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arXiv:cond-mat/0205037 · Physical Review Letters

Nucleation, Growth, and Stabilization of Bose-Einstein Condensate Vortex Lattices

A. A. Penckwitt, R. J. Ballagh, Crispin W. Gardiner

Published Dec 11, 2002• 129 citations
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Abstract

We give a simple unified theory of vortex nucleation and vortex lattice formation in which (i) the thermal cloud plays a crucial role; (ii) the basic process is due to growth of the condensate from a rotating thermal cloud, which provides gain for certain surface modes of nonzero angular momentum; (iii) vortices appear initially as the result of a linear interference between the far fields of the condensate and the surface modes; and (iv) the description applies from the initiation process up to the final stabilization of the lattice. We have simulated the growth of vortex lattices from a rotating thermal cloud, and their production using a rotating trap.

DOI
10.1103/physrevlett.89.260402

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We give a simple unified theory of vortex nucleation and vortex lattice formation in which (i) the thermal cloud plays a crucial role; (ii) the basic process is due to growth of the condensate from a rotating thermal cloud, which provides gain for certain surface modes of nonzero angular momentum; (iii) vortices appear initially as the result of a linear interference between the far fields of the condensate and the surface modes; and (iv) the description applies from the initiation process up to the final stabilization of the lattice. We have simulated the growth of vortex lattices from a rotating thermal cloud, and their production using a rotating trap.
We develop a stochastic Gross-Pitaveskii theory suitable for the study of Bose-Einstein condensation in a rotating dilute Bose gas. The theory is used to model the dynamical and equilibrium properties of a rapidly rotating Bose gas quenched through the critical point for condensation, as in the experiment of Haljan et al. [Phys. Rev. Lett. 87, 210403 (2001)]. In contrast to stirring a vortex-free condensate, where topological constraints require that vortices enter from the edge of the condensate, we find that phase defects in the initial noncondensed cloud are trapped en masse in the emerging condensate. Bose-stimulated condensate growth proceeds into a disordered vortex configuration. At sufficiently low temperature the vortices then order into a regular Abrikosov lattice in thermal equilibrium with the rotating cloud. We calculate the effect of thermal fluctuations on vortex ordering in the final gas at different temperatures, and find that the BEC transition is accompanied by lattice melting associated with diminishing long-range correlations between vortices across the system.
We study the problem of vortex nucleation in rotating two-dimensional Bose–Einstein condensate confined in a harmonic trap. We show that, within the Gross–Pitaevskii theory with the boundary condition of vanishing of the order parameter at infinity, topological defects nucleation occurs via the creation of vortex-antivortex pairs far from the cloud center, where the modulus of the order parameter is small. Then vortices move toward the center of the cloud and antivortices move in the opposite direction but never disappear. We also discuss the role of surface modes.
The nucleation of vortices and the resulting structures of vortex arrays in dilute, trapped, zero-temperature Bose-Einstein condensates are investigated numerically. Vortices are generated by rotating a three-dimensional, anisotropic harmonic atom trap. The condensate ground state is obtained by propagating the Gross-Pitaevskii equation in imaginary time. Vortices first appear at a rotation frequency significantly larger than the critical frequency for vortex stabilization, consistent with a critical velocity mechanism for vortex nucleation. At higher frequencies, the structures of the vortex arrays are strongly influenced by trap geometry.
Numerical simulations of vortex motion in a trapped Bose-Einstein condensate were performed by solving the two-dimensional Gross-Pitaevskii equation in the presence of a simple phenomenological model of interaction between the condensate and the finite temperature thermal cloud. The log (base e) of total energy, trap energy, quantum energy, kinetic energy, internal energy and z-component of the angular momentum vs time were compared with f(x)=a+bx for that time when the vortices come in in the condensate. The increasing/decay rate of these energies and L_{z} were studied as a function of dissipation.
We present a quantum-mechanical treatment of the mechanical stirring of Bose-Einstein condensates using classical field techniques. In our approach the condensate and excited modes are described using a Hamiltonian classical field method in which the atom number and (rotating frame) energy are strictly conserved. We simulate a T=0T=0T=0 quasi-two-dimensional condensate perturbed by a rotating anisotropic trapping potential. Vacuum fluctuations in the initial state provide an irreducible mechanism for breaking the initial symmetries of the condensate and seeding the subsequent dynamical instability. Highly turbulent motion develops and we quantify the emergence of a rotating thermal component that provides the dissipation necessary for the nucleation and motional damping of vortices in the condensate. Vortex lattice formation is not observed, rather the vortices assemble into a spatially disordered vortex liquid state. We discuss methods we have developed to identify the condensate in the presence of an irregular distribution of vortices, determine the thermodynamic parameters of the thermal component, and extract damping rates from the classical field trajectories.