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arXiv:1403.1316 · Physical Review B

Evolution of magnetic structure driven by synthetic spin-orbit coupling in a two-component Bose-Hubbard model

Jize Zhao, Shijie Hu, Jun Chang, Fawei Zheng, Ping Zhang, Xiaoqun Wang

Published Aug 13, 2014• 26 citations

Abstract

We study the evolution of magnetic structures driven by a synthetic spin-orbit coupling in a one-dimensional two-component Bose-Hubbard model. In addition to the Mott insulator-superfluid transition, in the Mott insulator phases we found a transition from a gapped ferromagnetic phase to a gapless chiral phase by increasing the strength of the spin-orbit coupling. Further increasing the spin-orbit coupling drives a transition from the gapless chiral phase to a gapped antiferromagnetic phase. These magnetic structures persist in superfluid phases. In particular, in the chiral Mott insulator and chiral superfluid phases, incommensurability is observed in characteristic correlation functions. These unconventional Mott insulator phase and superfluid phase demonstrate the different effects arising from the competition between the kinetic energy and the spin-orbit coupling.

DOI: 10.1103/physrevb.90.085117

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We study the evolution of magnetic structures driven by a synthetic spin-orbit coupling in a one-dimensional two-component Bose-Hubbard model. In addition to the Mott insulator-superfluid transition, in the Mott insulator phases we found a transition from a gapped ferromagnetic phase to a gapless chiral phase by increasing the strength of the spin-orbit coupling. Further increasing the spin-orbit coupling drives a transition from the gapless chiral phase to a gapped antiferromagnetic phase. These magnetic structures persist in superfluid phases. In particular, in the chiral Mott insulator and chiral superfluid phases, incommensurability is observed in characteristic correlation functions. These unconventional Mott insulator phase and superfluid phase demonstrate the different effects arising from the competition between the kinetic energy and the spin-orbit coupling.

We study the effect of the synthetic spin-orbit coupling in a two-component Bose-Hubbard model in one dimension by employing the density-matrix renormalization group method. A ferromagnetic long-range order emerges in both Mott-insulator and superfluid phases resulting from the spontaneous breaking of the

{Z}_{2}

symmetry, when the spin-orbit coupling term becomes comparable to the hopping kinetic energy and the intercomponent interaction is smaller than the intracomponent one as well. This effect is expected to be detectable with the present realization of the synthetic spin-orbit coupling in experiments.

We investigate magnetic properties in the superfluid and Mott-insulating states of two-component bosons with spin-orbit (SO) coupling in two-dimensional square optical lattices. The spin-independent hopping integral

t

and SO coupled one $\ensuremath{\lambda}$ are fitted from band-structure calculations in the continuum, which exhibit oscillations with increasing SO coupling strength. The magnetic superexchange model is derived in the Mott-insulating state with one particle per site, characterized by the Dzyaloshinsky-Moriya interaction. In the limit of $|\ensuremath{\lambda}|\ensuremath{\ll}|t|$, we find a spin spiral Mott state whose pitch value is the same as that in the incommensurate superfluid state, while in the opposite limit $|t|\ensuremath{\ll}|\ensuremath{\lambda}|$, the ground state exhibits a $2\ifmmode\times\else\texttimes\fi{}2$ in-plane spin pattern.

We consider a square optical lattice in two dimensions and study the effects of both the strength and symmetry of spin-orbit coupling and Zeeman field on the ground-state, i.e., Mott-insulator (MI) and superfluid (SF), phases and phase diagram, i.e., MI-SF phase-transition boundary, of the two-component Bose-Hubbard model. In particular, based on a variational Gutzwiller ansatz, our numerical calculations show that the spin-orbit-coupled SF phase is a nonuniform (twisted) one, with its phase (but not the magnitude) of the order parameter modulating from site to site. Fully analytical insights into the numerical results are also given.

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.

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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.