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 $^3$ He-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.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 $^3$He-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.

arXiv:1312.5289Physical Review AFeb 21, 201468 citations

Bose-Einstein Condensates with Spin-Orbit Interaction

Tin-Lun Ho, Shizhong Zhang

Motivated by recent experiments carried out by Spielman's group at NIST, we study a general scheme for generating families of gauge fields, spanning the scalar, spin-orbit, and non-Abelian regimes. The NIST experiments, which impart momentum to bosons while changing their spin state, can in principle realize all these. In the spin-orbit regime, we show that a Bose gas is a spinor condensate made up of two non-orthogonal dressed spin states carrying different momenta. As a result, its density shows a stripe structure with a contrast proportional to the overlap of the dressed states, which can be made very pronounced by adjusting the experimental parameters.Motivated by recent experiments carried out by Spielman's group at NIST, we study a general scheme for generating families of gauge fields, spanning the scalar, spin-orbit, and non-Abelian regimes. The NIST experiments, which impart momentum to bosons while changing their spin state, can in principle realize all these. In the spin-orbit regime, we show that a Bose gas is a spinor condensate made up of two non-orthogonal dressed spin states carrying different momenta. As a result, its density shows a stripe structure with a contrast proportional to the overlap of the dressed states, which can be made very pronounced by adjusting the experimental parameters.

Physical Review LettersOct 6, 2011473 citations

Spin–orbit-coupled Bose–Einstein condensates

Y.-J. Lin, Karina Jiménez-García, Ian B. Spielman

arXiv:1103.3522NatureMar 1, 20112,101 citations

Visualization of Bose-Einstein Condensates | NIST

Peter M Ketcham, David L. Feder, William P. Reinhardt +2 more

Mar 1, 19990 citations

Interference of spin-orbit–coupled Bose-Einstein condensates

Sh. Mardonov, M. Palmero, Michele Modugno +2 more

Interference of atomic Bose-Einstein condensates, observed in free expansion experiments, is a basic characteristic of their quantum nature. The ability to produce synthetic spin-orbit coupling in Bose-Einstein condensates has recently opened a new research field. Here we theoretically describe interference of two noninteracting spin-orbit coupled Bose-Einstein condensates in an external synthetic magnetic field. We demonstrate that the spin-orbit and the Zeeman couplings strongly influence the interference pattern determined by the angle between the spins of the condensates, as can be seen in time-of-flight experiments. We show that a quantum backflow, being a subtle feature of the interference, is, nevertheless, robust against the spin-orbit coupling and applied synthetic magnetic field.Interference of atomic Bose-Einstein condensates, observed in free expansion experiments, is a basic characteristic of their quantum nature. The ability to produce synthetic spin-orbit coupling in Bose-Einstein condensates has recently opened a new research field. Here we theoretically describe interference of two noninteracting spin-orbit coupled Bose-Einstein condensates in an external synthetic magnetic field. We demonstrate that the spin-orbit and the Zeeman couplings strongly influence the interference pattern determined by the angle between the spins of the condensates, as can be seen in time-of-flight experiments. We show that a quantum backflow, being a subtle feature of the interference, is, nevertheless, robust against the spin-orbit coupling and applied synthetic magnetic field.

arXiv:1409.5889Europhysics Letters (EPL)Jun 1, 201419 citations

^3

He-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.