Spin-wave excitation plays important roles in the investigation of the magnetic phases. In this paper, we study the spin-wave excitation spectra of two-component Bose gases with spin–orbit coupling in a deep square optical lattice using the spin-wave theory. We find that, while the excitation spectrum of the vortex crystal phase is gapless with a linear dispersion in the vicinity of the minimum point, the spectra of the commensurate spiral spin phase and the skyrmion crystal phase are gapped. Significantly, the spin fluctuations strongly destabilize the classical ground state of the skyrmion phase with the appearance of an imaginary part in the eigenfrequencies of spin excitations. Such features of the spin excitation spectra provide further insights into the exotic spin phases.
Spin-wave excitation plays important roles in the investigation of the magnetic phases. In this paper, we study the spin-wave excitation spectra of two-component Bose gases with spin–orbit coupling in a deep square optical lattice using the spin-wave theory. We find that, while the excitation spectrum of the vortex crystal phase is gapless with a linear dispersion in the vicinity of the minimum point, the spectra of the commensurate spiral spin phase and the skyrmion crystal phase are gapped. Significantly, the spin fluctuations strongly destabilize the classical ground state of the skyrmion phase with the appearance of an imaginary part in the eigenfrequencies of spin excitations. Such features of the spin excitation spectra provide further insights into the exotic spin phases.
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 study ultracold bosonic atoms with synthetic three-dimensional spin-orbit (SO) coupling in a cubic optical lattice. In the superfluidity phase, the lowest energy band exhibits one, two, or four pairs of degenerate single-particle ground states depending on the SO-coupling strengths, which can give rise to condensate states with spin stripes for weak atomic interactions. In the deep Mott-insulator regime, the effective spin Hamiltonian of the system combines three-dimensional Heisenberg exchange interactions, anisotropy interactions, and Dzyaloshinskii-Moriya interactions. Based on Monte Carlo simulations, we numerically demonstrate that the resulting Hamiltonian with an additional Zeeman field has a rich phase diagram with spiral, stripe, vortex crystal, and especially Skyrmion crystal spin textures in each xy-plane layer. The obtained Skyrmion crystals can be tunable with square and hexagonal symmetries in a columnar manner along the z axis, and moreover are stable against the interlayer spin-spin interactions in a large parameter region.
We investigate the ground-state properties of Bose-Bose mixtures with Rashba-type spin-orbit (SO) coupling in a square lattice. The system displays rich physics from the deep Mott insulator (MI) all the way to the superfluid (SF) regime. In the deep MI regime, exotic spin-ordered phases arise due to the effective Dzyaloshinskii-Moriya type of superexchange interactions. By employing the nonperturbative bosonic dynamical mean-field theory (BDMFT), we numerically study and establish the stability of these magnetic phases against increasing hopping amplitude. We show that as hopping is increased across the MI to SF transition, exotic superfluid phases with magnetic textures emerge. In particular, we identify an exotic spin-spiral magnetic texture with spatial period 3 in the superfluid close to the MI-SF transition.
We investigate the ground state of two-dimensional Bose-Einstein condensates with Rashba spin-orbit coupling in square optical lattices and demonstrate the existence of rich phases with different lattice structures, which is closely related to the degenerate structure of single particle energy spectrum induced by the competition of spin-orbit coupling and optical lattices. We find that the ground state is in the phase with either parity-time-reversal or parity symmetry by direct numerical simulation. We show the phase diagram of ground state in the whole regime of spin-orbit coupling strength, and particularly find that the system supports multi-fold vortex lattices, in which ground state holds half-quantum vortex lattices, vortex-antivortex pair lattices and fundamental vortex lattices, simultaneously, when single particle energy minimums touch the boundary of the first Brillouin zone.
We study the ground-state phases of two-dimensional spin-orbit coupled spin-2 Bose-Einstein condensates in a one-dimensional spin-dependent optical lattice. Due to the competition among optical lattice, spin-orbit coupling and spin-exchange interaction, the exotic ground-state phases are found, i.e. three types of the stripe phases and three types of the supersolid phases. The spin-exchange interaction can adjust the direction of the stripe in the stripe phase and generate various vortex lattice structures in the supersolid phase, which shows that the spin-exchange interaction plays an important role in the formation of the stripe and supersolid phases of spin-orbit coupled spin-2 Bose-Einstein condensates in an optical lattice.
We study the physics of interacting spin-1 bosons in an optical lattice using a variational Gutzwiller technique. We compute the mean-field ground state wave function and discuss the evolution of the condensate, spin, nematic, and singlet order parameters across the superfluid-Mott transition. We then extend the Gutzwiller method to derive the equations governing the dynamics of low energy excitations in the lattice. Linearizing these equations, we compute the excitation spectra in the superfluid and Mott phases for both ferromagnetic and antiferromagnetic spin-spin interactions. In the superfluid phase, we recover the known excitation spectrum obtained from Bogoliubov theory. In the nematic Mott phase, we obtain gapped, quadratically dispersing particle and hole-like collective modes, whereas in the singlet Mott phase, we obtain a nondispersive gapped mode, corresponding to the breaking of a singlet pair. For the ferromagnetic Mott insulator, the Gutzwiller mean-field theory only yields particle-hole-like modes but no Goldstone mode associated with long-range spin order. To overcome this limitation, we supplement the Gutzwiller theory with a Schwinger boson mean-field theory which captures superexchange-driven fluctuations. In addition to the gapped particle-hole-like modes, we obtain a gapless quadratically dispersing ferromagnetic spin-wave Goldstone mode. We discuss the evolution of the singlet gap, particle-hole gap, and the effective mass of the ferromagnetic Goldstone mode as the superfluid-Mott phase boundary is approached from the insulating side. We discuss the relevance and validity of Gutzwiller mean-field theories to spinful systems, and potential extensions of this framework to include more exotic physics which appears in the presence of spin-orbit coupling or artificial gauge fields.