Solitons in spin-orbit-coupled spin-2 spinor Bose-Einstein condensates

We investigate the different types of matter-wave solitons in spin-orbit-coupled spin-2 spinor Bose-Einstein condensates. Using mean-field theory and adopting the multiscale perturbation method, the original five-component Gross-Pitaevskii spin-orbit-coupled spin-2 spinor Bose-Einstein condensate model can be reduced to a single effective nonlinear Schrödinger equation, which allows us to find analytical soliton solutions of this system. In this way, for different regimes of the spin-orbit coupling, Raman coupling, and interatomic interactions, we find approximate bright and dark soliton solutions. Particularly, the type of solitons depends on the dispersion properties of the system. When the lowest-energy band has a single-well structure, we find there only exist positive mass bright or dark solitons due to the dispersion coefficient of effective nonlinear Shrödinger equation always positive. However, when the lowest-energy band has a double-well structure, there will appear positive (negative) mass bright or dark solitons because the sign of the dispersion coefficient can be positive (negative) under different momentum. We employ direct numerical simulation of the original five-component Gross-Pitaevskii equations to confirm the analytical results.

Figure 1

Quasimomentum $k_m$ corresponding to the minimum of energy (white line) vs $\mathrm{\Omega }$ for (a) $\gamma =1$, (b) $\gamma =3$, (c) $\gamma =5$, (d) $\gamma =7$. The cyan and pink shading region represents $P>0$ and $P<0$, respectively.

Figure 2

The lowest branch of the linear energy spectrum for different Raman frequencies $\mathrm{\Omega }$ with $\gamma =5$.

Figure 3

The (a) group velocity and (b) dispersion coefficient regions for different $k$ in $\gamma -\mathrm{\Omega }$ plane.

Figure 4

Density profiles of the stationary solitons, bright soliton for $\gamma =5,\mathrm{\Omega }=10(\mathrm{\Omega }<{\mathrm{\Omega }}_{*}),k=0,\kappa =0$ in top panels, dark soliton for $\gamma =5,\mathrm{\Omega }=60(\mathrm{\Omega }>{\mathrm{\Omega }}_{*}),k=k_m=0,\theta =0$ in bottom panels, $c_0=1,c_1=0.5,c_2=0.5,{\omega }_0=10,\epsilon =0.1$.

Figure 5

Density profiles of the stationary solitons, bright soliton for $\gamma =5,\mathrm{\Omega }=10(\mathrm{\Omega }<{\mathrm{\Omega }}_{*}),k=k_m=-8,\kappa =0$ for $c_0=1,c_1=-0.5,c_2=-0.5$ in top panels, dark soliton for $\gamma =5,\mathrm{\Omega }=30(\mathrm{\Omega }<{\mathrm{\Omega }}_{*}),k=k_m=-8,\kappa =0$ for $c_0=1,c_1=0.5,c_2=0.5$ in bottom panels, ${\omega }_0=10,\epsilon =0.1$.

Figure 6

Evolution profiles of the moving solitons. Moving bright soliton for $\gamma =5,\mathrm{\Omega }=30(\mathrm{\Omega }<{\mathrm{\Omega }}_{*}),k=-2\ne k_m,\kappa =1,{\omega }_0=10$ in top panel, moving dark soliton for $\gamma =5,\mathrm{\Omega }=60(\mathrm{\Omega }>{\mathrm{\Omega }}_{*}),k=-2\ne k_m,\theta =\pi /10,{\omega }_0=10$ in bottom panel; $c_0=1,c_1=0.5,c_2=0.5,\epsilon =0.1$.