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Physical Review A

Atomic soliton reservoir: How to increase the critical atom number in negative-scattering-length Bose-Einstein gases

Humberto Michinel, Víctor M. Pérez‐García, Raúl de la Fuente

Published Aug 1, 1999• 27 citations
Publisher

Abstract

We study the stabilization of a large negative scattering length Bose-Einstein condensate by using a multisoliton fringe system. Each fringe behaves like a quasiparticle and the whole cloud forms a stable system when the trapping in one or two directions is switched off. The resulting system can be used as a coherent source of atomic solitons. A discussion on how to generate the soliton fringe system experimentally is made.

DOI
10.1103/physreva.60.1513

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We study the stabilization of a large negative scattering length Bose-Einstein condensate by using a multisoliton fringe system. Each fringe behaves like a quasiparticle and the whole cloud forms a stable system when the trapping in one or two directions is switched off. The resulting system can be used as a coherent source of atomic solitons. A discussion on how to generate the soliton fringe system experimentally is made.
It is shown that simultaneously changing the scattering length of an elongated, harmonically trapped Bose-Einstein condensate from positive to negative and inverting the axial portion of the trap, so that it becomes expulsive, results in a train of self-coherent solitonic pulses. Each pulse is itself a nondispersive attractive Bose-Einstein condensate that rapidly self-cools. The axial trap functions as a waveguide. The solitons can be made robustly stable with the right choice of trap geometry, number of atoms, and interaction strength. Theoretical and numerical evidence suggests that such a pulsed atomic soliton laser can be made in present experiments.
We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically 7Li.{}^{7}\mathrm{Li}.7Li. Our method is to solve the time-dependent nonlinear Schr\"odinger equation numerically. For an isolated condensate, with no gain or loss, we find that the system is stable (apart from quantum tunneling) if the particle number N is less than a critical number Nc.{N}_{c}.Nc​. For N>Nc,N>{N}_{c},N>Nc​, the system collapses to high-density clumps in a region near the center of the trap. The time for the onset of collapse is on the order of one trap period. Within numerical uncertainty, the results are consistent with the formation of a ``black hole'' of infinite density fluctuations, as predicted by Ueda and Huang [Phys. Rev. A (to be published)]. We numerically obtain ${N}_{c}\ensuremath{\approx}1251.$ We then include gain-loss mechanisms, i.e., the gain of atoms from a surrounding ``thermal cloud,'' and the loss due to two- and three-body collisions. The number N now oscillates in a steady state, with a period of about 145 trap periods. We obtain ${N}_{c}\ensuremath{\approx}1260$ as the maximum value in the oscillations.
We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates. Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multisoliton states emerge as a nonlinear continuation of the appropriate excited eigenstates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states are dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally, we present experimental realizations of multisoliton states including a three-soliton state consisting of two solitons oscillating around a stationary one and compare the relevant results to the predictions of the theoretical mean-field model.
We discuss Bose-Einstein condensation in a trapped atomic gas and analyze how the sign of the scattering length a and the ratio \ensuremath{\eta} of the interaction between particles to the level spacing in the trap influence the behavior of the condensate wave function ${\ensuremath{\psi}}_{0}$. We find that for a<0a<0a<0 and $\ensuremath{\eta}\ensuremath{\ll}1$ it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For $\ensuremath{\eta}\ensuremath{\gg}1$ a negative scattering length prevents the formation of the condensate. If a>0a>0a>0, then an increase of density is accompanied by the evolution of ${\ensuremath{\psi}}_{0}$ to a comparatively wide quasihomogeneous distribution.