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Journal of Physics A Mathematical and Theoretical

Soliton collisions in spin–orbit coupled spin-1 Bose–Einstein condensates

Juan-Juan Qi, Dun Zhao, Wu‐Ming Liu

Published May 19, 2023• 8 citations
Publisher

Abstract

Abstract We investigate analytically the effects of spin–orbit coupling (SOC) for the dynamics of soliton collisions in spin-1 Bose–Einstein condensates (BECs). Applying the non-standard Hirota’s bilinear method, we derive some exact one- and two-soliton solutions for the one-dimensional system of a spin–orbit coupled spin-1 BEC, which clearly shows how the dynamics of the solitons in spinor BECs can be engineered by SOC. Under SOC, the soliton collisions of ferromagnetic-polar type, ferromagnetic-ferromagnetic type and polar-polar type are discussed in details. Comparisons for the soliton states between the systems with and without SOC are displayed, a remarkable phenomenon is that the SOC can lead to the split of a soliton.

DOI
10.1088/1751-8121/acd737

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Abstract We investigate analytically the effects of spin–orbit coupling (SOC) for the dynamics of soliton collisions in spin-1 Bose–Einstein condensates (BECs). Applying the non-standard Hirota’s bilinear method, we derive some exact one- and two-soliton solutions for the one-dimensional system of a spin–orbit coupled spin-1 BEC, which clearly shows how the dynamics of the solitons in spinor BECs can be engineered by SOC. Under SOC, the soliton collisions of ferromagnetic-polar type, ferromagnetic-ferromagnetic type and polar-polar type are discussed in details. Comparisons for the soliton states between the systems with and without SOC are displayed, a remarkable phenomenon is that the SOC can lead to the split of a soliton.
In this paper, we investigate a five-component Gross–Pitaevskii equation, which is demonstrated to describe the dynamics of an F=2 spinor Bose–Einstein condensate in one dimension. By employing the Hirota method with an auxiliary function, we obtain the explicit bright one- and two-soliton solutions for the equation via symbolic computation. With the choice of polarization parameter and spin density, the one-soliton solutions are divided into four types: one-peak solitons in the ferromagnetic and cyclic states and one- and two-peak solitons in the polar states. For the former two, solitons share the similar shape of one peak in all components. Solitons in the polar states have the one- or two-peak profiles, and the separated distance between two peaks is inversely proportional to the value of polarization parameter. Based on the asymptotic analysis, we analyze the collisions between two solitons in the same and different states.
Solitons play a fundamental role in the dynamics of nonlinear excitations. Here we explore the motion of solitons in one-dimensional Bose-Einstein condensates subjected to a spin-orbit coupling (SOC). We demonstrate that the spin dynamics of solitons is governed by a nonlinear Bloch equation. The spin dynamics affects the orbital motion of solitons leading to spin-orbit effects in the dynamics of macroscopic quantum objects (mean-field solitons). The latter perform oscillations with a frequency determined by the SOC, Raman coupling, and intrinsic nonlinearity. These findings reveal unique features of solitons affected by the SOC, which are confirmed by analytical considerations and numerical simulations of the underlying Gross-Pitaevskii equations.
We theoretically investigate the dynamics of polar bright soliton under the influence of spin-orbit coupling (SOC) in spin-1 three component Bose-Einstein condensate (BEC). Periodically oscillating dark-bright-dark solitons are found to be induced by the SOC with their multifrequency oscillations jointly determined by the interparticle nonlinear interaction and the SOC strength. Explicit formulas are provided to identify these frequencies, which are in good agreement with the numerical simulation results. A linear Zeeman interaction is further introduced to break the time-reversal symmetry and change the polarity of the spinor BECs, which results in the periodic transition of the system from polar state to ferromagnetic state.
Abstract We address effects of spin–orbit coupling (SOC), phenomenologically added to a two-component Bose–Einstein condensate composed of particles moving by Lévy flights, in one- and two-dimensional (1D) and (2D) settings. The corresponding system of coupled Gross–Pitaevskii equations includes fractional kinetic-energy operators, characterized by the Lévy index, α < 2 (the normal kinetic energy corresponds to α = 2). The SOC terms, with strength λ, produce strong effects in the 2D case: they create families of stable solitons of the semi-vortex and mixed-mode types in the interval of 1 < α < 2, where the supercritical collapse does not admit the existence of stable solitons in the absence of the SOC. At λ → 0, amplitudes of these solitons vanish ∼λ 1/(α−1).
Recently, research of solitons in Bose–Einstein condensates has become a popular topic. Here, we mainly study exact analytical solutions of Gross–Pitaevskii equations describing spin-orbit coupled spin-1 Bose–Einstein condensates. To begin with, we show the analytical relation between different types of one-dimensional spin-orbit coupling and Zeeman effect. In addition, we find a transformation that can simplify the three-component Gross–Pitaevskii equations with spin-orbit coupling into the nonlinear Schrödinger equation. The abundant stripe phase and dynamic characteristics of the system are investigated.
We present an analysis of two-dimensional (2D) matter-wave solitons, governed by the pseudospinor system of Gross-Pitaevskii equations with self- and cross attraction, which includes the spin-orbit coupling (SOC) in the general Rashba-Dresselhaus form, and, separately, the Rashba coupling and the Zeeman splitting. Families of semivortex (SV) and mixed-mode (MM) solitons are constructed, which exist and are stable in free space, as the SOC terms prevent the onset of the critical collapse and create the otherwise missing ground states in the form of the solitons. The Dresselhaus SOC produces a destructive effect on the vortex solitons, while the Zeeman term tends to convert the MM states into the SV ones, which eventually suffer delocalization. Existence domains and stability boundaries are identified for the soliton families. For physically relevant parameters of the SOC system, the number of atoms in the 2D solitons is limited by ∼1.5×10^{4}. The results are obtained by means of combined analytical and numerical methods.