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arXiv:1609.04694 · Physical Review Letters

Diffused Vorticity and Moment of Inertia of a Spin-Orbit Coupled Bose-Einstein Condensate

S. Stringari

Published Apr 5, 2017• 46 citations
arXivHTMLPDF

Abstract

By developing the hydrodynamic theory of spinor superfluids, we calculate the moment of inertia of a harmonically trapped Bose-Einstein condensate with spin-orbit coupling. We show that the velocity field associated with the rotation of the fluid exhibits diffused vorticity, in contrast to the irrotational behavior characterizing a superfluid. Both Raman-induced and Rashba spin-orbit couplings are considered. In the first case the moment of inertia takes the rigid value at the transition between the plane wave and the single minimum phase, while in the latter case the rigid value is achieved in the limit of isotropic Rashba coupling. A procedure to generate the rigid rotation of the fluid and to measure the moment of inertia is proposed. The quenching of the quantum of circulation h/m, caused by Raman-induced spin-orbit coupling in a toroidal geometry, is also discussed.

DOI
10.1103/physrevlett.118.145302

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By calculating the density response function we identify the excitation spectrum of a Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling. We find that the velocity of sound along the direction of spin-orbit coupling is deeply quenched and vanishes when one approaches the second-order phase transition between the plane-wave and the zero momentum quantum phases. We also point out the emergence of a roton minimum in the excitation spectrum for small values of the Raman coupling, providing the onset of the transition to the stripe phase. Our findings point out the occurrence of a strong anisotropy in the dynamic behavior of the gas. A hydrodynamic description accounting for the collective oscillations in both uniform and harmonically trapped gases is also derived.
By applying a position-dependent detuning to a spin-orbit-coupled Hamiltonian with equal Rashba and Dresselhaus coupling, we exploit the behavior of the angular momentum of a harmonically trapped Bose-Einstein condensed atomic gas and discuss the distinctive role of its canonical and spin components. By developing the formalism of spinor hydrodynamics, we predict the precession of the dipole oscillation caused by the synthetic rotational field, in analogy with the precession of the Foucault pendulum, the excitation of the scissors mode, following the sudden switching off of the detuning, and the occurrence of Hall-like effects. When the detuning exceeds a critical value, we observe a transition from a vortex free, rigidly rotating quantum gas to a gas containing vortices with negative circulation which results in a significant reduction of the total angular momentum.
Hydrodynamic theory of the spinor BEC condensate with Rashba spin-orbit coupling is presented. A close mathematical analogy of the Rashba-BEC model to the recently developed theory of chiral magnetism is found. Hydrodynamic equations for mass density, superfluid velocity, and the local magnetization are derived. The mass current is shown to contain an extra term proportional to the magnetization direction, as a result of the Rashba coupling. Elementary excitations around the two known ground states of the Rashba-BEC Hamiltonian, the plane-wave and the stripe states, are worked out in the hydrodynamic framework, highlighting the cross-coupling of spin and superflow velocity excitations due to the Rashba term.
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Hydrodynamic theory of the spinor BEC condensate with Rashba spin-orbit coupling is presented. A close mathematical analogy of the Rashba-Bose-Einstein condensate model to the recently developed theory of chiral magnetism is found. Hydrodynamic equations for mass density, superfluid velocity, and the local magnetization are derived. The mass current is shown to contain an extra term proportional to the magnetization direction, as a result of the Rashba coupling. Elementary excitations around the two known ground states of the Rashba-Bose-Einstein condensate Hamiltonian, the plane-wave, and the stripe states, are worked out in the hydrodynamic framework, highlighting the cross coupling of spin and superflow velocity excitations due to the Rashba term.
By developing a hydrodynamic formalism, we investigate the expansion dynamics of the single-minimum phase of a binary spin–orbit coupled Bose–Einstein condensate, after releasing from an external harmonic trap. We find that the expansion of the condensate along the direction of the spin–orbit coupling is dramatically slowed down near the transition between the single-minimum phase and the plane-wave phase. Such a slow expansion, resembling a form of an effective localization, is due to the quenching of the superfluid motion which results in a strong increase of the effective mass. In the single-minimum phase the anisotropic expansion of the Bose gas, which is spin balanced at equilibrium, is accompanied by the emergence of a local spin polarization. Our analytic scaling solutions emerging from hydrodynamic picture are compared with a full numerical simulation based on the coupled Gross–Pitaevskii equations.