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Quantum-Atom Optics Downunder (QAO)

Dynamical formation of bright solitons in the collapse of Bose-Einstein condensates

Beata J. Dąbrowska-Wüster, Sebastian Wüster, Matthew J. Davis

Published Jan 1, 2007• 0 citations
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Abstract

We model the formation of bright atomic solitons due to collapse of Bose-Einstein condensates with attractive interactions reported by S. L. Cornish et al., [Phys. Rev. Lett. 96 170401 (2006)] in a realistic three dimensional situation. We show that mean-field theory does not adequately explain the experiment, while the inclusion of quantum fluctuations gives rise to bright soliton formation at the appropriate time scales. The solitons are produced either in-phase or out-of-phase and their number increases with the strength of the attractive interaction.

DOI
10.1364/qao.2007.qwe28

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We model the formation of bright atomic solitons due to collapse of Bose-Einstein condensates with attractive interactions reported by S. L. Cornish et al., [Phys. Rev. Lett. 96 170401 (2006)] in a realistic three dimensional situation. We show that mean-field theory does not adequately explain the experiment, while the inclusion of quantum fluctuations gives rise to bright soliton formation at the appropriate time scales. The solitons are produced either in-phase or out-of-phase and their number increases with the strength of the attractive interaction.
We model the dynamics of formation of multiple, long-lived, bright solitary waves (BSWs) in the collapse of Bose–Einstein condensates with attractive interactions as studied in the experiment of Cornish et al (2006 Phys. Rev. Lett. 96 170401). We use both mean-field and approximate quantum field simulation techniques. While a number of separated wave packets form as observed in the experiment, they do not have a repulsive π phase difference as has been previously inferred. We observe that the inclusion of quantum fluctuations causes soliton dynamics to be predominantly repulsive in one-dimensional (1D) simulations independent of their initial relative phase. However, indicative 3D simulations do not show a similar effect. In contrast, in 3D quantum noise has a negative impact on BSW lifetimes. Finally, we show that condensate oscillations, after the collapse, may serve to deduce three-body recombination rates.
We demonstrate the formation of bright solitons in coupled defocusing nonlinear Schroedinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type.
We observe bright matter-wave solitons form during the collapse of (85)Rb condensates in a three-dimensional (3D) magnetic trap. The collapse is induced by using a Feshbach resonance to suddenly switch the atomic interactions from repulsive to attractive. Remnant condensates containing several times the critical number of atoms for the onset of instability are observed to survive the collapse. Under these conditions a highly robust configuration of 3D solitons forms such that each soliton satisfies the condition for stability and neighboring solitons exhibit repulsive interactions.
The dynamics of an elongated attractive Bose-Einstein condensate in an axisymmetric harmonic trap is studied. It is shown that density fringes caused by self-interference of the condensate order parameter seed modulational instability. The latter has novel features in contradistinction to the usual homogeneous case known from nonlinear fiber optics. Several open questions in the interpretation of the recent creation of the first matter-wave bright soliton train [Nature (London) 417, 150 (2002)]] are addressed. It is shown that primary transverse collapse, followed by secondary collapse induced by soliton-soliton interactions, produces bursts of hot atoms at different time scales.
Generation, interaction, and detection of dark solitons in Bose-Einstein condensates are studied. In particular, we focus on the dynamics resulting from phase imprinting and density engineering. We show that solitons slow down significantly when the trap is opened and that soliton phase shifts after binary interactions cannot be observed with present experiments. Finally, motivated by the recent experimental results of Cornish et al. [Phys. Rev Lett. 85, 1795 (2000)], we analyze the stability of dark solitons under changes of the scattering length and thereby demonstrate a new way to detect them. Our theoretical and numerical results compare well with the existing experimental ones and provide guidance for future experiments.