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arXiv:1012.5472 · Physical Review A

Domain-wall solutions of spinor Bose-Einstein condensates in an optical lattice

Zai-Dong Li, Qiuyan Li, Peng-Bin He, J.-Q. Liang, W. M. Liu, Guangsheng Fu

Published Jan 28, 2010• 32 citations
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Abstract

We studied the static and dynamic domain-wall solutions of spinor Bose-Einstein condensates trapped in an optical lattice. The single and double domain-wall solutions are constructed analytically. Our results show that the magnetic field and light-induced dipolar interactions play important roles for both the formation of different domain walls and the adjusting of domain-wall width and velocity. Moreover, these interactions can drive the motion of the domain wall in Bose ferromagnet systems similar to the way the external magnetic field or the spin-polarized current drives it in fermion ferromagnets.

DOI
10.1103/physreva.81.015602

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Abstract A dynamical theory is presented for the domain wall in the spinor Bose-Einstein condensate of “effective” one dimension. The formulation is based on the time-dependent Landau-Ginzburg (LG) theory written in terms of the spinor order parameter. The procedure is carried out in such a way that an adiabatic change of the collective coordinates which are given by the kink position as well as the phase function built in the spinor, is adapted to the canonical term (alias geometric phase) in the LG Lagrangian. Two problems are discussed: The first one is to explore the translational motion of the kink center in the presence of the pinning potential, which results in the quantum potential problem. The other one concerns the steering of the domain wall by modulating the externally driven magnetic field assisted with dissipation. The present attempt would shed light on the spinor Bose-Einstein condensates from a novel viewpoint.
In this chapter, we discuss the magnetic solitons achieved in atomic spinor Bose-Einstein condensates (BECs) confined within optical lattice. Spinor BECs at each lattice site behave like spin magnets and can interact with each other through the static magnetic dipole-dipole interaction (MDDI), due to which the magnetic soliton may exist in blue-detuned optical lattice. By imposing an external laser field into the lattice or loading atoms in a red-detuned optical lattice, the light-induced dipole-dipole interaction (LDDI) can produce new magnetic solitons. The long-range couplings induced by the MDDI and ODDI play a dominant role in the spin dynamics in an optical lattice. Compared with spin chain in solid material, the nearest-neighbor approximation, next-nearest-neighbor approximation, and long-range case are discussed, respectively.
Solitons of dipolar spinor condensates confined in a one-dimensional optical lattice are studied in terms of the equation of motion of the spinor which is reduced to the sine-Gordon equation in the limit of strong dipole–dipole interaction and weak external magnetic field. It is shown that the solitons obtained analytically can be easily controlled by adjusting the light-induced dipolar interaction, which is realizable in the optical lattice created by red-detuned laser beams with modulating intensity. The possible creation and detection schemes are also proposed.
We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. A modified Landau-Lifshitz equation is derived and exact magnetic soliton solutions are obtained analytically. Our results show that the time oscillation of the soliton size can be controlled in practical experiment by adjusting of the light-induced dipole-dipole interaction. Moreover, the elastic collision of two solitons is investigated.
We consider coherent states of weakly interacting bosons under the conditions of external resonant excitation, with a focus on a two-dimensional polariton fluid driven by a plane electromagnetic wave near the ground state. The coherent driving breaks the U(1) symmetry explicitly, which prevents the occurrence of quantum vortices in a uniform scalar condensate. Surprisingly, a spinor (two-component) system of the same kind admits topological excitations, such as domain walls of relative phase or confined half-vortex molecules, typical of a freely evolving spinor Bose system. Opposite-phase domains arise from the spontaneous breakdown of the spin symmetry (Z2)(\mathbb{Z}_2)(Z2​). Domain walls form with time even when the initial state of the system is uniform or completely disordered; they fall into different topological types distinguished by the total phase variation in the transverse direction. One type of domain walls is similar to ``magnetic'' solitons in Bose-Einstein condensates and exhibits nonzero spin polarization whose sign depends on the direction of motion. Domain walls of the second type, by contrast, behave like monopoles with broken spatiotemporal symmetry and tend to move in certain preferred directions. The interaction of vortices and domain walls results in a long-range ordering of the system.