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Physical Review Research

Phases, instabilities and excitations in a two-component lattice model with photon-mediated interactions

Leon Carl, Rodrigo Rosa-Medina, Sebastian D. Huber, Tilman Esslinger, Nishant Dogra, Tena Dubček

Published Jul 11, 2023• 10 citations
Publisher

Abstract

A comprehensive overview of the phase diagram, transitions, and low-energy excitations in a two-component spin Bose-Hubbard system with photon-mediated interactions is provided. The system features emergent antiferromagnetic ordered phases, stabilized by the interplay of short- and global-range interactions, and spin-exchange excitations with a tunable gap. It can be readily realized in cold-atom experiments with optical cavities.

DOI
10.1103/physrevresearch.5.l032003

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A comprehensive overview of the phase diagram, transitions, and low-energy excitations in a two-component spin Bose-Hubbard system with photon-mediated interactions is provided. The system features emergent antiferromagnetic ordered phases, stabilized by the interplay of short- and global-range interactions, and spin-exchange excitations with a tunable gap. It can be readily realized in cold-atom experiments with optical cavities.
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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.
We analyze the quantum phases of multicomponent Bose-Hubbard models in optical superlattices based on a mean-field method, that is, the decoupling approximation. The global phase diagrams exhibit complex patterns with various charge-density-wave orders for both one- and two-component cases. We further calculate the effective spin excitations for the two-component case in the strong-coupling region at unit filling, and show the existence of a spin-density-wave order. The results of our study can be tested straightforwardly with current cold-atom experimental techniques.
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Advances in pure optical trapping techniques now allow the creation of degenerate Bose gases with internal degrees of freedom. Systems such as 87Rb,39K^{87}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}^{39}\mathrm{K}87Rb,39K, or 23Na^{23}\mathrm{Na}23Na in the F=1F=1F=1 hyperfine state offer an ideal platform for studying the interplay of superfluidity and quantum magnetism. Motivated by the experimental developments, we study ground-state phases of a two-component Bose gas loaded on an optical lattice. The system is described effectively by the Bose-Hubbard Hamiltonian with on-site and near-neighbor spin-spin interactions. An important feature of our investigation is the inclusion of interconversion (spin-flip) terms between the two species, which has been observed in optical lattice experiments. Using mean-field theory and quantum Monte Carlo simulations, we map out the phase diagram of the system. A rich variety of phases is identified, including antiferromagnetic (AF) Mott insulators and ferromagnetic and AF superfluids.
Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin et al., Nature (London) 609, 485 (2022)], we study a one-dimensional version of the two-component extended Bose-Hubbard model via the density-matrix renormalization group method. By using the nearest-neighbor and on-site interaction parameters from the experiment, we start by mapping the quantum phase diagram in the hopping parameter ${t}_{A}\text{\ensuremath{-}}{t}_{B}$ plane with boson densities ${\ensuremath{\rho}}_{A}={\ensuremath{\rho}}_{B}=1/2$. In addition to the density-wave phase reported in the experiment, we find several regimes of superfluidity when one or both hopping parameters are large enough, and interestingly there is a supercounterfluid phase at moderate and comparable hopping parameters. The universality classes of these phase transitions are analyzed from the correlation functions, excitation gaps, and entanglement entropy. In particular, a Berezinskii-Kosterlitz-Thouless type is recognized for several gapped-to-gapless transitions. In addition, we also study the quantum phase transitions by varying ${\ensuremath{\rho}}_{B}$ from 0 to 1 while keeping ${\ensuremath{\rho}}_{A}=1/2$. We identify a supersolid phase in a wide range of $1/2<{\ensuremath{\rho}}_{B}<1$. Our work paves the way for realizing exotic many-body phases in cold-atom experiments upon proper tuning of experimental parameters.