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Emergent crystallinity and frustration with Bose–Einstein condensates in multimode cavities

Nature Physics volume 5, pages 845–850 (2009)Cite this article

Abstract

We propose that condensed-matter phenomena involving the spontaneous emergence and dynamics of crystal lattices can be realized using Bose–Einstein condensates coupled to multimode optical cavities. It is known that, in the case of a transversely pumped single-mode cavity, the atoms crystallize at either the even or the odd antinodes of the cavity mode at sufficient pump laser intensity, thus spontaneously breaking a discrete translational symmetry. Here we demonstrate that, in multimode cavities, crystallization involves the spontaneous breaking of a continuous translational symmetry, through a variant of Brazovskii’s transition, thus paving the way for realizations of compliant lattices and associated phenomena, such as dislocations, frustration, glassiness and even supersolidity, in ultracold atomic settings, where quantum effects have a dominant role. We apply a functional-integral formalism to explore the role of fluctuations in this correlated many-body system, to calculate their effect on the threshold for ordering, and to determine their imprint on the correlations of the light emitted from the cavity.

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Figure 1: The layered atom–cavity system.
Figure 2: Ordered state with defects.
Figure 3: Effects due to frustration.

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References

  1. Kim, E. & Chan, M. H. W. Observation of superflow in solid helium. Science 305, 1941–1944 (2004).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Asboth, 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).

    Article  ADS  Google Scholar 

  4. Lewenstein, M. et al. in Proc. of ICAP Innsbruck (eds Roos, C. F., Häffner, H. & Blatt, R.) 201–211 (AIP Conf. Proc. No. 869, AIP, 2006).

    Google Scholar 

  5. 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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Vuletic, V. & Chu, S. Laser cooling of atoms, ions, or molecules by coherent scattering. Phys. Rev. Lett. 84, 3787–3790 (2000).

    Article  ADS  Google Scholar 

  8. Lev, B. L. et al. Prospects for the cavity-assisted laser cooling of molecules. Phys. Rev. A 77, 023402 (2008).

    Article  ADS  Google Scholar 

  9. 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).

    Article  ADS  Google Scholar 

  10. Brazovskii, S. Phase transition of an isotropic system to an inhomogenous state. Zh. Eksp. Teor. Fiz. 68, 175–185 (1975) (Sov. Phys. JETP 41, 85–89 (1975)).

  11. Góral, K., Santos, L. & Lewenstein, M. Quantum phases of dipolar bosons in optical lattices. Phys. Rev. Lett. 88, 170406 (2002).

    Article  ADS  Google Scholar 

  12. Yi, S., Li, T. & Sun, C. P. Novel quantum phases of dipolar Bose gases in optical lattices. Phys. Rev. Lett. 98, 260405 (2007).

    Article  ADS  Google Scholar 

  13. Walls, D. F. & Milburn, G. J. Quantum Optics (Springer, 2008).

    Book  Google Scholar 

  14. Hadzibabic, Z., Krüger, P., Cheneau, M., Battelier, B. & Dalibard, J. Berezinskii–Kosterlitz–Thouless crossover in a trapped atomic gas. Nature 441, 1118–1121 (2006).

    Article  ADS  Google Scholar 

  15. Abrikosov, A., Gorkov, L. P. & Dzyaloshinski, I. E. Methods of Quantum Field Theory in Statistical Physics (Dover, 1975).

    MATH  Google Scholar 

  16. Keldysh, L. V. Diagram technique for nonequilibrium processes. Sov. Phys. JETP 20, 1018–1025 (1965).

    MathSciNet  Google Scholar 

  17. Kamenev, A. & Levchenko, A. Keldysh technique and nonlinear sigma-model: Basic principles and applications. Adv. Phys. 58, 197–319 (2009).

    Article  ADS  Google Scholar 

  18. Lifshitz, E. M. & Pitaevskii, L. P. Statistical Physics, Part 2 (Course of Theoretical Physics, Vol. 9, Pergamon, 1980).

    Google Scholar 

  19. Alexander, S. & McTague, R. Should all crystals be bcc? Landau theory of solidification and crystal nucleation. Phys. Rev. Lett. 41, 702–705 (1978).

    Article  ADS  Google Scholar 

  20. Siegman, A. E. Lasers (University Science Books, 1986).

    Google Scholar 

  21. Leibler, L. Theory of microphase separation in block copolymers. Macromolecules 13, 1602–1617 (1980).

    Article  ADS  Google Scholar 

  22. Swift, J. & Hohenberg, P. C. Hydrodynamic fluctuations at the convective instability. Phys. Rev. A 15, 319–328 (1977).

    Article  ADS  Google Scholar 

  23. Hohenberg, P. C. & Swift, J. B. Metastability in fluctuation-driven first-order transitions: Nucleation of lamellar phases. Phys. Rev. E 52, 1828–1845 (1995).

    Article  ADS  Google Scholar 

  24. 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).

    Article  Google Scholar 

  25. Altman, E., Demler, E. & Lukin, M. D. Probing many-body correlations of ultra-cold atoms via noise correlations. Phys. Rev. A. 70, 013603 (2004).

    Article  ADS  Google Scholar 

  26. Horak, P. et al. Optical kaleidoscope using a single atom. Phys. Rev. Lett. 88, 043601 (2002).

    Article  ADS  Google Scholar 

  27. Salzburger, T., Domokos, P. & Ritsch, H. Enhanced atom capturing in a high-Q cavity by help of several transverse modes. Opt. Express 10, 1204–1214 (2002).

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by NSF PHY08-47469 (B.L.L.), AFOSR FA9550-09-1-0079 (B.L.L.), DOE DE-FG02-07ER46453 (S.G.) and NSF DMR09-06780 (P.M.G.). P.M.G. gratefully acknowledges the hospitality of the Aspen Center for Physics.

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Authors and Affiliations

  1. Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

    Sarang Gopalakrishnan, Benjamin L. Lev & Paul M. Goldbart

  2. Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

    Sarang Gopalakrishnan & Paul M. Goldbart

  3. Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

    Paul M. Goldbart

Authors
  1. Sarang Gopalakrishnan
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  2. Benjamin L. Lev
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All authors contributed equally to this work.

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Correspondence to Sarang Gopalakrishnan.

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Gopalakrishnan, S., Lev, B. & Goldbart, P. Emergent crystallinity and frustration with Bose–Einstein condensates in multimode cavities. Nature Phys 5, 845–850 (2009). https://doi.org/10.1038/nphys1403

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