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Dicke quantum phase transition with a superfluid gas in an optical cavity


A phase transition describes the sudden change of state of a physical system, such as melting or freezing. Quantum gases provide the opportunity to establish a direct link between experiments and generic models that capture the underlying physics. The Dicke model describes a collective matter–light interaction and has been predicted to show an intriguing quantum phase transition. Here we realize the Dicke quantum phase transition in an open system formed by a Bose–Einstein condensate coupled to an optical cavity, and observe the emergence of a self-organized supersolid phase. The phase transition is driven by infinitely long-range interactions between the condensed atoms, induced by two-photon processes involving the cavity mode and a pump field. We show that the phase transition is described by the Dicke Hamiltonian, including counter-rotating coupling terms, and that the supersolid phase is associated with a spontaneously broken spatial symmetry. The boundary of the phase transition is mapped out in quantitative agreement with the Dicke model. Our results should facilitate studies of quantum gases with long-range interactions and provide access to novel quantum phases.

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Figure 1: Concept of the experiment.
Figure 2: Analogy to the Dicke model.
Figure 3: Observation of the phase transition.
Figure 4: Steady state in the self-organized phase.
Figure 5: Phase diagram.

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  1. Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995)

    Article  ADS  CAS  PubMed  Google Scholar 

  2. Davis, K. B. et al. Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995)

    ADS  CAS  PubMed  Google Scholar 

  3. Regal, C. A., Greiner, M. & Jin, D. S. Observation of resonance condensation of fermionic atom pairs. Phys. Rev. Lett. 92, 040403 (2004)

    ADS  CAS  PubMed  Google Scholar 

  4. Zwierlein, M. W. et al. Condensation of pairs of fermionic atoms near a Feshbach resonance. Phys. Rev. Lett. 92, 120403 (2004)

    ADS  CAS  PubMed  Google Scholar 

  5. Bartenstein, M. et al. Collective excitations of a degenerate gas at the BEC-BCS crossover. Phys. Rev. Lett. 92, 203201 (2004)

    ADS  CAS  PubMed  Google Scholar 

  6. Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002)

    ADS  CAS  PubMed  Google Scholar 

  7. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)

    MathSciNet  Google Scholar 

  8. Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996)

    ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  9. Lahaye, T., Menotti, C., Santos, L., Lewenstein, M. & Pfau, T. The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72, 126401 (2009)

    ADS  Google Scholar 

  10. Asbóth, J. K., Domokos, P. & Ritsch, H. Correlated motion of two atoms trapped in a single-mode cavity field. Phys. Rev. A 70, 013414 (2004)

    ADS  Google Scholar 

  11. Asbóth, J. K., Ritsch, H. & Domokos, P. Collective excitations and instability of an optical lattice due to unbalanced pumping. Phys. Rev. Lett. 98, 203008 (2007)

    ADS  PubMed  Google Scholar 

  12. Domokos, P. & Ritsch, H. Collective cooling and self-organization of atoms in a cavity. Phys. Rev. Lett. 89, 253003 (2002)

    ADS  PubMed  Google Scholar 

  13. Nagy, D., Szirmai, G. & Domokos, P. Self-organization of a Bose-Einstein condensate in an optical cavity. Eur. Phys. J. D 48, 127–137 (2008)

    ADS  CAS  Google Scholar 

  14. Black, A. T., Chan, H. W. & Vuletić, V. Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering. Phys. Rev. Lett. 91, 203001 (2003)

    ADS  PubMed  Google Scholar 

  15. Inouye, S. et al. Superradiant Rayleigh scattering from a Bose-Einstein condensate. Science 285, 571–574 (1999)

    CAS  PubMed  Google Scholar 

  16. Yoshikawa, Y., Torii, Y. & Kuga, T. Superradiant light scattering from thermal atomic vapors. Phys. Rev. Lett. 94, 083602 (2005)

    ADS  PubMed  Google Scholar 

  17. Slama, S., Bux, S., Krenz, G., Zimmermann, C. & Courteille, P. W. Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity. Phys. Rev. Lett. 98, 053603 (2007)

