Atom-light crystallization of Bose-Einstein condensates in multimode cavities: Nonequilibrium classical and quantum phase transitions, emergent lattices, supersolidity, and frustration

Abstract

The self-organization of a Bose-Einstein condensate in a transversely pumped optical cavity is a process akin to crystallization: when pumped by a laser of sufficient intensity, the coupled matter and light fields evolve, spontaneously, into a spatially modulated pattern, or crystal, whose lattice structure is dictated by the geometry of the cavity. In cavities having multiple degenerate modes, the quasi-continuum of possible lattice arrangements, and the continuous symmetry breaking associated with the adoption of a particular lattice arrangement, give rise to phenomena such as phonons, defects, and frustration, which have hitherto been unexplored in ultracold atomic settings involving neutral atoms. The present work develops a nonequilibrium field-theoretic approach to explore the self-organization of a BEC in a pumped, lossy optical cavity. We find that the transition is well described, in the regime of primary interest, by an effective equilibrium theory. At nonzero temperatures, the self-organization occurs via a fluctuation-driven first-order phase transition of the Brazovskii class; this transition persists to zero temperature, and crosses over into a quantum phase transition of a new universality class. We make further use of our field-theoretic description to investigate the role of nonequilibrium fluctuations on the self-organization transition, as well as to explore the nucleation of ordered-phase droplets, the nature and energetics of topological defects, supersolidity in the ordered phase, and the possibility of frustration controlled by the cavity geometry. In addition, we discuss the range of experimental parameters for which we expect the phenomena described here to be observable, along with possible schemes for detecting ordering and fluctuations via either atomic correlations or the correlations of the light emitted from the cavity.

Self-ordering dynamics of ultracold atoms in multicolored cavity fields

“…Even more complex results could be expected from a generalization to fermionic particles [5] or particles with several internal levels [30]. Of course, one of the most interesting aspects and motivations of this approach is the fact that only minor additions to current experimental setups are required and the theoretical model for the current generations of experiments have proven to be surprisingly accurate and reliable [6,8,17,31,32].…”

“…A particular interesting generalization was introduced by considering this ordering phenomenon in degenerate multi-mode cavity fields and restricting the degrees of freedom of the particle motion to a 2D plane [16]. This opened a new possible route to study a wealth of important quantum solid state phenomena like emergent crystallinity, liquid crystalline phases [16,17] or quantum neural network models [18] in a well controllable atom-optical configuration. Due to the inherent complexity and technical difficulty of degenerate multi-mode setups, which require at least a 2D geometry, theoretical modeling as well as experimental implementations of such setups are very challenging and have, to our knowledge, not been implemented to date.…”

Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

“…We also indicate how to relate the operators of the master equation (2) to the field content and choice of time contour in a Keldysh action (see also Refs. [15,18,42]). …”

“…To treat the interplay between external driving, dissipation and many-body interactions in a more general setting, we next develop a unified approach to describe phase transitions in open quantum systems based on Keldysh path integrals [15][16][17][18][19][20][21]. This approach is used to analyze the driven Dicke model in the presence of finite-size effects and atomic dissipative processes.…”

Quantum charge glasses of itinerant fermions with cavity-mediated long-range interactions

“…It was shown that a quantum phase transition in the universality class of the (solvable) infinite-range Ising quantum spin glass [13,14] occurs, potentially enabling comparison between experiment and the theory of spin glasses. In a related paper [15][16][17], Gopalakrishnan et al provided experimental details and detection methods for the spin glass phase.…”