Disorder-Driven Density and Spin Self-Ordering of a Bose-Einstein Condensate in a Cavity

Farokh Mivehvar, Francesco Piazza, and Helmut Ritsch
Phys. Rev. Lett. 119, 063602 – Published 9 August 2017
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Abstract

We study spatial spin and density self-ordering of a two-component Bose-Einstein condensate via collective Raman scattering into a linear cavity mode. The onset of the Dicke superradiance phase transition is marked by a simultaneous appearance of a crystalline density order and a spin-wave order. The latter spontaneously breaks the discrete Z2 symmetry between even and odd sites of the cavity optical potential. Moreover, in the superradiant state the continuous U(1) symmetry of the relative phase of the two condensate wave functions is explicitly broken by the cavity-induced position-dependent Raman coupling with a zero spatial average. Thus, the spatially averaged relative condensate phase is locked at either π/2 or π/2. This continuous symmetry breaking and relative condensate phase locking by a zero-average Raman field can be considered as a generic order-by-disorder process similar to the random-field-induced order in the two-dimensional classical ferromagnetic XY spin model. However, the seed of the random field in our model stems from quantum fluctuations in the cavity field and is a dynamical entity affected by self-ordering. The spectra of elementary excitations exhibit the typical mode softening at the superradiance threshold.

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  • Received 23 May 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.063602

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Farokh Mivehvar1,*, Francesco Piazza2, and Helmut Ritsch1

  • 1Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
  • 2Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany

  • *Corresponding author. farokh.mivehvar@uibk.ac.at

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Issue

Vol. 119, Iss. 6 — 11 August 2017

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