The occupation number of a magnetically trapped Bose-Einstein condensate is limited for atoms with attractive interactions. It has been predicted that, as this limit is approached, the condensate will collapse by a collective process. The measured spread in condensate number for samples of 7 Li atoms undergoing thermal equilibration is consistent with the occurrence of such collapses. [ S0031-9007(98) The attainment of Bose-Einstein condensation (BEC) in dilute atomic gases has provided a new domain for studying the nonlinear effects of interactions in thermodynamic systems. Among the gases in which BEC has been observed, 7 Li is unique in having a negative triplet s-wave scattering length a. Because a , 0, the effective interaction between atoms is attractive, and the BEC phenomenon is substantially altered. Attractive interactions were long believed to make a condensate unstable and thus prevent BEC [1,2], but it is now known that, for a confined gas, a metastable condensate can exist as long as its occupation number, N 0 , remains small [3]. Such condensates are predicted to be rich in physics, exhibiting properties such as solitonlike behavior [4] and macroscopic quantum tunneling [5]. In particular, complex dynamical behavior is expected as N 0 approaches its stability limit [6][7][8]. In this Letter, we describe experimental investigations of this behavior.Attractive interactions limit N 0 because, at a maximum number N m , the compressibility of the condensate becomes negative and it will implosively collapse. By equating the positive zero-point kinetic energy to the negative interaction energy, it is found that N m ϳ ᐉ͞jaj when the condensate is confined to volume ᐉ 3 . The stability limit is more precisely determined from numerical solution of the nonlinear Schrödinger equation (NLSE) [9]. For 7 Li in our magnetic trap, a 21.46 nm [10] and ᐉ ഠ 3 mm, which yield a stability limit of ϳ1250 atoms.As the gas is cooled below the critical temperature for BEC, N 0 grows until N m is reached. The condensate then collapses spontaneously if N 0 $ N m , or the collapse can be initiated by thermal fluctuations or quantum tunneling for N 0 & N m [5,7]. During the collapse, the condensate shrinks on the time scale of the trap oscillation period. As the density rises, the rates for inelastic collisions such as dipolar decay and three-body molecular recombination increase. These processes release sufficient energy to immediately eject the colliding atoms from the trap, thus reducing N 0 . The ejected atoms are very unlikely to further interact with the gas before leaving the trap, since the density of noncondensed atoms is low. As the collapse proceeds, the collision rate grows quickly enough that the density remains small compared to jaj 23 and the condensate remains a dilute gas [7,8].Both the collapse and the initial cooling process displace the gas from thermal equilibrium. As long as N 0 is smaller than its equilibrium value, as determined by the total number and average energy of the trapped atoms, the condensate...
