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arXiv:1412.4512 · Physical Review A

Hysteresis and metastability of Bose-Einstein-condensed clouds of atoms confined in ring potentials

A. Roussou, George D. Tsibidis, J. Smyrnakis, Manolis Magiropoulos, Nikolaos K. Efremidis, Andrew David Jackson, G. M. Kavoulakis

Published Feb 13, 2015• 9 citations
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Abstract

We consider a Bose-Einstein-condensed cloud of atoms which rotate in a toroidal or annular potential. Assuming one-dimensional motion, we evaluate the critical frequencies associated with the effect of hysteresis and the critical coupling for stability of the persistent currents. We perform these calculations using both the mean-field approximation and the method of numerical diagonalization of the many-body Hamiltonian which includes corrections due to the finiteness of the atom number.

DOI
10.1103/physreva.91.023613

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We consider a Bose-Einstein-condensed cloud of atoms which rotate in a toroidal or annular potential. Assuming one-dimensional motion, we evaluate the critical frequencies associated with the effect of hysteresis and the critical coupling for stability of the persistent currents. We perform these calculations using both the mean-field approximation and the method of numerical diagonalization of the many-body Hamiltonian which includes corrections due to the finiteness of the atom number.
Abstract We consider a Bose–Einstein condensate, which is confined in a very tight toroidal/annular trap, in the presence of a potential, which breaks the axial symmetry of the Hamiltonian. We investigate the stationary states of the condensate, when its density distribution co-rotates with the symmetry-breaking potential. As the strength of the potential increases, we have a gradual transition from vortex excitation to solid-body-like motion. Of particular importance are states where the system is static and yet it has a nonzero current/circulation, which is a realization of persistent currents/reflectionless potentials.
Motivated by recent experiments on Bose-Einstein condensed atoms which rotate in annular and/or toroidal traps, we study the effect of the finiteness of the atom number NNN on the states of lowest energy for a fixed expectation value of the angular momentum, under periodic boundary conditions. To attack this problem, we develop a general strategy, considering a linear superposition of the eigenstates of the many-body Hamiltonian, with amplitudes that we extract from the mean-field approximation. This many-body state breaks the symmetry of the Hamiltonian; it has the same energy to leading order in NNN as the mean-field state and the corresponding eigenstate of the Hamiltonian, however, it has a lower energy to subleading order in NNN and thus it is energetically favorable.