenz; J.P. Kotthaus; K. Karrai Optical cooling of a micromirror of wavelength size, Appl. Phys. Lett., Volume 90 (2007), p. 104101

[90] J. Reichel Microchip traps and Bose–Einstein condensation, Appl. Phys. B, Volume 74 (2002), p. 469

[91] R. Gehr; J. Volz; G. Dubois; T. Steinmetz; Y. Colombe; B. Lev; R. Long; J. Estève; J. Reichel Cavity-based single atom preparation and high-fidelity hyperfine state readout, Phys. Rev. Lett., Volume 104 (2010), p. 203602

[92] S.R. Jefferts; C. Monroe; E.W. Bell; D.J. Wineland Coaxial-resonator-driven rf (Paul) trap for strong confinement, Phys. Rev. A, Volume 51 (1995), p. 3112

[93] D.M. Harber; J.M. Obrecht; J.M. McGuirk; E.A. Cornell Measurement of the Casimir–Polder force through center-of-mass oscillations of a Bose–Einstein condensate, Phys. Rev. A, Volume 72 (2005), p. 033610

[94] H. Häffner; T. Beier; N. Hermansphan; H. Kluge; W. Quint; S. Stahl; J. Verdú; G. Werth High-accuracy measurement of the magnetic moment anomaly of the electron bound in hydrogenlike carbon, Phys. Rev. Lett., Volume 85 (2000), p. 5308

[95] J. Verdú; S. Djekić; S. Stahl; T. Valenzuela; M. Vogel; G. Werth; T. Beier; H. Kluge; W. Quint Electronic g factor of hydrogenlike oxygen ¹⁶O⁷⁺, Phys. Rev. Lett., Volume 92 (2004), p. 093002

[96] D.M. Lucas; B.C. Keitch; J.P. Home; G. Imreh; M.J. McDonnell; D.N. Stacey; D.J. Szwer; A.M. Steane A long-lived memory qubit on a low-decoherence quantum bus, 2007 (preprint) | arXiv

[97] J.D. Jost; J.P. Home; J.M. Amini; D. Hanneke; R. Ozeri; C. Langer; J.J. Bollinger; D. Leibfried; D.J. Wineland Entangled mechanical oscillators, Nature, Volume 459 (2009), p. 683

[98] I. Bouchoule; H. Perrin; A. Kuhn; M. Morinaga; C. Salomon Neutral atoms prepared in Fock states of a one-dimensional harmonic potential, Phys. Rev. A, Volume 59 (1999), p. R8

[99] J. Hecker Denschlag; J.E. Simsarian; H. Häffner; C. McKenzie; A. Browaeys; D. Cho; K. Helmerson; S.L. Rolston; W.D. Phillips A Bose–Einstein condensate in an optical lattice, J. Phys. B: At. Mol. Opt. Phys., Volume 35 (2002), pp. 3095-3110

[100] I.B. Spielman; P.R. Johnson; J.H. Huckans; C.D. Fertig; S.L. Rolston; W.D. Phillips; J.V. Porto Collisional deexcitation in a quasi-two-dimensional degenerate bosonic gas, Phys. Rev. A, Volume 73 (2006), p. 020702(R)

[101] T. Müller; S. Fölling; A. Widera; I. Bloch State preparation and dynamics of ultracold atoms in higher lattice orbitals, Phys. Rev. Lett., Volume 99 (2007), p. 200405

[102] L. Förster; M. Karski; J.-M. Choi; A. Steffen; W. Alt; D. Meschede; A. Widera; E. Monatno; J.H. Lee; W. Rakreungdet; P.S. Jessen Microwave control of atomic motion in optical lattices, Phys. Rev. Lett., Volume 103 (2009), p. 233001

[103] G.-B. Jo; Y. Shin; S. Will; T.A. Pasquini; M. Saba; W. Ketterle; D.E. Pritchard; M. Vengalattore; M. Prentiss Long phase coherence time and number squeezing of two Bose–Einstein condensates on an atom chip, Phys. Rev. Lett., Volume 98 (2007), p. 030407

[104] T. Schumm; S. Hofferberth; L.M. Andersson; S. Wildermuth; S. Groth; I. Bar-Joseph; J. Schmiedmayer; P. Krüger Matter-wave interferometry in a double well on an atom chip, Nat. Phys., Volume 1 (2005), p. 57

[105] A.D. Cronin; J. Schmiedmayer; D.E. Pritchard Optics and interferometry with atoms and molecules, Rev. Mod. Phys., Volume 81 (2009), p. 1052

[106] Y. Colombe; T. Steinmetz; G. Dubois; F. Linke; D. Hunger; J. Reichel Strong atom-field coupling for Bose–Einstein condensates in an optical cavity on a chip, Nature, Volume 450 (2007), p. 272

[107] T. Niemczyk; F. Deppe; H. Huebl; E.P. Menzel; F. Hocke; M.J. Schwarz; J.J. Garcia-Ripoll; D. Zueco; T. Hümmer; E. Solano; A. Marx; R. Gross Circuit quantum electrodynamics in the ultrastrong-coupling regime, Nat. Phys., Volume 6 (2010), pp. 772-776

