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Physical Review A

Nonlinear atom optics with bright matter-wave soliton trains

Vanessa Y. F. Leung, Andrew G. Truscott, K. G. H. Baldwin

Published Dec 31, 2002• 26 citations
Publisher

Abstract

Bright-soliton train creation and evolution in a Bose-Einstein condensate is simulated numerically using the experimental conditions of K. E. Strecker et al. [Nature 417, 150 (2002)] as a starting point. We identify the controlling factors that dictate soliton number, phase imprinting, and stability. Reliable production of multiple phase-engineered condensed-matter pulses can have practical applications to future nonlinear atom optics experiments, which we illustrate with an example of colinear scattering between repulsive solitons.

DOI
10.1103/physreva.66.061602

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Bright-soliton train creation and evolution in a Bose-Einstein condensate is simulated numerically using the experimental conditions of K. E. Strecker et al. [Nature 417, 150 (2002)] as a starting point. We identify the controlling factors that dictate soliton number, phase imprinting, and stability. Reliable production of multiple phase-engineered condensed-matter pulses can have practical applications to future nonlinear atom optics experiments, which we illustrate with an example of colinear scattering between repulsive solitons.
The results of one experiment (Strecker et. al.), is numerically simulated to demonstrate that a mean-field approach is capable of describing an attractive condensate in an area of nonlinear behavior such as soliton creation, and to investigate the soliton interactions by extending the experimental parameters. In the experiment being studied, the released BEC formed a train of multiple solitons which oscillated collectively in a weak harmonic potential for many cycles, each soliton kept apart from its neighbor by the alternating phase structure of the ensemble. This result suggests the possibility of designing a series of self-focussing, phase-engineered coherent matter pulses as the basis of future experiments in non-linear atom optics. Experimentally, a quasi-1D condensate was formed in a box-like potential with significantly tighter confinement in the transverse than the axial dimension. Manipulation of a Feshbach resonance rapidly tuned the scattering length of the atoms from positive to negative, resulting in a condensate which became attractive at, or shortly after, its release. Most of the unconfined atoms were ejected in a burst, leaving behind a small proportion of remnant atoms as solitons. These were allowed to evolve as they propagated along the axial potential of a far red-detuned laser field for a short time before being imaged.
We review recent experimental and theoretical work on the creation of bright matter wave solitons in Bose–Einstein condensates. In two recent experiments, solitons are formed from Bose–Einstein condensates of 7 Li by utilizing a Feshbach resonance to switch from repulsive to attractive interactions. The solitons are made to propagate in a one-dimensional potential formed by a focused laser beam. For repulsive interactions, the wavepacket undergoes dispersive wavepacket spreading, while for attractive interactions, localized solitons are formed. In our experiment, a multi-soliton train containing up to ten solitons is observed to propagate without spreading for a duration of 2 s. Adjacent solitons are found to interact repulsively, in agreement with a calculation based on the nonlinear Schrödinger equation assuming that the soliton train is formed with an alternating phase structure. The origin of this phase structure is not entirely clear.
Solitons are localized wave packets whose dispersion is compensated by a nonlinearity. Solitons are observed in many wave settings including optics, fluids, plasmas, and matter-waves. Bright matter-wave solitons were first created by quenching the interactions in a quasi-one dimensional atomic Bose-Einstein condensate (BEC) from repulsive to attractive. Under some conditions a train of up to 10 solitons was formed. Neighboring solitons were observed to repel one another, an effect that was attributed to an alternating π-0-π phase distribution. There has been a theoretical debate whether this phase structure is inherent to the formation of the train, or if it evolves through a series of mergers and annihilations between neighboring solitons that are in-phase, and hence attractive. This paper shows that the interaction quench initiates a modulation instability (MI) in which weak perturbations undergo a nonlinear amplification, resulting in their exponential growth. Results show that the number of solitons is consistent with the initial size of the condensate divided by 2πξ. Furthermore, once formed, there are few solitons lost to merger or annihilation collisions. From this, we conclude that the soliton train is created with an alternating phase structure, rather than evolving into one.
We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.
Quantum phase engineering is demonstrated with two techniques that allow the spatial phase distribution of a Bose-Einstein condensate (BEC) to be written and read out. A quantum state was designed and produced by optically imprinting a phase pattern onto a BEC of sodium atoms, and matter-wave interferometry with spatially resolved imaging was used to analyze the resultant phase distribution. An appropriate phase imprint created solitons, the first experimental realization of this nonlinear phenomenon in a BEC. The subsequent evolution of these excitations was investigated both experimentally and theoretically.