Vortex Dynamics in a Spin-Orbit-Coupled Bose-Einstein Condensate

Abstract

Vortices in a one-component dilute atomic ultracold Bose–Einstein condensate (BEC) usually arise as a response to externally driven rotation. Apart from a few special situations, these vortices are singly quantized with unit circulation (Fetter, Rev Mod Phys 81, 647–691, 2009). Recently, the NIST group has constructed a two-component BEC with a spin-orbit-coupled Hamiltonian involving Pauli matrices (Spielman, Phys Rev A 79, 063613, 2009; Y.-J. Lin et al., Nature 462, 628–632, 2009; Y.-J. Lin et al., Nature 471, 83–87, 2011), and I here study the dynamics of a two-component vortex in such a spin-orbit-coupled condensate. These spin-orbit-coupled BECs use an applied magnetic field to split the hyperfine levels. Hence, they rely on a focused laser beam to trap the atoms. In addition, two Raman laser beams create an effective (or synthetic) gauge potential. The resulting spin-orbit Hamiltonian is discussed in some detail. The various laser beams are fixed in the laboratory, so that it is not feasible to nucleate a vortex by an applied rotation that would need to rotate all the laser beams and the magnetic field. In a one-component BEC, a vortex can also be created by a thermal quench, starting from the normal state and suddenly cooling deep into the condensed state (Freilich et al., Science 329, 1182–1185, 2010). I propose that a similar method would work for a vortex in a spin-orbit-coupled BEC. Such a vortex has two components, and each has its own circulation quantum number (typically $0,\pm 1$). If both components have the same circulation, I find that the composite vortex should execute uniform precession, like that observed in a single-component BEC (Freilich et al., Science 329, 1182–1185, 2010). In contrast, if one component has unit circulation and the other has zero circulation, then some fraction of the dynamical vortex trajectories should eventually leave the condensate, providing clear experimental evidence for this unusual vortex structure. In the context of exciton–polariton condensates, such a vortex is known as a “half-quantum vortex” (Rubo, Phys Rev Lett 99, 106401, 2007; Lagoudakis et al., Science 326, 974–976, 2009).