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Bulletin of the American Physical Society

Macroscopic quantum tunneling of a single vortex in a rotating Bose-Einstein condensate

Kinjal Dasbiswas, Alan T. Dorsey

Published Feb 28, 2012• 0 citations
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Icy tornadoes in the quantum world - Josephson junctions of Bose-Einstein condensates : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematical Physics at Centre for Theoretical Chemistry and Physics, New Zealand Institute for Advanced Study, Massey University, Albany, New Zealand

G. F. Jaritz

This thesis presents a theoretical study of ultra-cold gases in, or close to a Bose- \nEinstein condensed phase. A system of two coupled Bose-Einstein condensates \nshows strong resemblance to Josephson junctions, consisting of two superconductors \nlinked via a thin insulating barrier. In these systems quantised ring \ncurrents across the barrier (Josephson vortices) have been detected. We concentrate \non similar macroscopic quantum states in our systems of linear and \nannular coupled Bose-Einstein condensates, and test them towards their potential \nfor showing macroscopic quantum tunnelling. \nFor the linear system we present a very detailed stability analysis of the stationary \nsolutions, the vortex and the soliton, using Bogoliubov-de Gennes theory. \nAn analytic approximation of the unstable mode is provided. We show that the \ntransition between vortices rotating in opposite directions is possible and propose \nan effective potential separating these two states. For the annular system \nof two coupled ring shaped condensates of different radii, we review the parameter \nregimes for finding vortices in the ground state. We show that pinning of \nvortices via a repulsive external potential is possible and suggest further steps \ntowards the detection of macroscopic quantum tunnelling.

•Jan 1, 2012•0 citations
We predict three-dimensional vortex solitons in a Bose—Einstein condensate under a complex potential, which is the combination of a two-dimensional parabolic trap along the transverse radial direction and a one-dimensional optical-lattice potential along the z axis direction. The vortex solitons are built in the form of a layer-chain structure made of several fundamental vortices along the optical-lattice direction. This has not been reported before in the three-dimensional Bose—Einstein condensate. By using a combination of the energy density functional method with direct numerical simulation, we find three-dimensional vortex solitons with topological charges χ = 1, χ = 2, and χ = 3. Moreover, the macroscopic quantum tunneling and chirp phenomena of the vortex solitons are shown in the evolution. Therein, the occurrence of macroscopic quantum tunneling provides the possibility for the experimental realization of quantum tunneling. Specifically, we successfully manipulate the vortex solitons along the optical lattice direction. The stability limits for dragging the vortex solitons from an initial fixed position to a prescribed location are further pursued.
In this paper we systematically study the double-layer vortex lattice model, which is proposed to illustrate the interplay between the physics of a fast rotating Bose-Einstein condensate and the macroscopic quantum tunneling. The phase diagram of the system is obtained. We find that under certain conditions the system will exhibit a phase transition which is a consequence of the competition between interlayer coherent hopping and the interlayer density-density interaction. In one phase the vortices in one layer coincide with those in the other layer. In another phase two sets of vortex lattices are staggered, and as a result the quantum tunneling between two layers is suppressed. To obtain the phase diagram we use the quantum Hall mean field and Thomas-Fermi mean field theories. Two different criteria for the transition taking place are obtained, which reveals some fundamental differences between these two mean-field states. The sliding mode excitation is also discussed.
This thesis presents a theoretical study of ultra-cold gases in, or close to a Bose- \nEinstein condensed phase. A system of two coupled Bose-Einstein condensates \nshows strong resemblance to Josephson junctions, consisting of two superconductors \nlinked via a thin insulating barrier. In these systems quantised ring \ncurrents across the barrier (Josephson vortices) have been detected. We concentrate \non similar macroscopic quantum states in our systems of linear and \nannular coupled Bose-Einstein condensates, and test them towards their potential \nfor showing macroscopic quantum tunnelling. \nFor the linear system we present a very detailed stability analysis of the stationary \nsolutions, the vortex and the soliton, using Bogoliubov-de Gennes theory. \nAn analytic approximation of the unstable mode is provided. We show that the \ntransition between vortices rotating in opposite directions is possible and propose \nan effective potential separating these two states. For the annular system \nof two coupled ring shaped condensates of different radii, we review the parameter \nregimes for finding vortices in the ground state. We show that pinning of \nvortices via a repulsive external potential is possible and suggest further steps \ntowards the detection of macroscopic quantum tunnelling.