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arXiv:cond-mat/0609468 · Physical Review A

Solitons in a trapped spin-1 atomic condensate

Wenxian Zhang, Özgür Esat Müstecaplıoğlu, Li You

Published Apr 2, 2007• 48 citations
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Abstract

We numerically investigate a particular type of spin soliton inside a trapped atomic spin-1 Bose-Einstein condensate with ferromagnetic interactions. Within the mean-field theory approximation, our study of the solitonic dynamics shows that the solitonic wave function, its center-of-mass motion, and the local spin evolutions are stable and are intimately related to the domain structures studied recently in spin-1 $^{87}\mathrm{Rb}$ condensates. We discuss a rotating reference frame wherein the dynamics of the solitonic local spatial spin distribution becomes time independent.

DOI
10.1103/physreva.75.043601

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We numerically investigate a particular type of spin soliton inside a trapped atomic spin-1 Bose-Einstein condensate with ferromagnetic interactions. Within the mean-field theory approximation, our study of the solitonic dynamics shows that the solitonic wave function, its center-of-mass motion, and the local spin evolutions are stable and are intimately related to the domain structures studied recently in spin-1 87Rb^{87}\mathrm{Rb}87Rb condensates. We discuss a rotating reference frame wherein the dynamics of the solitonic local spatial spin distribution becomes time independent.
We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find that this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.
We have investigated the dynamics of bright solitons in a spin–orbit coupled spin-1 Bose–Einstein condensate analytically and numerically. By using the hyperbolic sine function as the trial function to describe a plane wave bright soliton with a single finite momentum, we have derived the motion equations of soliton’s spin and center of mass, and obtained its exact analytical solutions. Our results show that the spin–orbit coupling couples the soliton’s spin with its center-of-mass motion, the spin oscillations induced by the exchange of atoms between components result in the periodical oscillation of center-of-mass, and the motion of center of mass of soliton can be viewed as a superposition of periodical and linear motions. Our analytical results have also been confirmed by the direct numerical simulations of Gross–Pitaevskii equations.
We study magnetic solitons, solitary waves of spin polarization (i.e., magnetization), in binary Bose-Einstein condensates in the presence of Rabi coupling. We show that the system exhibits two types of magnetic solitons, called $2\ensuremath{\pi}$ and $0\ensuremath{\pi}$ solitons, characterized by a different behavior of the relative phase between the two spin components. $2\ensuremath{\pi}$ solitons exhibit a $2\ensuremath{\pi}$ jump of the relative phase, independent of their velocity, the static domain wall explored by Son and Stephanov being an example of such $2\ensuremath{\pi}$ solitons with vanishing velocity and magnetization. $0\ensuremath{\pi}$ solitons instead do not exhibit any asymptotic jump in the relative phase. Systematic results are provided for both types of solitons in uniform matter. Numerical calculations in the presence of a one-dimensional harmonic trap reveal that a $2\ensuremath{\pi}$ soliton evolves in time into a $0\ensuremath{\pi}$ soliton, and vice versa, oscillating around the center of the trap. Results for the effective mass, the Landau critical velocity, and the role of the transverse confinement are also discussed.
We model the nonlinear behavior of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or antiferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional optical lattice potential. We show that both types of BECs exhibit dynamical instabilities and may form spatially localized multicomponent structures. The localized states of the spinor matter waves take the form of vector gap solitons and self-trapped waves that exist only within gaps of the linear Bloch-wave band-gap spectrum. Of special interest are the nonlinear localized states that do not exhibit a common spatial density profile shared by all condensate components, and consequently cannot be described by the single mode approximation (SMA) frequently employed within the framework of the mean-field treatment. We show that the non-SMA states can exhibits Josephson-like internal oscillations and self-magnetization, i.e., intrinsic precession of the local spin. Finally, we demonstrate that nonstationary states of a spinor BEC in a lattice exhibit coherent undamped spin-mixing dynamics, and that their controlled conversion into a stationary state can be achieved by the application of an external magnetic field.
We analyze the dynamics of both population and spin densities, emerging from the spatial overlap between two distinct polar bright solitons in spin-1 spinor condensates. The dynamics of overlapping solitons in scalar condensates exhibits soliton fusion, atomic switching from one soliton to another, and repulsive dynamics depending on the extent of overlap and the relative phase between the solitons. The scalar case also helps us understand the dynamics of the vector solitons in which the ratio between spin-dependent and spin-independent interaction strengths also plays a vital role. In the absence of spin-changing collisions, we observe Josephson-like oscillations for each spin component leading to the emergence of oscillating domain walls. In the presence of spin-dependent interactions, the overlapping polar solitons may emerge as ferromagnetic solitons or oscillatons or a combination of both. In the end, we discuss the experimental procedure to observe the same dynamics using a rubidium spin-1 Bose-Einstein condensate setup.
Ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support localized dark-soliton excitations that show periodic density dynamics in real space. In addition to the density feature, the solitons also carry a localized pseudospin magnetization that exhibits a rich and tunable dynamics. Analytical results for Rashba-type spin-orbit coupling and spin-invariant interactions predict a conserved magnitude and precessional motion for the soliton magnetization that allows for the simulation of spin-related geometric phases recently seen in electronic transport measurements.