In this paper we study the scattering of solitons in a binary Bose-Einstein Condensate (BEC) including SO- and Rabi-couplings. To this end, we derive a reduced ODE model in view to provide a variational description of the collisional dynamics. Also, we assume negative intra- and inter-component interaction strengths, such that one obtains localized solutions even in absence of external potentials. By performing extensive numerical simulations of this model we observe that, for specific conditions, the final propagation velocity of the scattered solitons could be highly sensitive to small changes in the initial conditions, being a possible signature of chaos. Additionally, there are infinitely many intervals of regularity emerging from the obtained chaotic-like regions and forming a fractal-like structure of reflection/transmission windows. Finally, we investigate how the value of the spin-orbit coupling strength changes the critical velocities, which are minimum/maximum values for the occurrence of solitons bound-states, as well as the fractal-like structure.
In this paper we study the scattering of solitons in a binary Bose-Einstein Condensate (BEC) including SO- and Rabi-couplings. To this end, we derive a reduced ODE model in view to provide a variational description of the collisional dynamics. Also, we assume negative intra- and inter-component interaction strengths, such that one obtains localized solutions even in absence of external potentials. By performing extensive numerical simulations of this model we observe that, for specific conditions, the final propagation velocity of the scattered solitons could be highly sensitive to small changes in the initial conditions, being a possible signature of chaos. Additionally, there are infinitely many intervals of regularity emerging from the obtained chaotic-like regions and forming a fractal-like structure of reflection/transmission windows. Finally, we investigate how the value of the spin-orbit coupling strength changes the critical velocities, which are minimum/maximum values for the occurrence of solitons bound-states, as well as the fractal-like structure.
We present the numerical results of the structure and dynamics of the self-bound ground state arising solely because of the presence of beyond-mean-field quantum fluctuation in spin-orbit- (SO-) coupled binary Bose-Einstein condensates in one dimension. We obtain an analytical soliton solution for nonzero SO coupling that matches quite well with the numerical results. Further, we investigate the dynamical stability of these solitons by adopting three protocols, such as (i) adding initial velocity to each component, (ii) quenching the SO- and Rabi-coupling parameters at initial and finite time, and (iii) allowing collision between the two spin components by giving equal and opposite direction velocity to them. For small velocity perturbation, the soliton has the presence of the breathing oscillation, while large velocity perturbations transform the soliton into moving solitons. The maximum breathing frequency exhibits power-law dependence on the Rabi-coupling frequency with an exponent $\ensuremath{\sim}0.16$. The quenching of SO and Rabi couplings results in several interesting dynamical features, such as dynamical phase transition from plane to stripe phase, dynamical flipping of the spin state, and secondary solitonic modes. In the absence of the SO and Rabi couplings, depending upon the velocity of the up- and down-spin components, the collision between them is either elastic or inelastic, which is consistent with the earlier numerical and experimental observations. However, in the presence of coupling parameters, the collision appears to be inelastic and quasielastic in nature.
Spin-orbit (SO) coupling can be introduced in a Bose-Einstein condensate (BEC) as a gauge potential acting only in a localized spatial domain. The effect of such a SO ``defect'' can be understood by transforming the system to the integrable vector model. The properties of the SO BEC change drastically if the SO defect is accompanied by the Zeeman splitting. In such a nonintegrable system, the SO defect qualitatively changes the character of soliton interactions and allows for formation of stable nearly scalar soliton complexes with almost all atoms concentrated in only one dark state. These solitons exist only if the number of particles exceeds a threshold value. We also report on the possibility of transmission and reflection of a soliton upon its scattering on the SO defect. Scattering strongly affects the pseudospin polarization and can induce pseudospin precession. The scattering can also result in almost complete atomic transfer between the dark states.
We consider coupled matter-wave bright solitons in spatial coherence spin–orbit coupled Bose–Einstein condensates (SOC-BECs) in optical and Rabi-coupling lattice (RL) potentials and find an effective potential for separation of coupled matter-wave solitons. We show that the Rabi lattice significantly affects the potential near the region of overlap between the solitons. We study the effects of Rabi lattice on the dynamics of solitons for different initial overlaps and show that the dynamics is controlled by the interplay between the Rabi lattice and inter-component interaction. We investigate that, by tuning the Rabi lattice strength, one can realize localize, periodic and splitting dynamics of the total density profile of the coupled solitons.
We introduce one- and two-dimensional (1D and 2D) continuum and discrete models for the two-component BEC, with the spin-orbit (SO) coupling of the Rashba type between the components, and attractive cubic interactions, assuming that the condensate is fragmented into a quasidiscrete state by a deep optical-lattice potential. In 1D, it is demonstrated, in analytical and numerical forms, that the ground states of both the discrete system and its continuum counterpart switch from striped bright solitons, featuring deep short-wave modulations of its profile, to smooth solitons, as the strength ratio of the inter- and intracomponent attraction, γ, changes from γ<1 to γ>1. At the borderline, γ=1, there is a continuous branch of stable solitons, which share a common value of the energy and interpolate between the striped and smooth ones. Unlike the 2D system, the 1D solitons, which do not represent the ground state at given γ, are nevertheless stable against small perturbations, and they remain stable too in collisions with other solitons. In 2D, a transition between two different types of discrete solitons, which represent the ground state, viz., semivortices and mixed modes, also takes place at γ=1. A specific property of 2D discrete solitons of both types is their discontinuous transition into a delocalized state at a critical value of the SO-coupling strength. We also address the continuum 2D model in the borderline case of γ=1, which was not studied previously, and demonstrate the existence of an energy-degenerate branch of dynamically stable solitons connecting the semivortex and the mixed mode. Last, it is demonstrated that 1D and 2D discrete solitons are mobile, in a limited interval of velocities.
The analogy between nonlinear optics and Bose-Einstein condensates (BECs) is a fascinating area of study due to the similarities in their underlying physical principles. Both systems are governed by similar nonlinear partial differential equations, which allow researchers to draw parallels between the behaviors observed in these two distinct fields. Among the phenomena observed, the soliton is of particular interest. In this chapter, we demonstrate the possibility of controlling the formation and dynamics of soliton molecules in binary dipolar Bose-Einstein condensates (BECs) with spin-orbit (SO) coupling. The study is carried out analytically using the variational approach and validated numerically through split-step Fourier simulations. Our results reveal that the integrity and stability of the soliton molecules are highly sensitive to the system’s physical parameters, particularly the interplay between local (contact) and nonlocal (dipolar) interactions in the presence of SO coupling. By appropriately tuning these interactions, one can effectively control the binding, oscillatory dynamics, and potential dissociation of the soliton molecules.
We investigate the moving matter-wave solitons in spin—orbit coupled Bose—Einstein condensates (BECs) by a perturbation method. Starting with the one-dimensional Gross—Pitaevskii equations, we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spin—orbit coupling. The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin—orbit coupled BECs. We find different types of moving solitons: dark—bright, bright—bright and dark—dark solitons. Interestingly, moving dark—dark soliton for attractive intra- and inter-species interactions is found, which depends on the Raman coupling. The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin—orbit coupling.