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arXiv:cond-mat/9801014 · Physical Review Letters

Growth and Collapse of a Bose-Einstein Condensate with Attractive Interactions

Charles A. Sackett, Henk T. C. Stoof, Randall G. Hulet

Published Mar 9, 1998• 172 citations
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Abstract

We consider the dynamics of a quantum degenerate trapped gas of ${}^{7}\mathrm{Li}$ atoms. Because the atoms have a negative $s$-wave scattering length, a Bose condensate of ${}^{7}\mathrm{Li}$ becomes mechanically unstable when the number of condensate atoms approaches a maximum value. We calculate the dynamics of the collapse that occurs when the unstable point is reached. In addition, we use the quantum Boltzmann equation to investigate the nonequilibrium kinetics of the atomic distribution during and after evaporative cooling. The condensate is found to undergo many cycles of growth and collapse before a stationary state is reached.

DOI
10.1103/physrevlett.80.2031

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We consider the dynamics of a quantum degenerate trapped gas of 7Li{}^{7}\mathrm{Li}7Li atoms. Because the atoms have a negative sss-wave scattering length, a Bose condensate of 7Li{}^{7}\mathrm{Li}7Li becomes mechanically unstable when the number of condensate atoms approaches a maximum value. We calculate the dynamics of the collapse that occurs when the unstable point is reached. In addition, we use the quantum Boltzmann equation to investigate the nonequilibrium kinetics of the atomic distribution during and after evaporative cooling. The condensate is found to undergo many cycles of growth and collapse before a stationary state is reached.
Evolution and collapse of a trapped Bose condensate with negative scattering length are predetermined by 3-body recombination of Bose-condensed atoms and by feeding of the condensate from the nonequilibrium thermal cloud. The collapse, starting once the number of condensate atoms reaches the critical value, ceases and turns to expansion when the density becomes so high that the recombination losses dominate over attractive interparticle interaction. As a result, we obtain a sequence of collapses, each of them followed by dynamic oscillations of the condensate. In every collapse the 3-body recombination burns only a part of the Bose-condensed atoms.
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.
Bose-Einstein condensation (BEC) of 7Li has been investigated. Because the effective interaction between 7Li atoms is attractive, the condensate occupation number N 0 is limited to ∼ 1250 atoms, and when this limit is exceeded, the condensate becomes unstable with respect to mechanical collapse. The interplay of this limit and the natural growth of the condensate during BEC leads to complicated dynamical behavior, which has been studied both theoretically and experimentally. It has been modeled by solving the quantum Boltzmann equation, in conjunction with results from the nonlinear Schrodinger equation. It is found that N0 oscillates rapidly as the condensate alternately fills and collapses, and that the oscillations can persist for many cycles before the gas comes to equilibrium. Experimental evidence for these oscillations was obtained by repeatedly producing a condensate and measuring N 0. The results were seen to vary randomly from one measurement to the next, which is to be expected as the timing of the oscillations is intrinsically stochastic. The distribution of N0 values occurring was measured, and provides quantitative information on the condensate growth and collapse. The equilibration process itself was also observed, by quenching the gas into degeneracy and observing its relaxation.\nIn order to carry out these experiments, sensitive measurement and analysis techniques were developed which enabled N0 to be determined in situ with an accuracy of +/-20% and a precision of +/-60 atoms. The theoretical tools used to study quantum degenerate gases were also applied to the important experimental technique of evaporative cooling, which led to substantial optimization and improvements. As part of this study, the rate constant for dipolar relaxation was measured to be 1.05 +/- 0.1 x 10-14 cm3/s, in agreement with theoretical predictions.
The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with attractive 1/r1/r1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit signatures known from the nonlinear dynamics of autonomous Hamiltonian systems. The two stationary solutions created in a tangent bifurcation at a critical value of the scattering length are identified as elliptical and hyperbolical fixed points, corresponding to stable and unstable stationary states of the condensate. The stable stationary state is surrounded by elliptical islands, corresponding to condensates periodically oscillating in time, whereas condensate wave functions in the unstable region undergo a collapse within finite time. For negative scattering lengths below the tangent bifurcation no stationary solutions exist, i.e., the condensate is always unstable and collapses.
Bose-Einstein condensation (BEC) of atoms with attractive interactions is profoundly different from BEC of atoms with repulsive interactions. We describe experiments with Bose condensates of 7Li atoms, which are weakly attracting at ultralow temperature. We measure the distribution of condensate occupation numbers occurring in the gas using a near-resonant optical probe to image the atom cloud. This data shows that the number is limited and demonstrates the dynamics of condensate growth and collapse due to the attractive interactions.