    ADS  CAS  PubMed  Google Scholar 

  18. Bonifacio, R. & De Salvo, L. Collective atomic recoil laser (CARL) optical gain without inversion by collective atomic recoil and self-bunching of two-level atoms. Nucl. Instrum. Methods 341, 360–362 (1994)

    ADS  CAS  Google Scholar 

  19. Sachdev, S. Quantum Phase Transitions (Cambridge Univ. Press, 1999)

    MATH  Google Scholar 

  20. Amico, L., Fazio, R., Osterloh, A. & Vedral, V. Entanglement in many-body systems. Rev. Mod. Phys. 80, 517–576 (2008)

    ADS  MathSciNet  CAS  MATH  Google Scholar 

  21. Osterloh, A., Amico, L., Falci, G. & Fazio, R. Scaling of entanglement close to a quantum phase transition. Nature 416, 608–610 (2002)

    ADS  CAS  PubMed  Google Scholar 

  22. Botet, R., Jullien, R. & Pfeuty, P. Size scaling for infinitely coordinated systems. Phys. Rev. Lett. 49, 478–481 (1982)

    ADS  CAS  Google Scholar 

  23. Dicke, R. H. Coherence in spontaneous radiation processes. Phys. Rev. 93, 99–110 (1954)

    ADS  CAS  MATH  Google Scholar 

  24. Hepp, K. & Lieb, E. H. On the superradiant phase transition for molecules in a quantized radiation field: the Dicke maser model. Ann. Phys. 76, 360–404 (1973)

    ADS  MathSciNet  CAS  Google Scholar 

  25. Wang, Y. K. & Hioe, F. T. Phase transition in the Dicke model of superradiance. Phys. Rev. A 7, 831–836 (1973)

    ADS  CAS  Google Scholar 

  26. Dimer, F., Estienne, B., Parkins, A. S. & Carmichael, H. J. Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system. Phys. Rev. A 75, 013804 (2007)

    ADS  Google Scholar 

  27. Andreev, A. F. & Lifshitz, I. M. Quantum theory of crystal defects. Sov. Phys. JETP 56, 2057–2068 (1969)

    CAS  Google Scholar 

  28. Chester, G. V. Speculations on Bose-Einstein condensation and quantum crystals. Phys. Rev. A 2, 256–258 (1970)

    ADS  Google Scholar 

  29. Leggett, A. J. Can a solid be “superfluid”? Phys. Rev. Lett. 25, 1543–1546 (1970)

    ADS  CAS  Google Scholar 

  30. Büchler, H. P. & Blatter, G. Supersolid versus phase separation in atomic Bose-Fermi mixtures. Phys. Rev. Lett. 91, 130404 (2003)

    ADS  PubMed  Google Scholar 

  31. Maschler, C., Mekhov, I. B. & Ritsch, H. Ultracold atoms in optical lattices generated by quantized light fields. Eur. Phys. J. D 46, 545–560 (2008)

    ADS  CAS  Google Scholar 

  32. Domokos, P. & Ritsch, H. Mechanical effects of light in optical resonators. J. Opt. Soc. Am. B 20, 1098–1130 (2003)

    ADS  CAS  Google Scholar 

  33. Gopalakrishnan, S., Lev, B. L. & Goldbart, P. M. Emergent crystallinity and frustration with Bose-Einstein condensates in multimode cavities. Nature Phys. 5, 845–850 (2009)

    ADS  CAS  Google Scholar 

  34. Murch, K. W., Moore, K. L., Gupta, S. & Stamper-Kurn, D. M. Observation of quantum-measurement backaction with an ultracold atomic gas. Nature Phys. 4, 561–564 (2008)

    CAS  Google Scholar 

  35. Orzel, C., Tuchman, A. K., Fenselau, M. L., Yasuda, M. & Kasevich, M. A. Squeezed states in a Bose-Einstein condensate. Science 291, 2386–2389 (2001)

