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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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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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  3. Paul M. Goldbart
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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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