Exotic complexes in one-dimensional Bose-Einstein condensates with spin-orbit coupling

Abstract

By means of the F-expansion method and intensive numerical simulations, the existence of three families of nonlinear matter waves including Jacobi elliptic functions, solitons, and triangular periodic functions, is demonstrated for spin-orbit coupled Bose-Einstein condensates with a linear potential. In addition, several complexes are obtained by taking two distinct solutions of each family or two distinct families. These solutions sustain different types of two-body interactions in the condensate that can be repulsive, attractive, or attractive and repulsive. Whereas the spin-orbit coupling destabilized these nonlinear matter waves, the linear potential leads to a stabilization. The numerical results are in excellent agreement with our analytical findings and it can be expected that the proposed robust solutions should be observable for experimentally relevant conditions.

Scattering of solitons in binary Bose-Einstein condensates with spin-orbit and Rabi couplings

“…We found that this quantity strictly increases with v 0 such that 1.7 δt col /T sv 2.0, with the left (right) sided extreme value reached when v 0 assumes the value corresponding to the left (right) edge of a window. So, it follows that the bouncing frequency ω = ω sv ( |d| 0.15 ) , (16) which establishes the condition of motion synchronization involving the solitons' translational and vibrational modes, which give rise to the intervals of regularity. This condition means that the bouncing motion is such that ω (n col − 1|n col ) bounce must approach a state of resonance with the shape vibration, ω (n col − 1|n col ) bounce = ω sv /(J + 3), from below by a suitable amount provided by Eq.…”

“…). The narrowing of the windows of a given structure results from the behavior of ω (n col − 1|n col ) bounce with v 0 , which decreases faster as close as v 0 is from the corresponding critical value in a such way that the greater the integer J is, smaller is the v 0 -interval in which the condition (16) holds and, consequently, narrower is the window.…”

“…Spin-orbit (SO) coupling was recently engineered in a neutral atomic Bose-Einstein condensate (BECs) by dressing two atomic spin states (hyperfine states |F = 1, m F = ±1 of a spin-1 87 Rb BEC) with a pair of laser beams [1]. This new scenario has motivated further studies on vector solitons and other nonlinear waves, such as, self-trapped states [2], vortices [3][4][5][6][7], Skyrmions [8], Dirac monopoles [9], dark solitons [10,11], bright solitons [12], gap solitons [13][14][15], exotic complexes [16], etc. Furthermore, many studies in BECs with SO coupling have shown interesting effects like the chiral confinement in quasirelativistic BECs [2], existence of a 'stripe phase' [17,18], tunneling dynamics [19][20][21], the partial wave scattering [22], the phenomenon of Zitterbewegung [23][24][25], the tunability of the SO coupling strength [26], traveling Majorana solitons [27], steadily moving solitons in a helicoidal gauge potential [28], negative-mass hydrodynamics [29], etc.…”

“…Analytical developments for search localized solutions in BECs with SO coupling was recently reported in quasi-one- [11][12][13][14][15][16][30][31][32][33][34][35][36][37][38][39][40][41] and quasi-two-dimensional [7,15,34,[42][43][44][45][46] systems. Specifically, in Ref.…”

Step, dip, and bell-shape traveling waves in a (2 + 1)-chemotaxis model with traction and long-range diffusion

“…The former is responsible for faster bacterial colonization of unoccupied regions, while the latter may be the signature of backward waves. In the flux limiting cases, the backward waves in a chemotactic system were shown to be responsible for a population saturation in a stable state accompanied by a transition toward unstable modes [45].…”