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Physical Review A

Two-component lattice bosons with cavity-mediated long-range interaction

Xin Guan, Jingtao Fan, Xiaofan Zhou, Gang Chen, Suotang Jia

Published Jul 15, 2019• 9 citations
Publisher

Abstract

In this paper, we consider a two-component atomic Bose lattice gas inside an optical cavity to explore a competition between the short-range collisional and cavity-mediated long-range interactions. Utilizing a self-consistent mean-field approach, we map out the ground-state phase diagrams showing the superfluid, lattice supersolid, Mott insulator, and spin-density wave phases. Unlike its single-component analog, this lattice supersolid is here characterized by the coexistence of the superfluid and the spin-density wave. Moreover, for the relatively small long-range interaction, the phase diagrams exhibit a correspondence between the parity of the lattice filling number and the spin imbalance. Finally, we propose how to detect the different quantum phases under current experimental setups.

DOI
10.1103/physreva.100.013617

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In this paper, we consider a two-component atomic Bose lattice gas inside an optical cavity to explore a competition between the short-range collisional and cavity-mediated long-range interactions. Utilizing a self-consistent mean-field approach, we map out the ground-state phase diagrams showing the superfluid, lattice supersolid, Mott insulator, and spin-density wave phases. Unlike its single-component analog, this lattice supersolid is here characterized by the coexistence of the superfluid and the spin-density wave. Moreover, for the relatively small long-range interaction, the phase diagrams exhibit a correspondence between the parity of the lattice filling number and the spin imbalance. Finally, we propose how to detect the different quantum phases under current experimental setups.
A high-finesse optical cavity allows the establishment of long-range interactions between bosons in an optical lattice when most cold-atom experiments are restricted to short-range interactions. Supersolid phases have recently been experimentally observed in such systems. Using both exact quantum Monte Carlo simulations and the Gutzwiller approximation, we study the ground-state phase diagrams of a two-dimensional Bose-Hubbard model with infinite-range interactions which describes such experiments. In addition to superfluid and insulating Mott phases, the infinite-range checkerboard interactions introduce charge-density waves and supersolid phases. We study here the system at various particle densities, elucidate the nature of the phases and quantum phase transitions, and discuss the stability of the phases with respect to phase separation. In particular we confirm the existence and stability of a supersolid phase detected experimentally.
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 wavelength 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 wavelengths, 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, nonsuperfluid and superfluid phases, respectively, displaying quasiperiodic density modulations, which in addition can exhibit structural and superfluid stripe formation. The onset of such structures is constrained by the on-site interaction and is favorable at fractional densities. Experimental observables are identified and discussed.
Motivated by experiments performed by Landig et al. [Nature (London) 532, 476 (2016)], we consider a two-dimensional Bose gas in an optical lattice, trapped inside a single mode superradiant Fabry-Perot cavity. The cavity mediates infinite-range checkerboard interactions between the atoms, which produces competition between Mott insulator, charge-density wave, superfluid, and supersolid phases. We calculate the phase diagram of this Bose gas in a homogeneous system and in the presence of a harmonic trap.
We consider bosonic atoms loaded into optical lattices with cavity-mediated infinite-range interactions. Competing short- and global-range interactions cultivate a rich phase diagram. With a systematic field-theoretical perspective, we present an analytical construction of a global ground-state phase diagram. We find that the infinite-range interaction enhances the fluctuation of the number density. In the strong-coupling regime, we find four branches of elementary excitations, with two being ``particlelike'' and two being ``holelike,'' and that the excitation gap becomes soft at the phase boundary between compressible phases and incompressible phases. We derive an effective theory describing compressible superfluid and supersolid states. To complement this perturbative study, we construct a self-consistent mean-field theory and find numerical results consistent with our theoretical analysis. We map out the phase diagram and find that a charge density wave may undergo a structure phase transition to a different charge density wave before it finally enters into the supersolid phase driven by increasing the hopping amplitude.
We numerically simulate strongly correlated ultracold bosons coupled to a high-finesse cavity field, pumped by a laser beam in the transverse direction. Assuming a weak classical\mathit{classical}classical optical lattice added in the cavity direction, we model this system by a generalized Bose-Hubbard model, which is solved by means of bosonic dynamical mean-field theory. The complete phase diagram is established, which contains two novel self-organized quantum phases, lattice supersolid and checkerboard solid, in addition to conventional phases such as superfluid and Mott insulator. At finite but low temperature, thermal fluctuations are found to enhance the buildup of the self-organized phases. We demonstrate that cavity-mediated long-range interactions can give rise to stable lattice supersolid and checkerboard solid phases even in the regime of strong sss-wave scattering. In the presence of a harmonic trap, we discuss coexistence of these self-organized phases, as relevant to experiments.
Engineering long-range interacting spin systems with ultra cold atoms offers the possibility to explore exotic magnetically ordered phases in strongly-correlated scenarios. Quantum gases in optical cavities provide a versatile experimental platform to further engineer photon-mediated interactions and access the underlying microscopic processes by probing the cavity field. Here, we study a two-component spin Bose-Hubbard system with cavity-mediated interactions. We provide a comprehensive overview of its phase diagram and transitions in experimentally relevant regimes. The interplay of different energy scales yields a rich phase diagram with superfluid and insulating phases exhibiting density modulation or spin ordering. In particular, the combined effect of contact and global-range interactions gives rise to an antiferromagnetically ordered phase for arbitrarily small spin-dependent light-matter coupling, while long-range and inter-spin contact interactions introduce regions of instability and phase separation in the phase diagram. We further study the low energy excitations above the antiferrogmagnetic phase. Besides particle-hole branches, it hosts spin-exchange excitations with a tunable energy gap. The studied lattice model can be readily realized in cold-atom experiments with optical cavities.