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Replica symmetry breaking in cold atoms and spin glasses

P. Rotondo, E. Tesio, and S. Caracciolo
Phys. Rev. B 91, 014415 – Published 14 January 2015
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  • INTRODUCTION
  • MODEL AND ZERO-FIELD LIMIT
  • DISPERSIVE REGIME AND RSB
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We consider a system composed by N atoms trapped within a multimode cavity, whose theoretical description is captured by a disordered multimode Dicke model. We show that in the resonant, zero-field limit the system exactly realizes the Sherrington-Kirkpatrick model. Upon a redefinition of the temperature, the same dynamics is realized in the dispersive, strong-field limit. This regime also gives access to spin-glass observables which can be used to detect replica symmetry breaking.

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    • Received 4 May 2014
    • Revised 29 September 2014

    DOI:https://doi.org/10.1103/PhysRevB.91.014415

    ©2015 American Physical Society

    Authors & Affiliations

    P. Rotondo1, E. Tesio2,*, and S. Caracciolo1

    • 1Dipartimento di Fisica, Università degli Studi di Milano and INFN, via Celoria 16, 20133 Milano, Italy
    • 2SUPA and Department of Physics, University of Strathclyde, 104 Rottenrow East, G04NG Glasgow, United Kingdom

    • *Present address: Orc Group, London, UK.

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    Vol. 91, Iss. 1 — 1 January 2015

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    Images

    • Figure 1
      Figure 1

      (a) Sketch of the multimode cavity setup. As in Ref. [22], N atoms are placed within a multimode cavity, kept at fixed positions by trapping beams (not shown in the figure) and pumped transversely. Ordering is strongest at the antinodes of the intracavity field (red full line), and atoms occupying even antinodes interact ferromagnetically with atoms at even antinodes, and antiferromagnetically with atoms at odd antinodes. (b) Upon adiabatic elimination of the upper state |e〉 [22], a Dicke interaction is realized by the |1〉−|2〉 transition and a field h (Rabi frequency hx, detuning hz).

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    • Figure 2
      Figure 2

      Phase diagram for the disordered multimode Dicke model; see [25]. At weak disorder (large J̃0/J̃), a critical temperature is found below which the system is ferromagnetic (FM) and exhibits superradiance (SR). Above this critical temperature and for weak disorder, the system is paramagnetic (PM) and exhibits normal radiance (NR). At relatively low temperatures and strong disorder (small J̃0/J̃), the system enters the spin-glass (SG) phase and displays RSB.

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    • Figure 3
      Figure 3

      Graphical representation of the interacting-replicated partition functions, with Z2 on the left and Z3 on the right. Each layer represents a HSK copy, interacting ferromagnetically with another replica with coupling strength yi.

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