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Physical Review A

Metastable Bose condensate made of atoms with attractive interaction

Edward Shuryak

Published Oct 1, 1996• 80 citations
Publisher

Abstract

Recent experiments with trapped cooled atoms have produced evidence for Bose-Einstein condensation (BEC). Among the atoms used are $^{7}\mathrm{Li}$, with attractive low-energy interaction. A potential barrier separating the condensed part from the collapse is studied and stability limits are established. The lifetime due to tunneling is estimated and is found to be very small. We further argue that BEC should have significant angular momentum L/N\ensuremath{\sim}1\ensuremath{\Elzxh} and thus both states with angular momentum ${\mathit{l}}_{\mathit{z}}$=0,1 should be ``macroscopically'' populated. Eventually, as rotation is slowed down, collapse and strong reheating should occur, in amusing resemblance to a supernova explosion. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.3151

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Recent experiments with trapped cooled atoms have produced evidence for Bose-Einstein condensation (BEC). Among the atoms used are 7Li^{7}\mathrm{Li}7Li, with attractive low-energy interaction. A potential barrier separating the condensed part from the collapse is studied and stability limits are established. The lifetime due to tunneling is estimated and is found to be very small. We further argue that BEC should have significant angular momentum L/N\ensuremath{\sim}1\ensuremath{\Elzxh} and thus both states with angular momentum lz{\mathit{l}}_{\mathit{z}}lz​=0,1 should be ``macroscopically'' populated. Eventually, as rotation is slowed down, collapse and strong reheating should occur, in amusing resemblance to a supernova explosion. \textcopyright{} 1996 The American Physical Society.
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.
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.
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
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.
Using the time-dependent mean-field Gross-Pitaevskii equation we study the dynamics of small repulsive Bose-Einstein condensed vortex states of 85Rb{}^{85}\mathrm{Rb}85Rb atoms in a cylindrical trap with low angular momentum $\ensuremath{\Elzxh}L$ per atom (L< 6),(L<~6),(L< 6), when the atomic interaction is suddenly turned attractive by manipulating the external magnetic field near a Feshbach resonance. Consequently, the condensate collapses and ejects atoms via explosion and a remnant condensate with a smaller number of atoms emerges that survives for a long time. Details of this collapse and explosion are compared critically with a similar experiment performed with zero angular momentum (L=0)(L=0)(L=0) by Donley et al. [Nature (London) 412, 295 (2001)]. A suggestion for a future experiment with the vortex state is made.