[108] D.M. Meekhof; C. Monroe; B.E. King; W.M. Itano; D.J. Wineland Generation of nonclassical motional states of a trapped atom, Phys. Rev. Lett., Volume 76 (1996), p. 1796

[109] J. Benhelm; G. Kirchmaier; C.F. Roos; R. Blatt Towards fault-tolerant quantum computing with trapped ions, Nat. Phys., Volume 4 (2008), p. 463

[110] T. Monz; K. Kim; W. Hänsel; M. Riebe; A.S. Villar; P. Schindler; M. Chwalla; M. Hennrich; R. Blatt Realization of the quantum Toffoli gate with trapped ions, Phys. Rev. Lett., Volume 102 (2009), p. 040501

[111] K.R. Brown; C. Ospelkaus; Y. Colombe; A.C. Wilson; D. Leibfried; D.J. Wineland Coupled quantized mechanical oscillators, Nature, Volume 471 (2011)

[112] M. Harlander; R. Lechner; M. Brownnutt; R. Blatt; W. Hänsel Trapped-ion antennae for the transmission of quantum information, Nature, Volume 471 (2011)

[113] H.B.G. Casimir; D. Polder The influence of retardation on the London–van der Waals forces, Phys. Rev., Volume 73 (1948), p. 360

[114] J.M. Obrecht; R.J. Wild; M. Antezza; L.P. Pitaevskii; S. Stringari; E.A. Cornell Measurement of the temperature dependence of the Casimir–Polder force, Phys. Rev. Lett., Volume 98 (2007), p. 063201

[115] D. Hunger; T. Steinmetz; Y. Colombe; C. Deutsch; T.W. Hänsch; J. Reichel Fiber Fabry–Perot cavity with high finesse, New J. Phys., Volume 12 (2010), p. 065038

[116] S. Stringari Collective excitations of a trapped Bose-condensed gas, Phys. Rev. Lett., Volume 77 (1996), p. 2360

[117] T. Kimura; H. Saito; M. Ueda A variational sum-rule approach to collective excitations of a trapped Bose–Einstein condensate, J. Phys. Soc. Jpn., Volume 68 (1999), p. 1477

[118] R. Fermani; S. Scheel; P.L. Knight Trapping cold atoms near carbon nanotubes: Thermal spin flips and Casimir–Polder potential, Phys. Rev. A, Volume 75 (2007), p. 062905

[119] A.K. Hüttel; G.A. Steele; B. Witkamp; M. Poot; L.P. Kouwenhoven; H.S.J. van der Zant Carbon nanotubes as ultrahigh quality factor mechanical resonators, Nano Lett., Volume 9 (2009), p. 2547

[120] P. Petrov; S. Machluf; S. Younis; R. Macaluso; T. David; B. Hadad; Y. Japha; M. Keil; E. Joselevich; R. Folman Trapping cold atoms using surface-grown carbon nanotubes, Phys. Rev. A, Volume 79 (2009), p. 043403

[121] I. Favero; K. Karrai Cavity cooling of a nanomechanical resonator by light scattering, New J. Phys., Volume 10 (2008), p. 095006

[122] I. Favero; S. Stapfner; D. Hunger; P. Paulitschke; J. Reichel; H. Lorenz; E.M. Weig; K. Karrai Fluctuating nanomechanical system in a high finesse optical microcavity, Opt. Express, Volume 17 (2009), pp. 12813-12820

[123] G. Raithel; W.D. Philipps; S.L. Rolston Collapse and revivals of wave packets in optical lattices, Phys. Rev. Lett., Volume 81 (1998), p. 3615

[124] A.J. Kerman; V. Vuletic; C. Chin; S. Chu Beyond optical molasses: 3D Raman sideband cooling of atomic cesium to high phase-space density, Phys. Rev. Lett., Volume 84 (2000), p. 439

[125] R. Miller; T.E. Northup; K.M. Birnbaum; A. Boca; A.D. Boozer; H.J. Kimble Trapped atoms in cavity QED: coupling quantized light and matter, J. Phys. B: At. Mol. Opt. Phys., Volume 38 (2005), p. 551

[126] M. Hofheinz; H. Wang; M. Ansmann; R.C. Bialczak; E. Lucero; M. Neeley; A.D. OʼConnell; D. Sank; J. Wenner; J.M. Martinis; A.N. Cleland Synthesizing arbitrary quantum states in a superconducting resonator, Nature, Volume 459 (2009), p. 546

[127] C.K. Law; J.H. Eberly Arbitrary control of a quantum electromagnetic field, Phys. Rev. Lett., Volume 76 (1996), p. 1055

[128] B.W. Shore; P.L. Knight The Jaynes–Cummings model, J. Mod. Opt., Volume 40 (1993), pp. 1195-1238

[129] H. Katori; T. Akatsuka Electric manipulation of spinless neutral atoms on a surface, Jpn. J. Appl. Phys., Volume 43 (2004), p. 358

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Dynamics of coupled multimode and hybrid optomechanical systems

Georg Heinrich; Max Ludwig; Huaizhi Wu; ...

C. R. Phys (2011)

Cavity optomechanics and cooling nanomechanical oscillators using microresonator enhanced evanescent near-field coupling

G. Anetsberger; E.M. Weig; J.P. Kotthaus; ...

C. R. Phys (2011)