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

Abstract

We consider the dynamics of a quantum degenerate trapped gas of 7 Li atoms. Because the atoms have a negative s-wave scattering length, a Bose condensate of 7 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. [S0031-9007(98) show in this paper that the dynamical behavior of a negative scattering length gas, such as 7 Li, is especially interesting, and offers the opportunity to directly observe and study macroscopic quantum tunneling.A negative scattering length a implies effectively attractive interactions. In a spatially homogeneous gas, these interactions lead to ordinary classical condensation into a liquid or solid, preventing Bose-Einstein condensation in the metastable region of the phase diagram [5]. However, confinement in an atom trap produces stabilizing forces that enable the formation of a metastable BoseEinstein condensate, if the number of condensed atoms is less than some maximum number N m . For a harmonic trap, Ruprecht et al. [6] showed that in mean-field theory N m Ӎ 0.57l͞jaj, where l ͑h͞mv͒ 1͞2 is the extent of the one-particle ground state in the harmonic trap [7]. For the 7 Li experiments of Ref. [8], N m Ӎ 1400 atoms, which agrees with the measured value.Although a condensate can exist in a trapped gas, it is predicted to be metastable and to decay by quantum or thermal fluctuations [9][10][11]. The condensate has only one unstable collective mode, which in the case of an isotropic trap corresponds to the breathing mode [12,13]. The condensate therefore collapses as a whole, either by thermal excitation over or by quantum mechanical tunneling through a macroscopic energy barrier in configuration space. The probability of forming small, dense clusters is greatly suppressed because of the large energy barrier for this process, compared to that for the breathing mode. This suppression can also be understood from the fact that the typical length scale for fluctuations of the condensate is the healing length, which is approximately equal to the condensate size near the instability point.Experimentally, it is also important to understand how such a condensate can be formed from a noncondensed cloud by means of evaporative cooling. This question was recently addressed by Gardiner et al. in the context of experiments with gases having a . 0 [14]. These authors neglect the coherent dynamics of the condensate and focus instead on the kinetics of condensation [15]. By treating the noncondensed atoms as a static "heat bath," they are able to derive a simple equation for the growth of the number of condensate particles that appears to fit well with experimental results [4]. The same approach, however, doe...

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

“…Bright solitons in higher dimensions are prone to a different type of instability due to the intrinsic collapse of solutions of the NLS equation [12]. The first experiments with attractive condensates suffered from this collapse instability [81,82,435,436] while the more recent experiments were able to focus on stable regimes and demonstrate bright soliton formation [40][41][42]. In fact, the key feature of these experiments was the quasi-1D nature of the attractive BEC realized in anisotropic traps as discussed in Sec.…”

Structure formation during the collapse of a dipolar atomic Bose-Einstein condensate

“…In the latter case, collapse occurs when the atomic interactions are sufficiently attractive. For the usual case of isotropic s-wave interactions experiments have demonstrated both global [5] and local collapse [7] depending upon, respectively, whether the imaginary healing length is of similar size or much smaller than the BEC [10]. During global collapse the monopole mode becomes dynamically unstable and the BEC evolves towards a point singularity, with the threshold for collapse generally exhibiting a weak dependence on trap geometry [11,12].…”

Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices

“…The mean-field interaction energies required for the observation of solitonic effects are in general smaller or of the order of one tenth of the recoil energy ω Br : for the most relevant case of 87 Rb atoms and 23 Na, this value corresponds to reasonable densities of the order of 10 14 cm −3 . The characteristic time for the modulational instability and soliton formation processes described in the previous sections is of the order of ω Br t ≃ 500, which means t ≃ 20 ms for 23 Rb atoms and t ≃ 3 ms for 87 Na.…”

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