Nonlinear scattering of atomic bright solitons in disorder

We observe nonlinear scattering of K atomic bright solitons launched in a onedimensional (1D) speckle disorder. We directly compare it with the scattering of non-interacting particles in the same disorder. The atoms in the soliton tend to be collectively either reflected or transmitted, in contrast with the behavior of independent particles in the singlescattering regime, thus demonstrating a clear nonlinear effect in scattering. The observed strong fluctuations in the reflected fraction, between zero and 100%, are interpreted as a consequence of the strong sensitivity of the system to the experimental conditions and in particular to the soliton velocity. This behavior is reproduced in a mean-field framework by Gross-Pitaevskii simulations, and mesoscopic quantum superpositions of the soliton being fully reflected and fully transmitted are not expected for our parameters. We discuss the conditions for observing such superpositions, which would find applications in atom interferometry beyond the standard quantum limit. editor’s choice Copyright c © EPLA, 2017 Introduction. – The physics of transport of particles in disorder is associated with different scenarios. In the absence of interaction, the simplest description is based on diffusion [1], but the coherence of the matter waves describing the particles can play a role, as in the phenomena of coherent backscattering [2–4] and Anderson localization [5–14]. However, in many physical systems, interactions cannot be ignored. In condensed-matter physics, interactions between electrons can strongly affect electric conductivity [15] and in optics, high-intensity light induces a nonlinear response of dielectrics, leading, for instance, to the optical Kerr effect, and thus spatial and/or temporal fluctuations of the index of refraction. Understanding the interplay between disorder and interactions in the transport of quantum particles is thus an important challenge. In a mean-field approach, one can use nonlinear wave equations in disordered media [16,17] in order to describe experimental observations of the competition between a weak nonlinearity and localization, in optics [18,19] or in ultra-cold quantum gases [20]. Beyond the mean-field approximation, many-body localization phenomena, leading to non-ergodic behavior, are predicted [21,22]. In this context, several problems of transport of interacting quantum gases in disorder have been studied [23–33]. We report here on a new phenomenon of nonlinear transport of quantum particles: nonlinear scattering of atomic bright solitons in an optical disorder. A soliton is a stable non-spreading wave packet, solution of a nonlinear wave equation, where a strong nonlinearity compensates dispersion. Solitons are ubiquitous in nonlinear wave physics [34,35]. Their propagation in a disordered medium is intriguing since the effect of the nonlinearity cannot be treated as a small perturbation of the non-interacting problem [36]. An atomic bright soliton is a 1D Bose-Einstein condensate of atoms with attractive interactions [37,38]. At the mean-field level, it is described by the Gross-Pitaevskii equation, which is identical to the so-called “nonlinear Schrödinger equation” used to describe the 1D propagation of light in Kerr media. This approach has been used to numerically study soliton nonlinear scattering on a narrow barrier [39–44]. Qualitatively similar results for a 1D disordered potential in the single-scattering regime can be expected. Experimentally, atomic bright soliton scattering has only been studied in the regime of negligible interaction energy, where the behavior resembles the one of non-interacting particles [45–47]. In this paper, we report the observation of nonlinear scattering of an atomic bright soliton in the regime where the interaction energy is of the order of the center-of-mass