    ADS  CAS  PubMed  Google Scholar 

  36. Brennecke, F., Ritter, S., Donner, T. & Esslinger, T. Cavity optomechanics with a Bose-Einstein condensate. Science 322, 235–238 (2008)

    ADS  CAS  PubMed  Google Scholar 

  37. Nagy, D., Asboth, J. K., Domokos, P. & Ritsch, H. Self-organization of a laser-driven cold gas in a ring cavity. Europhys. Lett. 74, 254–260 (2006)

    ADS  CAS  Google Scholar 

  38. Asbóth, J. K., Domokos, P., Ritsch, H. & Vukics, A. Self-organization of atoms in a cavity field: threshold, bistability, and scaling laws. Phys. Rev. A 72, 053417 (2005)

    ADS  Google Scholar 

  39. Lambert, N., Emary, C. & Brandes, T. Entanglement and the phase transition in single-mode superradiance. Phys. Rev. Lett. 92, 073602 (2004)

    ADS  PubMed  Google Scholar 

  40. Vidal, J. & Dusuel, S. Finite-size scaling exponents in the Dicke model. Europhys. Lett. 74, 817–822 (2006)

    ADS  CAS  Google Scholar 

  41. Maschler, C., Ritsch, H., Vukics, A. & Domokos, P. Entanglement assisted fast reordering of atoms in an optical lattice within a cavity at T = 0. Opt. Commun. 273, 446–450 (2007)

    ADS  CAS  Google Scholar 

  42. Mekhov, I. B., Maschler, C. & Ritsch, H. Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity quantum electrodynamics. Nature Phys. 3, 319–323 (2007)

    ADS  CAS  Google Scholar 

  43. Mekhov, I. B. & Ritsch, H. Quantum nondemolition measurements and state preparation in quantum gases by light detection. Phys. Rev. Lett. 102, 020403 (2009)

    ADS  PubMed  Google Scholar 

  44. Öttl, A., Ritter, S., Köhl, M. & Esslinger, T. Hybrid apparatus for Bose-Einstein condensation and cavity quantum electrodynamics: single atom detection in quantum degenerate gases. Rev. Sci. Instrum. 77, 063118 (2006)

    ADS  Google Scholar 

  45. Brennecke, F. et al. Cavity QED with a Bose–Einstein condensate. Nature 450, 268–271 (2007)

    ADS  CAS  PubMed  Google Scholar 

  46. Pitaevskii, L. & Stringari, S. Bose-Einstein Condensation 161–176 (Oxford Univ. Press, 2003)

    MATH  Google Scholar 

  47. Nagy, D., Kónya, G., Szirmai, G. & Domokos, P. Dicke-model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity. Phys. Rev. Lett. 104, 130401 (2010)

    ADS  CAS  PubMed  Google Scholar 

  48. Greiner, M., Bloch, I., Mandel, O., Hänsch, T. W. & Esslinger, T. Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Phys. Rev. Lett. 87, 160405 (2001)

    ADS  CAS  PubMed  Google Scholar 

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We thank G. Blatter, I. Carusotto, P. Domokos, A. Imamoglu, S. Leinss, R. Mottl, L. Pollet, H. Ritsch and M. Troyer for discussions. Financial funding from NAME-QUAM (European Commission Seventh Framework Programme Future and Emerging Technologies Open Scheme, grant number 225187) and QSIT (ETH Zürich) is acknowledged. C.G. acknowledges support from an ETH Fellowship.

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The data was taken and analysed by K.B. and C.G. The theoretical analysis was mainly performed by F.B. and T.E. The relation to the Dicke model was realized by F.B. The experimental concept was developed by T.E. All authors contributed extensively to the discussion of the results as well as to the preparation of the manuscript.

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Correspondence to Tilman Esslinger.

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The authors declare no competing financial interests.

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Baumann, K., Guerlin, C., Brennecke, F. et al. Dicke quantum phase transition with a superfluid gas in an optical cavity. Nature 464, 1301–1306 (2010).

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