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arXiv:1503.08605 · Physical Review A

Nonequilibrium dynamics of spin-orbit-coupled lattice bosons

H. T. Ng

Published Oct 30, 2015• 6 citations
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Abstract

We study the nonequilibrium dynamics of two-component bosonic atoms in a one-dimensional optical lattice in the presence of spin-orbit coupling. In the Mott-insulating regime, the two-component bosonic system at unity filling can be described by the quantum spin $XXZ$ model. The atoms are initially prepared in their lower spin states. The system becomes out of equilibrium by suddenly introducing spin-orbit coupling to the atoms. The system shows the relaxation and nonstationary dynamics, respectively, in the different interaction regimes. We find that the time average of magnetization is useful to characterize the many-body dynamics. The effects of even and odd numbers of sites are discussed. Our result sheds light on nonequilibrium dynamics due to the interplay between spin-orbit coupling and atomic interactions.

DOI
10.1103/physreva.92.043634

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We study the nonequilibrium dynamics of two-component bosonic atoms in a one-dimensional optical lattice in the presence of spin-orbit coupling. In the Mott-insulating regime, the two-component bosonic system at unity filling can be described by the quantum spin XXZXXZXXZ model. The atoms are initially prepared in their lower spin states. The system becomes out of equilibrium by suddenly introducing spin-orbit coupling to the atoms. The system shows the relaxation and nonstationary dynamics, respectively, in the different interaction regimes. We find that the time average of magnetization is useful to characterize the many-body dynamics. The effects of even and odd numbers of sites are discussed. Our result sheds light on nonequilibrium dynamics due to the interplay between spin-orbit coupling and atomic interactions.
Spin-orbit-coupled bosons can exhibit rich equilibrium phases at low temperature and in the presence of particle-particle interactions. In the case with a 1D synthetic spin-orbit interaction, it has been observed that the ground state of a Bose gas can be a normal phase, stripe phase, or magnetized phase in different parameter regimes. The magnetized states are doubly degenerate and consist of a many-particle two-state system. In this work, we investigate the nonequilibrium quantum dynamics by switching on a simple one-dimensional optical lattice potential as external perturbation to induce resonant couplings between the magnetized phases, and predict a quantum spin dynamics which cannot be obtained in the single-particle systems. In particular, due to particle-particle interactions, the transition of the Bose condensate from one magnetized phase to the other is forbidden when the external perturbation strength is less than a critical value, and a full transition can occur only when the perturbation exceeds such critical strength. This phenomenon manifests itself a dynamical phase transition, with the order parameter defined by the time-averaged magnetization over an oscillation period, and the critical point behavior being exactly solvable. The thermal fluctuations are also considered in detail. From numerical simulations and exact analytic studies we show that the predicted many-body effects can be well observed with the current experiments.
Motivated by recent experiments on trapped ultracold bosonic atoms in an optical lattice potential, we consider the nonequilibrium dynamic properties of such bosonic systems for a number of experimentally relevant situations. When the number of bosons per lattice site is large, there is a wide parameter regime where the effective boson interactions are strong, but the ground state remains a superfluid (and not a Mott insulator): we describe the conditions under which the dynamics in this regime can be described by a discrete Gross-Pitaevskii equation. We describe the evolution of the phase coherence after the system is initially prepared in a Mott insulating state, and then allowed to evolve after a sudden change in parameters places it in a regime with a superfluid ground state. We also consider initial conditions with a ``\ensuremath{\pi} phase'' imprint on a superfluid ground state (i.e., the initial phases of neighboring wells differ by \ensuremath{\pi}), and discuss the subsequent appearance of the density wave order and ``Schr\"odinger cat,'' i.e., macroscopic quantum interference, states.
Motivated by recent experimental advances, we study two-component spin-orbit coupled ultracold bosonic atoms in two dimensions on a square optical lattice. Using a Bose-Hubbard model with spin-conserving and non-spin-conserving nearest neighbour hoppings and spin-dependent on-site density-density interaction, our goal is to characterize phase separation and spin structure in the weakly interacting and deep Mott regimes. \nFor the weakly coupled regime, we decouple interactions through a real space uniform density mean field theory. At zero temperature, this gives an analytic condition for the phase separation transition driven by inter- relative to intracomponent interaction. Solving the self-consistent equations at finite temperature reveals entropic remixing in the phase separated regime and a more surprising entropy driven phase separation in the mixed regime. This is a consequence of complex interplay between interaction and spin-orbit coupling, and can be explained through the effect of component imbalance on the effective single-particle dispersion relation. We also provide an alternate explanation based on thermal occupation of eigenstates with a characteristic imbalance.\nIn the strongly interacting Mott regime, we derive an effective spin Hamiltonian describing the magnetic phases of the Mott insulator. The competition between anisotropic {Heisenberg} and Dzyaloshinskii-Moriya interactions gives rise to various ferromagnetic, antiferromagnetic, spiral, stripe, vortex, and skyrmion phases. On basis of classical Monte-Carlo simulations in the literature, we reconstruct the phase diagram with a classical variational approach, while magnon excitation spectra and quantum fluctuations are calculated with Holstein-Primakoff transformation and subsequent spin wave expansion. The analysis shows that states with ferromagnetic or antiferromagnetic ordering of boson species are protected against thermal fluctuations by a gap, and well described by classical states. States with equal superposition of boson species at each lattice site are subject to relatively large quantum fluctuations, which may cause breakdown of the states within their classical parameter space regions. The dispersion relations are gapless and linear around the minima to lowest order in the spin wave expansion.
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 ttt 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 investigate properties of an ultracold, two-component bosonic gas in a square optical lattice at unit filling. In addition to density-density interactions, the atoms are subject to coherent light-matter interactions that couple different internal states. We examine the influence of this coherent coupling on the system and its quantum phases by using Gutzwiller mean-field theory as well as bosonic dynamical mean-field theory. We find that the interplay of strong interspecies repulsion and coherent coupling affects the Mott insulator to superfluid transition and shifts the tip of the Mott lobe toward higher values of the tunneling amplitude. In the strongly interacting Mott regime, the resulting Bose-Hubbard model can be mapped onto an effective spin Hamiltonian that offers additional insights into the observed phenomena.
We study the topological phases in spin-orbit-coupled dipolar bosons in a one-dimensional optical lattice. The magnetic dipolar interactions between atoms give rise to intersite interactions. In the Mott-insulating regime, this system can be described by the quantum XYZ spin model with Dzyaloshinskii-Moriya interactions in a transverse field. We focus on investigating the effect of dipolar interactions on the topological phase. The topological phase can be shown when spin-orbit coupling combines with the repulsive dipolar interaction. We find that the dipolar interaction can broaden the range of parameters of spin-orbit coupling and transverse field for exhibiting the topological phase. The sum of spin correlations between the two nearest-neighboring atoms can be used to indicate the topological phase. This may be useful for detecting topological phases in experiments.