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Register a new userPhase separation and hidden vortices induced by spin-orbit coupling in spin-1 Bose-Einstein condensates
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We investigate phase separation and hidden vortices in spin-orbit coupled ferromagnetic BoseEinstein condensates with rotation and Rabi coupling. The hidden vortices are invisible in density distribution but are visible in phase distribution, which can carry angular momentum like the ordinary quantized vortices. In the absence of the rotation, we observe the phase separation induced by the spin-orbit coupling and determine the entire phase diagram of the existence of phase separation. For the rotation case, in addition to the phase separation, we demonstrate particularly that the spin-orbit coupling can result in the hidden vortices and hidden vortex-antivortex pairs. The corresponding entire phase diagrams are determined, depending on the interplay of the spin-orbit coupling strength, the rotation frequency, and Rabi frequency, which reveals the critical condition of the occurrence of the hidden vortices and vortex-antivortex pairs. The hidden vortices here are proved to be long-lived in the time scale of experiment by the dynamic analysis. These findings not only provide a clear illustration of the phase separation in spin-orbit coupled spinor Bose-Einstein condensates, but also open a new direction for investigating the hidden vortices in high-spin quantum system.
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We analytically and numerically investigate the ground state of the spin-orbit coupled spin-1 Bose-Einstein condensates in an external parabolic potential. When the spin-orbit coupling strength $kappa$ is comparable with that of the trapping potential, the density distribution centers of different components of the spinor condensate deviate evidently from the trap center in the plane wave and stripe phases. When $kappagg1$, the magnitude of this deviation decreases as $kappa$ is getting larger and larger. Correspondingly, periphery half-skyrmions textures arise. This deviation can be reflected by the non-uniform magnetic moment in the $z$ direction, $mathcal{F}_z$. With the manipulation of the external trap, the local magnitude of $mathcal{F}_z$ can be increased evidently. This kind of increase of $mathcal{F}_z$ is also observed in the square vortex lattice phase of the condensate.
We investigate the fractionalized Skyrmion excitations induced by spin-orbit coupling in rotating and rapidly quenched spin-1 Bose-Einstein condensates. Our results show that the fractionalized Skyrmion excitation depends on the combination of spin-orbit coupling and rotation, and it originates from a dipole structure of spin which is always embedded in three vortices constructed by each condensate component respectively. When spin-orbit coupling is larger than a critical value, the fractionalized Skyrmions encircle the center with one or several circles to form a radial lattice, which occurs even in the strong ferromagnetic/antiferromagnetic condensates. We can use both the spin-orbit coupling and the rotation to adjust the radial lattice. The realization and the detection of the fractionalized Skyrmions are compatible with current experimental technology.
We revisit ground states of spinor Bose-Einstein condensates with a Rashba spin-orbit coupling, and find that votices show up as a direct consequence of spontaneous symmetry breaking into a combined gauge, spin, and space rotation symmetry, which determines the vortex-core spin state at the rotating center. For the continuous combined symmetry, the total spin rotation about the rotating axis is restricted to $2pi$, whereas for the discrete combined symmetry, we further need 2F quantum numbers to characterize the total spin rotation for the spin-$F$ system. For lattice phases we find that in the ground state the topological charge for each unit cell vanishes. However, we find two types of highly symmetric lattices with a nontrivial topological charge in the spin-$frac{1}{2}$ system based on the symmetry classification, and show that they are skyrmion crystals.
The phase diagram of lowest-energy vortices in the polar phase of spin-1 Bose--Einstein condensates is investigated theoretically. Singly quantized vortices are categorized by the local ordered state in the vortex core and three types of vortices are found as lowest-energy vortices, which are elliptic AF-core vortices, axisymmetric F-core vortices, and N-core vortices. These vortices are named after the local ordered state, ferromagnetic (F), antiferromagnetic (AF), broken-axisymmetry (BA), and normal (N) states apart from the bulk polar (P) state. The N-core vortex is a conventional vortex, in the core of which the superfluid order parameter vanishes. The other two types of vortices are stabilized when the quadratic Zeeman energy is smaller than a critical value. The axisymmetric F-core vortex is the lowest-energy vortex for ferromagnetic interaction, and it has an F core surrounded by a BA skin that forms a ferromagnetic-spin texture, as exemplified by the localized Mermin--Ho texture. The elliptic AF-core vortex is stabilized for antiferromagnetic interaction; the vortex core has both nematic-spin and ferromagnetic orders locally and is composed of the AF-core soliton spanned between two BA edges. The phase transition from the N-core vortex to the other two vortices is continuous, whereas that between the AF-core and F-core vortices is discontinuous. The critical point of the continuous vortex-core transition is computed by the perturbation analysis of the Bogoliubov theory and the Ginzburg--Landau formalism describes the critical behavior. The influence of trapping potential on the core structure is also investigated.
Motivated by a goal of realizing spin-orbit coupling (SOC) beyond one-dimension (1D), we propose and analyze a method to generate an effective 2D SOC in bilayer BECs with laser-assisted inter-layer tunneling. We show that an interplay between the inter-layer tunneling, SOC and intra-layer atomic interaction can give rise to diverse ground state configurations. In particular, the system undergoes a transition to a new type of stripe phase which spontaneously breaks the time-reversal symmetry. Different from the ordinary Rashba-type SOC, a fractionalized skyrmion lattice emerges spontaneously in the bilayer system without external traps. Furthermore, we predict the occurrence of a tetracritical point in the phase diagram of the bilayer BECs, where four different phases merge together. The origin of the emerging different phases is elucidated.
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