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Quantum Electronics and Laser Science Conference

Direct observation of growth and collapse of a Bose-Einstein condensate with attractive interactions

Jordan M. Gerton, Ionuţ D. Prodan, Randall G. Hulet, Dmitry Strekalov

Published Nov 13, 2002• 2 citations
Publisher

Abstract

Summary form only given. Quantum theory predicts that Bose-Einstein condensation (BEC) of a spatially homogeneous gas with attractive interactions is precluded by a conventional phase transition into either a liquid or solid. When confined to a trap, however, such a condensate can form provided that its occupation number No does not exceed a limiting value. The stability limit is determined by a balance between self-attraction and a repulsion arising from position-momentum uncertainty under conditions of spatial confinement. Near the stability limit, self-attraction can overwhelm the repulsion, causing the condensate to collapse. Growth of the condensate, therefore, is punctuated by intermittent collapses, which are triggered either by macroscopic quantum tunneling or thermal fluctuation. The data presented here are the first direct observations of the growth and collapse of Bose Einstein condensates with attractive interactions.

DOI
10.1109/qels.2001.962162

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Summary form only given. Quantum theory predicts that Bose-Einstein condensation (BEC) of a spatially homogeneous gas with attractive interactions is precluded by a conventional phase transition into either a liquid or solid. When confined to a trap, however, such a condensate can form provided that its occupation number No does not exceed a limiting value. The stability limit is determined by a balance between self-attraction and a repulsion arising from position-momentum uncertainty under conditions of spatial confinement. Near the stability limit, self-attraction can overwhelm the repulsion, causing the condensate to collapse. Growth of the condensate, therefore, is punctuated by intermittent collapses, which are triggered either by macroscopic quantum tunneling or thermal fluctuation. The data presented here are the first direct observations of the growth and collapse of Bose Einstein condensates with attractive interactions.
The point of instability of a Bose-Einstein condensate (BEC) due to attractive interactions was studied. Stable 85Rb BECs were created and then caused to collapse by slowly changing the atom-atom interaction from repulsive to attractive using a Feshbach resonance. At a critical value, an abrupt transition was observed in which atoms were ejected from the condensate. By measuring the onset of this transition as a function of number and attractive interaction strength, we determined the stability condition to be N(absolute value of a) / a(ho) = 0.459+/-0.012+/-0.054, slightly lower than the predicted value of 0.574.
Summary form only given. Bose-Einstein condensation (BEC) of trapped atomic vapor has been realized in several atomic species. The static and dynamical properties of BEC crucially depend on the sign of the interatomic interaction. When the interaction is attractive, BEC in a spatially uniform 3D system is unstable to collapse into a denser phase. In a spatially confined system, however, the zero-point energy serves as a kinetic obstacle against collapse, allowing metastable BEC to be formed if the number of BEC atoms is below a certain critical number. Above the critical number of atoms, BEC collapses. The BEC with attractive interactions, therefore, has been restricted to a small number of atoms (/spl sim/1000) and the number has not been controllable.
Among the species that have Bose-condensed, lithium 7 and rubidium 85 form unique condensates in that atoms interact attractively and that the energy barrier that stabilizes the gaseous Bose-Einstein condensates originates from the zero-point motion of atoms. This paper reviews some unique features of these new states of matter that are distinguished from those of other species with repulsive interactions. These include the density instability, macroscopic quantum tunneling, intermittent implosion, shellstructure formation, and partial quantization of circulation. 1. METASTABILITY AND DENSITY INSTABILITY OF THE CONDENSATE Atoms with attractive interactions are believed not to undergo Bose-Einstein condensation in the uniform 3D system. It is therefore appropriate to begin by discussing why attractive Bose-Einstein condensates (BEes) have been realized in trapped systems [1, 2]. A trapped BEe has three characteristic energies, namely, the kinetic, potential and interaction energies. The kinetic energy arises from the uncertainty principle, and is proportional to R-2 where R is the linear dimension of BEe. The trapping potential is usually harmonic, and therefore the potential energy is proportional to R2. The mean-field interaction energy is proportional to NoaR-3, where No and a denote the number of condensate atoms and the s-wave scattering length, respectively. The interaction energy and hence a are negative for attractive systems. The sum of these three energies F = No(AR-2 + BR2 CNolaIR-3), where A, B, Care positive constants, gives the total energy of the system which has a metastable minimum if No is smaller than a certain critical value Nc.lt is at this local minimum where a metastable BEe is believed to be formed. If No is larger than Nc' there is no metastable minimum and the condensate is bound to collapse to the R = 0 state, which is a metallic phase. It is clear from the above argument that the zero-point energy due to confinement serves as a kinetic obstacle against collapse, allowing the metastable BEe to be formed. For the case of attractive interactions, the lowest-energy collective mode is the
The nature of Bose-Einstein condensation (BEC) in atomic vapours depends critically on the mean-field interaction of the atoms. When this interaction is attractive, the number of atoms in the condensate is limited. The interplay of this limit and the natural growth of the condensate during BEC leads to complicated dynamical behaviour. We develop a model for this behaviour based on the nonlinear Schrödinger equation and the quantum Boltzmann equation. The condensate occupation number is predicted to oscillate rapidly as the condensate alternately fills and collapses, and the oscillations are seen to persist for many cycles before the gas comes to equilibrium. Experimental evidence for these oscillations in the case of 7 Li is presented, along with details of the experimental apparatus and methods.