Spin-orbit coupled condensates typically have two or more components. Each component has quantized circulation, but they need not be the same, leading to the possibility of half-quantized vortices with unit circulation in only one component.
I use a time-dependent Lagrangian formalism and a variational trial function to study the dynamics of a two-component vortex in a spin-orbit coupled Bose-Einstein condensate (BEC). For a single-component BEC, various experiments have validated this theoretical approach, for example a thermal quench that yields a quantized vortex in roughly 25% of trials. To be definite, I assume the specific spin-orbit form used in recent NIST experiments, which introduces a spatial asymmetry because of the external Raman laser beams. I here generalize this formalism to include a two-component order parameter that has quantized circulation in each component but not necessarily with the same circulation. For example a singly quantized vortex in just one component yields a BEC analog of the half-quantum vortex familiar in 3He-A and in p-wave chiral superconductors. This and other unusual two-component vortices have both periodic trajectories and unbounded trajectories that leave the condensate, depending on the initial conditions. The optimized phase of the order parameter induces a term in the particle current that cancels the contribution from the vector potential, leaving pure circulating current around the vortex.
The vortex-vortex interaction in two-component Bose-Einstein condensates is shown to present characteristic effects not possible in single-component condensates. In particular, vortices in different components undergo separate, but concentric, orbits for both the same and opposite circulation. In addition, contrary to the well-known behavior in single-component condensates, vortices with the same circulation created in the less dense component merge in the presence of dissipation, allowing for the creation of metastable vortices with more than one quantum of circulation.
Three types of vortex-pair are identified in two-component Bose–Einstein condensates (BEC) of different kinds of spin-orbit coupling. One type holds the two vortices in one component of the twocomponent condensates. Both the other two types hold a vortex in each component of the twocomponent condensates, and exhibit meron-pair textures that have either null or unit topological charge, respectively. The cores of the two vortices are connected by a string of the relative phase jump. These vortex pairs can be generated from a vortex-free wave packet by incorporating different non- Abelian gauge field into the BEC. When a Rabi coupling is introduced, the distance between the two cores is effectively controlled by the Rabi coupling strength and a transition of vortex configurations is observed.
Static and dynamic properties of vortices in a two-component Bose-Einstein condensate with Rashba spin-orbit coupling are investigated. The mass current around a vortex core in the plane-wave phase is found to be deformed by the spin-orbit coupling, and this makes the dynamics of the vortex pairs quite different from those in a scalar Bose-Einstein condensate. The velocity of a vortex-antivortex pair is much smaller than that without spin-orbit coupling, and there exist stationary states. Two vortices with the same circulation move away from each other or unite to form a stationary state.
Multiply quantized vortices (MQVs) within single-component Bose-Einstein condensates are unstable and decay rapidly. We show that MQVs can be stabilized by adding a small number of atoms of a second species to the vortex cores, and that these atoms remain in the vortex core as the system evolves. A consequence of the stabilization is that nearby corotating vortices can orbit in the opposite sense to their individual rotations when enough of the second species is present. This has implications concerning the imaging of vortices, as well as quantum turbulence and vortex nucleation in two-component condensates, such as those involving mixtures of 87Rb and 133Cs.
Using a (1+2)-dimensional boson-vortex duality between nonlinear electrodynamics and a two-component compressible Bose-Einstein condensate with spin-orbit (SO) coupling, we obtain hydrodynamic continuity and Euler equations where the phase defect and nondefect degrees of freedom enter separately, and a separate equation encompassing quantization of circulation. We obtain the generalized force on vortices under SO coupling, and associate the linear confinement of vortices due to SO coupling with instanton fluctuations of the dual theory.