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Physical Review A

Management of Bose-Einstein condensates by a spatially periodic modulation of the atomic s -wave scattering length

Guangjiong Dong, Bambi Hu

Published Jan 29, 2007• 28 citations
Publisher

Abstract

We investigate the effect of the position-dependent $s$-wave scattering length (SSL) on Bose-Einstein condensate (BEC) dynamics. In particular, we study the propagation of a BEC within a finite regime where the SSL, tuned by a periodic magnetic or optical field, results in the Bragg scattering of the BEC. We have predicted a matter-wave optical limiting process and bistability, which have potential applications like a matter wave limiter, a BEC mirror or cavity, and an atomic switch. The first phenomenon is a direct result of this periodic spatial tuning, showing that the position-dependent tuning of the SSL has the potential to result in novel properties of ultracold atomic gases.

DOI
10.1103/physreva.75.013625

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We investigate the effect of the position-dependent sss-wave scattering length (SSL) on Bose-Einstein condensate (BEC) dynamics. In particular, we study the propagation of a BEC within a finite regime where the SSL, tuned by a periodic magnetic or optical field, results in the Bragg scattering of the BEC. We have predicted a matter-wave optical limiting process and bistability, which have potential applications like a matter wave limiter, a BEC mirror or cavity, and an atomic switch. The first phenomenon is a direct result of this periodic spatial tuning, showing that the position-dependent tuning of the SSL has the potential to result in novel properties of ultracold atomic gases.
We briefly review our recent work on spatial tuning of Bose-Einstein condensation (BEC). We first study spatially periodic tuning of the s-wave scattering length for controlling the propagation of a BEC matter wave, and find matter wave limiting processing and bistability. Second, we show that a stable BEC with natural attractive interaction could be formed by tuning the s -wave scattering length with a Gaussian optical field, but the condensed atom number should be less than a critical value. Further, we apply Thomas-Fermi approximation to obtain a formula for this critical value.
In this paper, we explore a scheme to tackle a challenging problem of stable Bose-Einstein condensates (BECs) with attractive atom interactions. In this scheme, the sss-wave scattering length is tuned in space, rather than in time as previously studied, by a far-off-resonant Gaussian optical field, from negative to positive in the center region of the potential well. We find that this tuning leads to coexisting repulsive and attractive interactions within a single atomic gas and consequently a stable BEC in the repulsive region. We investigate the ground-state properties of the tuned BECs and show them to exhibit a strikingly different spatial density distribution from a conventional one with a positive sss-wave scattering length. The tuned BEC is formed only when the condensed number is less than a critical number. We derive a formula for the critical number.
We demonstrate submicron spatial control of interatomic interactions in a Bose-Einstein condensate of ytterbium (Yb). A pulsed optical standing wave, tuned near an optical Feshbach resonance, varies the s-wave scattering length continuously across the standing wave pattern. The modulated mean-field energy with a spatial period every 278 nm is monitored by a diffraction pattern in a time-of-flight image. We observe a wide scattering length control of up to 250 nm. The demonstrated spatial modulation of the scattering length proves that high resolution control of atomic interactions is possible.
In this paper, we consider a Gross-Pitaevskii (GP) equation with a time-dependent nonlinearity and a spatiotemporal complex linear term which describes the dynamics of matter-wave solitons in Bose-Einstein condensates (BECs) with time-dependent interatomic interactions in a parabolic potential in the presence of feeding or loss of atoms. We establish the integrability conditions under which analytical solutions describing the modulational instability and the propagation of both bright and dark solitary waves on a continuous wave background are obtained. The obtained integrability conditions also appear as the conditions under which the solitary waves of the BECs can be managed by controlling the functional gain or loss parameter. For specific BECs, the dynamics of bright and dark solitons are investigated analytically through the found exact solutions of the GP equation. Our results show that under the integrability conditions, the gain or loss parameter of the GP equation can be used to manage the motion of both bright and dark solitons. We show that for BECs with loss (gain) of atoms, the bright and dark solitons during their propagation have a compression (broadening) in their width. Furthermore, under a safe range of parameters and under the integrability conditions, it is possible to squeeze a bright soliton of BECs with loss of atoms into the assumed peak matter density, which can provide an experimental tool for investigating the range of validity of the 1D GP equation. Our results also reveal that under the conditions of the solitary wave management, neither the injection or the ejection of atoms from the condensate affects the soliton peak during its propagation.
We study the motion of bright matter-wave solitons in nonlinear potentials, produced by periodic or random spatial variations of the atomic scattering length. We obtain analytical results for the soliton motion, the radiation of matter wave, and the radiative soliton decay in such configurations of the Bose-Einstein condensate. The stable regimes of propagation are analyzed. The results are in remarkable agreement with the numerical simulations of the Gross-Pitaevskii equation with periodic or random spatial variations of the mean field interactions.