Mobile vector soliton in a spin-orbit coupled spin-11 condensate

We study the formation of bound states and three-component bright vector solitons in a quasi-one-dimensional spin-orbit-coupled hyperfine spin $f=1$ Bose-Einstein condensate using numerical solution and variational approximation of a mean-field model. In the antiferromagnetic domain, the solutions are time-reversal symmetric, and the component densities have multi-peak structure. In the ferromagnetic domain, the solutions violate time-reversal symmetry, and the component densities have single-peak structure. The dynamics of the system is not Galelian invariant. From an analysis of Galelian invariance, we establish that the single-peak ferromagnetic vector solitons are true solitons and can move maintaining constant component densities, whereas the antiferromagnetic solitons cannot move with constant component densities

Vector solitons in a spin-orbit coupled spin-22 Bose-Einstein condensate

Five-component minimum-energy bound states and mobile vector solitons of a spin-orbit-coupled quasi-one-dimensional hyperfine-spin-2 Bose-Einstein condensate are studied using the numerical solution and variational approximation of a mean-field model. Two distinct types of solutions with single-peak and multi-peak density distribution of the components are identified in different domains of interaction parameters. From an analysis of Galilean invariance and time-reversal symmetry of the Hamiltonian, we establish that vector solitons with multi-peak density distribution preserve time-reversal symmetry, but cannot propagate maintaining the shape of individual components. However, those with single-peak density distribution violate time-reversal symmetry of the Hamiltonian, but can propagate with a constant velocity maintaining the shape of individual components

Phase separation in a spin-orbit coupled Bose-Einstein condensate

We study a spin-orbit (SO) coupled hyperfine spin-1 Bose-Einstein condensate (BEC) in a quasi-one-dimensional trap. For a SO-coupled BEC in a one-dimensional box, we show that in the absence of the Rabi term, any non-zero value of SO coupling will result in a phase separation among the components for a ferromagnetic BEC, like $^{87}$Rb. On the other hand, SO coupling favors miscibility in a polar BEC, like $^{23}$Na. In the presence of a harmonic trap, which favors miscibility, a ferromagnetic BEC phase separates, provided the SO-coupling strength and number of atoms are greater than some critical value. The Rabi term favors miscibility irrespective of the nature of the spin interaction: ferromagnetic or polar

Spontaneous symmetry breaking in a spin-orbit coupled f=2f=2 spinor condensate

We study the ground-state density profile of a spin-orbit coupled $f=2$ spinor condensate in a quasi-one-dimensional trap. The Hamiltonian of the system is invariant under time reversal but not under parity. We identify different parity- and time-reversal-symmetry-breaking states. The time-reversal-symmetry breaking is possible for degenerate states. A phase separation among densities of different components is possible in the domain of time-reversal-symmetry breaking. Different types of parity- and time-reversal-symmetry-breaking states are predicted analytically and studied numerically. We employ numerical and approximate analytic solutions of a mean-field model in this investigation to illustrate our findings