Bright solitons in a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate

Abstract

We study a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate with repulsive contact interactions by both the variational method and the imaginary time evolution of the GrossPitaevskii equation. The dipoles are completely polarized along one direction in the 2D plane to provide an effective attractive dipole-dipole interaction. We find two types of solitons as the ground states arising from such attractive dipole-dipole interactions: a plane wave soliton with a spatially varying phase and a stripe soliton with a spatially oscillating density for each component. Both types of solitons possess smaller size and higher anisotropy than the soliton without spin-orbit coupling. Finally, we discuss the properties of moving solitons, which are nontrivial because of the violation of Galilean invariance.

Magnetic stripe soliton and localized stripe wave in spin-1 Bose-Einstein condensates

“…is a bright soliton in the parameter region g0+g2 BEC [37][38][39][40]. The stripe solitons for spin states |↑ and |↓ are formed by the superposition of such bright-dark solitons at two band minima, leading to strong out-ofphase density modulations for two states, as shown in Fig.…”

“…Localized stripe wave-In stripe solitons discussed in either spin-1/2 BEC [37][38][39][40] or above magnetic stripe soliton, the striped density modulation resides on a bright or dark soliton background. Here such density background is given by |U | 2 + |V | 2 , which can be tuned to be uniform by the spin-dependent interaction γ, therefore the stripe soliton for states |↑ and |↓ is neither bright nor dark, but a localized stripe wave.…”

“…The recent experimental realization of spin-orbit coupling for ultracold atoms [21][22][23][24][25][26][27][28][29][30][31][32][33] opens a new avenue for exploring soliton physics through engineering atomic band dispersions [34][35][36][37][38][39][40]. In a spin-1/2 BEC, the spinorbit coupling displays a double well band dispersion, and the simultaneous occupation of two momentum space minima opens the possibility for generating solitons with internal spatial structures, i.e., the stripe density modulation [37][38][39][40]. However, the intrinsic Raman coupling for the realization of spin-orbit coupling mixes two spin states, which demands the same spatial density for different spins, therefore only certain types of stripe solitons such as bright-bright or dark-dark can exist [37][38][39][40].…”

“…In a spin-1/2 BEC, the spinorbit coupling displays a double well band dispersion, and the simultaneous occupation of two momentum space minima opens the possibility for generating solitons with internal spatial structures, i.e., the stripe density modulation [37][38][39][40]. However, the intrinsic Raman coupling for the realization of spin-orbit coupling mixes two spin states, which demands the same spatial density for different spins, therefore only certain types of stripe solitons such as bright-bright or dark-dark can exist [37][38][39][40]. A natural question is whether general types of stripe solitons, such as magnetic stripe solitons (dark-bright or dark-antidark types) could be generated by tuning the band dispersion beyond that for spin-1/2 spin-orbit coupling.…”

Formation, stability, and dynamics of vector bright solitons in a trapless Bose–Einstein condensate with spin–orbit coupling

“…For the non-interacting system (g=0) with SOC, we gradually switch on the SOC and simultaneously switch off the external potential according to the ramp function given by equation (5). It is observed that the two matter-wave packages are always spatially separated, showing phase separation along y-direction, which is similar to the SOcoupled dipolar BEC [50]. With time going on, the initially solitary-like wave packets are unstable and spread out gradually, accompanied by weak excitations, as shown in figure 1 for κ(t)=0.5f (t).…”