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|[rsquo]|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.