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arXiv:0801.0383 · Physical Review A

Vortex-lattice formation and melting in a nonrotating Bose-Einstein condensate

Gary Ruben, David M. Paganin, Michael J. Morgan

Published Jul 24, 2008• 22 citations
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Abstract

Numerical simulations of the interference of a three-way segmented nonrotating Bose-Einstein condensate reveal the production of a honeycomb vortex lattice containing significant numbers of vortices and antivortices. If confined within a trap, the lattice subsequently melts, exhibiting a rich assortment of vortex-antivortex interactions. In contrast with nonlinear vortex production mechanisms previously described for Bose-Einstein condensates, the process here is shown to be primarily one of linear superposition, with initial vortex locations approximately described by a linear theory of wave packet interference.

DOI
10.1103/physreva.78.013631

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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 report on the observation of vortex formation in a Bose-Einstein condensate of 87Rb^{87}\text{R}\text{b}87Rb atoms. Vortices are generated by superimposing an oscillating excitation to the trapping potential introduced by an external magnetic field. For small amplitudes of the external excitation field we observe a bending of the cloud axis. Increasing the amplitude we observe formation of a growing number of vortices in the sample. Shot-to-shot variations in both vortex number and position within the condensed cloud are observed, probably due to the intrinsic vortex nucleation dynamics. We discuss the possible formation of vortices and antivortices in the sample as well as possible mechanisms for vortex nucleation.
We investigate a shift in the critical temperature of rotating Bose-Einstein condensates mediated by the melting of the vortex lattice. Numerical simulations reveal that this temperature exhibits contrasting behavior depending on the system configuration: a negative shift occurs for fixed trap potentials due to the expansion of the condensate, while a positive shift is observed for fixed volumes, where vortex-lattice rigidity suppresses thermal fluctuations. We introduce a vortex-energy model that captures the role of vortex interactions, the positional energy of the vortex lattice, as well as the phase transition and how the vortex lattice disappears. The findings provide insights into the thermodynamic properties of rotating condensates and the dynamics of vortex-lattice melting, offering potential parallels with other quantum systems such as type-II superconductors.
Quantized vortices play a key role in superfluidity and superconductivity. We have observed the formation of highly ordered vortex lattices in a rotating Bose-condensed gas. These triangular lattices contained over 100 vortices with lifetimes of several seconds. Individual vortices persisted up to 40 seconds. The lattices could be generated over a wide range of rotation frequencies and trap geometries, shedding light on the formation process. Our observation of dislocations, irregular structure, and dynamics indicates that gaseous Bose-Einstein condensates may be a model system for the study of vortex matter.
We numerically study the dynamics of vortex lattice formation in a rotating cigar-shaped Bose-Einstein condensate. The study is a three-dimensional simulation of the Gross-Pitaevskii equation with a phenomenological dissipation term. The simulations reveal previously unknown dynamical features of the vortex nucleation process, in which the condensate undergoes a strongly turbulent stage and the penetrating vortex lines vibrate rapidly. The vibrations arise from spontaneous excitation of Kelvin waves on the protovortices during a surface wave instability, caused by an inhomogeneity of the condensate density along the elongated axial direction.