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arXiv:1912.06142 · Physical Review Research

Strongly interacting spin-orbit coupled Bose-Einstein condensates in one dimension

Siddhartha Saha, E. J. König, Junhyun Lee, J. H. Pixley

Published Mar 4, 2020• 9 citations
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Abstract

This work theoretically studies spin-1 bosons with antiferromagnetic interactions and synthetic spin-orbit coupling in a one-dimensional lattice, showing the appearance of a robust superfluid spin-liquid phase and a correlated charge density wave. Signatures of these states can be observed in ultracold gases of ${}^{23}$Na in an optical lattice within experimentally accessible parameters.

DOI
10.1103/physrevresearch.2.013252

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Ultracold bosons in optical lattices are one of the few systems where bosonic matter is known to exhibit strong correlations. Here we push the frontier of our understanding of interacting bosons in optical lattices by adding synthetic spin-orbit coupling, and show that new kinds of density- and chiral-orders develop. The competition between the optical lattice period and the spin-orbit coupling length - which can be made comparable in experiments - along with the spin hybridization induced by a transverse field (i.e., Rabi coupling) and interparticle interactions create a rich variety of quantum phases including uniform, non-uniform and phase-separated superfluids, as well as Mott insulators. The spontaneous symmetry breaking phenomena at the transitions between them are explained by a two-order-parameter Ginzburg-Landau model with multiparticle umklapp processes. Finally, in order to characterize each phase, we calculated their experimentally measurable crystal momentum distributions. PACS numbers: 67.85.-d,67.85.Hj,67.85.Fg.
The internal degrees of freedom provided by ultracold atoms provide a route for realizing higher dimensional physics in systems with limited spatial dimensions. Nonspatial degrees of freedom in these systems are dubbed ``synthetic dimensions.'' This connection is useful from an experimental standpoint but complicated by the fact that interactions alter the condensate ground state. Here we use the Gross-Pitaevskii equation to study the ground-state properties of a spin-1 Bose gas under the combined influence of an optical lattice, spatially varying spin-orbit coupling, and interactions at the mean-field level. The associated phases depend on the sign of the spin-dependent interaction parameter and the strength of the spin-orbit field. We find ``charge''- and spin-density-wave phases which are directly related to helical spin order in real space and affect the behavior of edge currents in the synthetic dimension. We determine the resulting phase diagram as a function of the spin-orbit coupling and spin-dependent interaction strength, considering both attractive (ferromagnetic) and repulsive (polar) spin-dependent interactions, and we provide a direct comparison of our results with the noninteracting case. Our findings are applicable to current and future experiments, specifically with 87Rb,7Li,41K^{87}\mathrm{Rb}, ^{7}\mathrm{Li}, ^{41}\mathrm{K}87Rb,7Li,41K, and 23Na^{23}\mathrm{Na}23Na.
We study the interplay between large-spin, spin-orbit coupling, and superfluidity for bosons in a two-dimensional optical lattice, focusing on the spin-1 spin-orbit-coupled system recently realized at the Joint Quantum Institute [Campbell et al., arXiv:1501.05984]. We find a rich quantum phase diagram where, in addition to the conventional phases---superfluid and insulator---contained in the spin-1 Bose-Hubbard model, there are new lattice symmetry breaking phases. For weak interactions, the interplay between two length scales, the lattice momentum and the spin-orbit wave vector, induce a phase transition from a uniform superfluid to a phase where bosons simultaneously condense at the center and edge of the Brillouin zone at a nonzero spin-orbit strength. This state is characterized by spin-density-wave order, which arises from the spin-1 nature of the system. Interactions suppress spin-density-wave order, and favor a superfluid only at the Brillouin zone edge. This state has spatially oscillating mean-field order parameters, but a homogeneous density. We show that the spin-density-wave superfluid phase survives in a two-dimensional harmonic trap, and thus establish that our results are directly applicable to experiments on 87Rb,7Li^{87}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}^{7}\mathrm{Li}87Rb,7Li, and 41K^{41}\mathrm{K}41K.
Recently spin-orbit (SO)-coupled superfluids in free space or harmonic traps have been extensively studied, motivated by the recent experimental realization of SO coupling for Bose-Einstein condensates (BEC). However, the rich physics of SO-coupled BEC in optical lattices has been largely unexplored. In this paper, we show that in a suitable parameter region the lowest Bloch state forms an isolated flat band in a one-dimensional SO-coupled optical lattice, which thus provides an experimentally feasible platform for exploring the recently celebrated topological flatband physics in lattice systems. We show that the flat band is preserved even with the mean-field interaction in BEC. We investigate the superfluidity of the BEC in SO-coupled lattices through dynamical and Landau stability analysis, and show that the BEC is stable on the whole flat band.
Synthetic spin-orbit coupling in ultracold atomic gases can be taken to extremes rarely found in solids. We study a two dimensional Hubbard model of bosons in an optical lattice in the presence of spin-orbit coupling strong enough to drive direct transitions from Mott insulators to superfluids. Here we find phase-modulated superfluids with finite momentum that are generated entirely by spin-orbit coupling. We investigate the rich phase patterns of the superfluids, which may be directly probed using time-of-flight imaging of the spin-dependent momentum distribution.