Ultracold bosons with cavity-mediated long-range interactions: A local mean-field analysis of the phase diagram

Abstract

Ultracold bosonic atoms in optical lattices self-organize into a variety of structural and quantum phases when placed into a single-mode cavity and pumped by a laser. Cavity optomechanical effects induce an atom density modulation at the cavity-mode wave length that competes with the optical lattice arrangement. Simultaneously short-range interactions via particle hopping promote superfluid order, such that a variety of structural and quantum coherent phases can occur. We analyze the emerging phase diagram in two dimensions by means of an extended Bose-Hubbard model using a local mean field approach combined with a superfluid cluster analysis. For commensurate ratios of the cavity and external lattice wave lengths the Mott insulator-superfluid transition is modified by the appearance of charge density wave and supersolid phases, at which the atomic density supports the buildup of a cavity field. For incommensurate ratios, the optomechanical forces induce the formation of Bose-glass and superglass phases, namely non-superfluid and superfluid phases, respectively, displaying quasi-periodic density modulations, which in addition can exhibit structural and superfluid stripe formation. The onset of such structures is constrained by the onsite interaction and is favourable at fractional densities. Experimental observables are identified and discussed.

Staggered ground states in an optical lattice

“…To gain better control over the longrange terms in an experimental scenario, a suitable combination of interaction processes would be required, i.e multiple attractive and repulsive long-range interactions or a large enough g such that offsite contact terms are possible [8,39]. Alternatively a setup exploiting lightmatter processes to induce synthetic interactions [40][41][42][43][44][45] could potentially be more efficient. However, in order to understand the effects of each process individually in this work, we will consider the parameters of Hamiltonian (8) to be independent variables.…”

Phase diagrams of the disordered Bose-Hubbard model with cavity-mediated long-range and nearest-neighbor interactions

“…In the following, we consider bosons trapped in an optical lattice with both short-range on-site and cavitymediated long-range interactions in the presence of disordered potential. The system is described by the Hamiltonian [32,37,38]:…”

“…In contrast to dipolar interactions which decays as 1/r 3 , cavity-mediated long-range interactions are global, which means that the interaction strength between two bosons does not decay with the distance between them. The ground state phase diagram of the extended BHM with cavitymediated long-range interactions has been investigated extensively with the help of mean-field theory [30][31][32][33][34], Gutzwiller ansatz [35,36], quantum Monte Carlo [33,[36][37][38], Variational Monte-Carlo [39], and exact diagonalization [40,41] in 1D, 2D, and 3D. The results show that by adding cavity-mediated long-range interactions, the extended BHM exhibits a richer phase diagram with additional density wave (DW) and supersolid (SS) phases.…”

The Effect of Disorder on the Phase Diagrams of Hard-Core Lattice Bosons With Cavity-Mediated Long-Range and Nearest-Neighbor Interactions

“…In the absence of disorder, with longrange interactions, the BHM exhibits a richer phase di-agram with additional density wave (DW) and supersolid (SS) phases [35][36][37][38]. The ground state phase diagram of the extended BHM with cavity-mediated longrange interactions has been investigated extensively with the help of mean-field theory [37,[39][40][41][42], Gutzwiller ansatz [38,43], quantum Monte Carlo [36,38,41], and Variational Monte-Carlo [44] methods in 1D, 2D, and 3D. The addition of disorder to the BHM with long-range interactions leads to additional phases.…”

“…The hard-core limit corresponds to large onsite interactions where the occupation of two bosons on the same lattice site is suppressed. The system is described by the Hamiltonian [35][36][37]:…”