We explore a new way of producing the Rashba spin-orbit coupling (SOC) for ultracold atoms by using a two-component (spinor) atomic Bose-Einstein condensate (BEC) confined in a bilayer geometry. The SOC of the Rashba type is created if the atoms pick
up a {pi} phase after completing a cyclic transition between four combined spin-layer states composed of two spin and two layer states. The cyclic coupling of the spin-layer states is carried out by combining an intralayer Raman coupling and an interlayer laser assisted tunneling. We theoretically determine the ground-state phases of the spin-orbit-coupled BEC for various strengths of the atom-atom interaction and the laser-assisted coupling. It is shown that the bilayer scheme provides a diverse ground-state phase diagram. In an intermediate range of the atom-light coupling two interlacing lattices of half- skyrmions and half-antiskyrmions are spontaneously created. In the strong-coupling regime, where the SOC of the Rashba-type is formed, the ground state represents plane-wave or standing-wave phases depending on the interaction between the atoms. A variational analysis is shown to be in a good agreement with the numerical results.
We theoretically explore atomic Bose-Einstein condensates (BECs) subject to position-dependent spin-orbit coupling (SOC). This SOC can be produced by cyclically laser coupling four internal atomic ground (or metastable) states in an environment where
the detuning from resonance depends on position. The resulting spin-orbit coupled BEC phase-separates into domains, each of which contain density modulations - stripes - aligned either along the x or y direction. In each domain, the stripe orientation is determined by the sign of the local detuning. When these stripes have mismatched spatial periods along domain boundaries, non-trivial topological spin textures form at the interface, including skyrmions-like spin vortices and anti-vortices. In contrast to vortices present in conventional rotating BECs, these spin-vortices are stable topological defects that are not present in the corresponding homogenous stripe-phase spin-orbit coupled BECs.
Equilibrium vortex formation in rotating binary Bose gases with a rotating frequency higher than the harmonic trapping frequency is investigated theoretically. We consider the system being evaporatively cooled to form condensates and a combined numer
ical scheme is applied to ensure the binary system being in an authentic equilibrium state. To keep the system stable against the large centrifugal force of ultrafast rotation, a quartic trapping potential is added to the existing harmonic part. Using the Thomas-Fermi approximation, a critical rotating frequency Omega_c is derived, which characterizes the structure with or without a central density hole. Vortex structures are studied in detail with rotation frequency both above and below ?Omega_c and with respect to the miscible, symmetrically separated, and asymmetrically separated phases in their nonrotating ground-state counterparts.
Formation of stationary 3D wave patterns generated by a small point-like impurity moving through a Bose-Einstein condensate with supersonic velocity is studied. Asymptotic formulae for a stationary far-field density distribution are obtained. Compari
son with three-dimensional numerical simulations demonstrates that these formulae are accurate enough already at distances from the obstacle equal to a few wavelengths.
Based on a velocity formula derived by matched asymptotic expansion, we investigate the dynamics of a circular vortex ring in an axisymmetric Bose-Einstein condensate in the Thomas-Fermi limit. The trajectory for an axisymmetrically placed and orient
ed vortex ring is entirely determined, revealing that the vortex ring generally precesses in condensate. The linear instability due to bending waves is investigated both numerically and analytically. General stability boundaries for various perturbed wavenumbers are computed. In particular, the excitation spectrum and the absolutely stable region for the static ring are analytically determined.
A hydrodynamic description is used to study the zero-temperature properties of a trapped spinor Bose-Einstein condensate in the presence of a uniform magnetic field. We show that, in the case of antiferromagnetic spin-spin interaction, the polar and
ferromagnetic configurations of the ground state can coexist in the trap. These two phases are spatially segregated in such a way that the polar state occupies the inner part while the ferromagnetic state occupies the outer part of the atomic cloud. We also derive a set of coupled hydrodynamic equations for the number density and spin density excitations of the system. It is shown that these equations can be analytically solved for the system in an isotropic harmonic trap and a constant magnetic field. Remarkably, the related low lying excitation spectra are completely determined by the solutions in the region occupied by the polar state. We find that, within the Thomas-Fermi approximation, the presence of a constant magnetic field does not change the excitation spectra which still possess the similar form of that obtained by Stringari.
