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arXiv:cond-mat/0506801 · Physical Review E

Condensation and vortex formation in a Bose gas upon cooling

Efim A. Brener, S. V. Iordanskiy, R. B. Saptsov

Published Jan 20, 2006• 3 citations
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Abstract

The mechanism for the transition of a Bose gas to the superfluid state via thermal fluctuations is considered. It is shown that in the process of external cooling some critical fluctuations (instantons) are formed above the critical temperature. The probability of the instanton formation is calculated in the three- and two-dimensional cases. It is found that this probability increases as the system approaches the transition temperature. It is shown that the evolution of an individual instanton is impossible without the formation of vortices in its superfluid part.

DOI
10.1103/physreve.73.016127

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The mechanism for the transition of a Bose gas to the superfluid state via thermal fluctuations is considered. It is shown that in the process of external cooling some critical fluctuations (instantons) are formed above the critical temperature. The probability of the instanton formation is calculated in the three- and two-dimensional cases. It is found that this probability increases as the system approaches the transition temperature. It is shown that the evolution of an individual instanton is impossible without the formation of vortices in its superfluid part.
The mechanism of transition of a Bose gas to the superfluid state via thermal fluctuations under the condition of external cooling at a temperature above the transition point is considered. The probability of formation of such critical fluctuations (instantons) is calculated; it is found that this probability increases as the system approaches the transition temperature. It is shown that the evolution of an individual instanton is impossible without the formation of vortices in its superfluid part.
We briefly review the theory of Bose-Einstein condensation in the two-dimensional trapped Bose gas and, in particular the relationship to the theory of the homogeneous two-dimensional gas and the Berezinskii-Kosterlitz-Thouless phase. We obtain a phase diagram for the trapped two-dimensional gas, finding a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose-Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose-Einstein condensate, a vortex pair plasma with fluctuating condensate phase and a thermal Bose gas. The thermal activation of vortex-antivortex pair formation is confirmed using finite-temperature classical field simulations.
We report on experiments and simulations of the growth of a Bose-Einstein condensate in which vortices are observed to form spontaneously in a non-rotating potential. Between 10% and 50% of experiments result in between one and three unambiguous vortex cores. We simulate a temperature quench of a Bose gas through the critical point using the stochastic Gross-Pitaevskii equation and find remarkable agreement with the experimental data. Faster cooling results in a higher probability of vortex formation, and we interpret these results in light of the Kibble-Zurek scenario for the formation of topological defects in continuous phase transitions.
We obtain a phase diagram for a trapped two-dimensional ultracold Bose gas. We find a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose–Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose–Einstein condensate, a vortex pair plasma with a fluctuating condensate phase, and a thermal Bose gas. The existence of the vortex pair phase could be verified using current experimental set-ups.
We discuss the stability of a homogeneous two-dimensional Bose gas at finite temperature against formation of isolated vortices. We consider a patch of several healing lengths in size and compute its free energy using the Euclidean formalism. Since we deal with an open system, which is able to exchange particles and angular momentum with the rest of the condensate, we use the symmetry-breaking (as opposed to the particle number conserving) formalism, and include configurations with all values of angular momenta in the partition function. At finite temperature, there appear sphaleron configurations associated to isolated vortices. The contribution from these configurations to the free energy is computed in the dilute gas approximation. We show that the Euclidean action of linearized perturbations of a vortex is not positive definite. As a consequence the free energy of the 2D Bose gas acquires an imaginary part. This signals the instability of the gas. This instability may be identified with the Berezinskii, Kosterlitz and Thouless (BKT) transition.