Finite-temperature dynamics of a single vortex in a Bose-Einstein condensate: Equilibrium precession and rotational symmetry breaking

Abstract

We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii equation, when constrained to a finite conserved angular momentum. In an isotropic trapping potential, the condensation of the classical field into an off-axis vortex state breaks the rotational symmetry of the system. We present a methodology to identify the condensate and the Goldstone mode associated with the broken rotational symmetry in the classical-field model. We also examine the variation in vortex trajectories and thermodynamic parameters of the field as the energy of the microcanonical field simulation is varied.

C-Field Methods for Non-Equilibrium Bose Gases

“…This results in a closed system, and the resulting Hamiltonian evolution of the field Φ(r) conserves the energy, normalisation, and any other first integrals which may be present, such as the momentum [20,21], angular momentum [58], or spinor-gas magnetisation [59].…”

“…However, dynamical calculations within a pure PGPE formalism are able to provide useful insights into the dynamics of degenerate Bose-gas systems in situations where a precise identification of the method with the full field theory is impractical [45,58,66]. The PGPE has also been used to establish the connection between c-field methods and more traditional theoretical methods based on U(1) symmetry breaking [61,67].…”

Nonequilibrium dynamics of vortex arrest in a finite-temperature Bose-Einstein condensate

“…Following [26], we choose physical parameters corresponding to 23 Na atoms confined in a strongly oblate trap, with trapping frequencies (ω r , ω z ) = 2π × (10, 2000) rad/s. The radial harmonic confinement defines the units of length (r 0 ≡ √h /mω r ) and time [one trap cycle (cyc) ≡ 2πω…”

“…Such a configuration is obtained as an ergodic classical-field equilibrium with fixed angular momentum on the order ofh per atom about the trap axis [23]. Due to the conservation of angular momentum, this rotating equilibrium configuration is stable, provided that the trapping potential remains invariant under rotations about its axis.…”

Stochastic projected Gross-Pitaevskii equation for spinor and multicomponent condensates

“…At low to moderate temperatures generalised mean field theories have been developed, and successfully modelled a number of experimental scenarios. The Zaremba-Nikuni-Griffin (ZNG) [28][29][30][31][32][33], projected Gross-Pitaevskii equation (PGPE) [34][35][36][37][38][39][40][41][42][43][44] (including applications to spinor condensates [45,46]), and number conserving [47][48][49] theories each have advantages for describing BEC evolution, namely, relative ease of handling thermal cloud dynamics, inclusion of many appreciably populated coherent modes, and inclusion of off-diagonal long range order, respectively. At temperatures well below the BEC transition (T c ), these effects are essential aspects of finite-temperature BEC physics.…”