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arXiv:cond-mat/0407634 · Journal of Physics B Atomic Molecular and Optical Physics

Tunnelling induced collapse of an atomic Bose–Einstein condensate in a double-well potential

E Sakellari, Nick P. Proukakis, Charles S. Adams

Published Sep 15, 2004• 12 citations
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Abstract

The stability of a low temperature Bose-Einstein condensate with attractive interactions in one and three dimensional double-well potentials is discussed. In particular, the tunnelling dynamics of a condensate under the influence of a time-dependent potential gradient is investigated. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. The sensitivity of this tunnelling induced collapse could provide a useful tool in the study of condensates with attractive interactions.

DOI
10.1088/0953-4075/37/18/009

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The stability of a low temperature Bose-Einstein condensate with attractive interactions in one and three dimensional double-well potentials is discussed. In particular, the tunnelling dynamics of a condensate under the influence of a time-dependent potential gradient is investigated. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. The sensitivity of this tunnelling induced collapse could provide a useful tool in the study of condensates with attractive interactions.
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The stability of a low temperature Bose-Einstein condensate with attractive interactions in one and three dimensional double-well potentials is discussed. In particular, the tunnelling dynamics of a condensate under the influence of a timedependent potential gradient is investigated. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. The sensitivity of this tunnelling induced collapse could provide a useful tool in the study of condensates with attractive interactions. PACS numbers: 03.75.Lm, 03.75.kkTunnelling induced collapse in time-dependent double-well potential 2
In this Thesis we apply the Gross-Pitaevskii equation (GPE) to describe properties of a dilute, near zero temperature Bose gas for various confining geometries. We start by reviewing some basic information about the density, the chemical potential and elementary excitations of a dilute atomic condensate confined in a single harmonic trap for a Bose condensate with repulsive and attractive interactions and we also discuss the stability in the case of attractive interactions. We extend our study to a one and three dimensional double-well trap. We investigate the eigenenergy levels and show that the nonlinearity leads to triangular structures which appear either in the ground or excited states for the case of a Bose condensate with attractive or repulsive interactions respectively. We apply the eigenenergy level picture to analyse Josephson effects induced when the barrier IS moved at a constant velocity across the trapping potential or by the application of a time-dependent potential gradient. The GPE simulations are compared to the predictions of a nonlinear two state model. Above a critical velocity there is a transition to a superposition of ground and excited states which leads to sudden changes in the population difference. The direction of Josephson flow depends critically on the initial state of the system and we discuss the feasibility of experimental control of the atomic flow using phase-imprinting. The stability of a low temperature Bose-Einstein condensate with attract interactions in one and three dimensional double-well potentiate is discussed. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. Finally we investigate the stability and tunnelling effects in a multi-well system.
Recent experiments with trapped cooled atoms have produced evidences for Bose-Einstein condensation. Among the atoms used are 7Li^7Li7Li ones, with attractive low energy interaction. Stability of their condensate is studied, with a conclusion that for a number of atoms below the critical value there exist a metastable minimum, separated from collapse by a potential barrier. The lifetime due to tunneling is estimated: it is unlikely to happen in the present experiment. Although in experimental conditions most of the atoms are not in the condensate, we argue that they only slightly affect the stability conditions for the condensate evaluated at T=0.
We consider the quantum dynamics of a neutral atom Bose- Einstein condensate in a double-well potential, including hard-sphere particle interactions. Using a mean-field factorization we show that the coherent oscillations due to tunnelling are suppressed when the number of atoms exceeds a critical value. An exact quantum solution, in a two-mode approximation, shows that the mean-field solution is modulated by a quantum collapse and revival sequence. Chaotic dynamics results when the potential is modulated.