We study ultracold bosons in three dimensions with an anisotropic Rashba-Dresselhaus spin-orbit coupling. We first carry out the exact summation of ladder diagrams for the two-boson
t matrix at zero energy. Then, with the
t matrix as the effective interaction, we find the ground-state phase diagrams of bosons in mean field as a function of the spin-orbit coupling, the anisotropy, and the scattering lengths between particles in the same and in different pseudospin states. The resulting phase diagrams have much richer structures than those obtained using mean-field couplings, exhibiting three different phases: a plane-wave condensate, a striped condensate, and an unstable phase. The differences between the present approach using the
t matrix compared to using mean-field couplings is significant for large scattering lengths, large spin-orbit-coupling strength, or small anisotropy.
In recent experiments, spin-orbit-coupled (SOC) bosonic gases in an optical lattice have been successfully prepared into any Bloch band [Hamner et al., Phys. Rev. Lett. 114, 070401 (2015)], which promises a viable contender in the competitive field of simulating gauge-related phenomena. However, the ground-state phase diagram of such systems in the superfluid regime is still lacking. Here we present a detailed study of the phase diagram in an optically trapped Bose gas with equal-weight Rashba and Dresselhaus SO coupling. We identify four different quantum phases, which include three normal phases and a mixed phase, by considering the wave vector
k1, the longitudinal $\ensuremath{\langle}{\ensuremath{\sigma}}_{z}\ensuremath{\rangle}$, and the transverse $\ensuremath{\langle}{\ensuremath{\sigma}}_{x}\ensuremath{\rangle}$ spin polarizations as three order parameters. The ground state of normal phases is a Bloch wave with a single wave vector
k1, which can position in arbitrary regions in the Brillouin zone. By contrast, the ground state of the mixed phase is a superposition of two Bloch waves with opposite
k1, which, remarkably, may lack periodicity even though the system's Hamiltonian is periodic. This mixed phase in the lattice setting can be seen as the counterpart of the stripe phase associated with the uniform SOC gas. Furthermore, due to the lattice-renormalized SOC, the phase diagram of the model system becomes significantly different from the uniform case when the lattice strength grows. Finally, a scheme for experimentally probing the mixed phase using Bragg spectroscopy is proposed.
We consider a spin-orbit coupled configuration of spin-1/2 interacting bosons with equal Rashba and Dresselhaus couplings. The phase diagram of the system at T=0 is discussed with special emphasis on the role of the interaction treated in the mean-field approximation. For a critical value of the density and of the Raman coupling we predict the occurrence of a characteristic tricritical point separating the spin mixed, the phase separated, and the zero momentum states of the Bose gas. The corresponding quantum phases are investigated analyzing the momentum distribution, the longitudinal and transverse spin polarization, and the emergence of density fringes. The effect of harmonic trapping as well as the role of the breaking of spin symmetry in the interaction Hamiltonian are also discussed.
We use the mean-field theory to analyze the ground-state phase diagrams of spin-orbit-coupled mass-imbalanced Fermi gases throughout the BCS-BEC evolution, including both the population-balanced and -imbalanced systems. Our calculations show that the competition between the mass and population imbalance and the Rashba-type spin-orbit coupling gives rise to very rich phase diagrams, involving normal, superfluid, and phase-separated regions. In addition, we find quantum phase transitions between the topologically trivial gapped superfluid and the nontrivial gapless superfluid phases, opening the way for the experimental observation of exotic phenomena with cold atom systems.