Coupling two order parameters in a quantum gas

Abstract

Controlling matter to simultaneously support coupled properties is of fundamental and technological importance (for example, in multiferroics or high-temperature superconductors). However, determining the microscopic mechanisms responsible for the simultaneous presence of different orders is difficult, making it hard to predict material phenomenology or modify properties. Here, using a quantum gas to engineer an adjustable interaction at the microscopic level, we demonstrate scenarios of competition, coexistence and mutual enhancement of two orders. For the enhancement scenario, the presence of one order lowers the critical point of the other. Our system is realized by a Bose-Einstein condensate that can undergo self-organization phase transitions in two optical resonators, resulting in two distinct crystalline density orders. We characterize the coupling between these orders by measuring the composite order parameter and the elementary excitations and explain our results with a mean-field free-energy model derived from a microscopic Hamiltonian. Our system is ideally suited to explore quantum tricritical points and can be extended to study the interplay of spin and density orders as a function of temperature.

Spinor Self-Ordering of a Quantum Gas in a Cavity

“…The organized state may be called a 'density-wave polariton condensate' in recognition of the joint light-matter-wave nature of the quasiparticles in the macroscopically occupied and coherent density-photon mode [37]. Roton instabilities and the extended Bose-Hubbard model have been realized [38][39][40], and similar systems employing a few degenerate cavity modes have created a supersolid [41], an intertwined spatial order [42], and supermode-densitywave polariton condensates [37]. Highly degenerate cavities have been used to engineer tunable-range photon mediated atom-atom interactions [43] that may lead to liquid crystalline states [44].…”

P -Band Induced Self-Organization and Dynamics with Repulsively Driven Ultracold Atoms in an Optical Cavity

“…A theoretical description of the phase boundaries revealed that an antisymmetric coupling to the P band of the pump lattice induces self-organization. This different lattice geometry for ∆ a > 0 could further lead to a qualitatively different coupling behavior in two-or multi-mode scenarios [17,32]. The observed cycling dynamic appears qualitatively in the phase diagram where limit cycles, chaos, and time crystal behavior were theoretically predicted in related models [26][27][28].…”

Spectrum, Landau–Zener theory and driven-dissipative dynamics of a staircase of photons

“…The last ten years have witnessed swift progress in quantum optics platforms where light and matter are strongly coupled and can be employed to engineer a variety of quantum phenomena: examples range from Bose-Einstein condensates coupled to optical cavity photons, where the Dicke transition is engineered [1,2], to the recent demonstration of supersolids [3] and phases with competing order parameters in a condensate trapped at the intersection of two optical cavities [4][5][6][7]. Most of these models realise scenarios where matter and light collectively interact as in the case of superradiant phase transitions or in 'Dicke-Hubbard' systems characterized by critical points separating a superfluid from a Mott insulating phase [8].…”