Discrete and continuum composite solitons in Bose-Einstein condensates with the Rashba spin-orbit coupling in one and two dimensions

Abstract

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.

Nonlinear gap modes and compactons in a lattice model for spin-orbit coupled exciton-polaritons in zigzag chains

“…Note that, under the above assumptions (w real and cylindrically symmetric), the integral defining σ is always real. We note that the resulting lattice equations (5), (10), with spin-orbit coefficients given by (9), (13), are not equivalent to the equations studied in [13][14][15][16]. In particular, we comment on the relation between the present model and that of [16], who considered a diamond chain with angles π/4 and a Rashba-type spin-orbit coupling.…”

“…Note that the (Wannier) basis functions are the same for both components, since we have assumed no spin-orbit splitting inside the wells, Ω=0, and w are basis functions of the linear problem. Note also that an analogous approach was used in [13] to derive lattice equations for the simpler problem of a pure 1D lattice with a standard spin-orbit coupling term ( i x - ¶ , linear in the spatial derivative) for atomic BEC's in optical lattices; similar models were also studied in [14][15][16]. For simplicity we will assume below that w(x, y) can be chosen real (which is typically the case in absence of OAM; the generalization to modes with nonzero OAM requires complex w(x, y) and will be treated in a separate work).…”

Flipping-shuttle oscillations of bright one- and two-dimensional solitons in spin-orbit-coupled Bose-Einstein condensates with Rabi mixing

“…where γ is the above-mentioned relative strength of the inter-component attraction, with respect to the self-attraction. Previous works, which addressed this system in the absence of the RC (d = 0), have revealed striped bright solitons, composed of alternating segments occupied by the two components (with opposite parities, even and odd), at γ < 1, and smooth solitons, with |φ + (x)| = |φ − (x)|, at γ > 1 [48]. In fact, scattering lengths of interactions between atoms which represent different components of the pseudo-spinor wave function are almost exactly equal [65], therefore we focus below, chiefly, on the case of γ = 1, which corresponds the Manakov's nonlinearity, in terms of optics models [56] (nevertheless, the case of γ = 1 is briefly considered too, see Fig.…”

“…In the former case, the 1D system produces stable striped solitons (see, e.g., Ref. [48]), built as patterns featuring multiple density peaks in the two components, with density maxima of one component coinciding with minima of the other. Accordingly, the two components of the striped solitons feature opposite spatial parities, one being even and the other odd.…”

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

“…This degree of freedom opens up a new avenue to study the fundamental properties of various topologic defects due to the close relationship between the spin and motional degrees of freedom [28][29][30][31][32][33][34][35][36][37][38][39][40]. In the presence of SOC, a variety new types of solitons, such as half-vortex gap solitons [41], discrete and continuum composite solitons [42], and many others, have been predicted. More specifically, the two-dimensional (2D) composite solitons [43] and stable 3D solitons without the ground state [44] in free space have been reported in a binary BEC under the effect of SOC, in which the stability mechanism comes from the balance between attractive nonlinearity and the modification of the dispersion induced by the SOC.…”