Physics beyond mean-field in ultracold gases on atom chips

The goal of the present project is to theoretically study hitherto unexplored manifestations of the non-mean-field dynamics in one-dimensional (1D) ultra cold atomic gases and to propose feasible experimental tests for the theoretical results to be implemented on the novel, atom-chip based setups. In particular, we plan to theoretically investigate the following problems: 1. Development of the theory of quantum dark or gray solitons in 1D degenerate atomic Bose gases with effective repulsive interactions, that describes atomic correlation properties within an individual soliton as well as an interference pattern formation during a collision of two solitons. 2. Establishing the conditions for the existence of the well-defined phase between two dark solitons; suggestion of an experimental scheme for observation of dark-soliton interference in a closed (ring-like) atomic waveguide; comparative study of the dark- and bright-soliton interference. 3. Development of a Bethe-ansatz-based theory of fluctuations of the relative phase between two tunnel- coupled 1D quasi condensates and search for manifestation of the non-mean-field effects in the spectrum of elementary excitations associated with the relative phase and atom-number difference fluctuations. 4. Search for the regimes of non-linear flow of a 1D quantum Bose gas through an obstacle and in other waveguide configurations that result in drastic reduction of the atomic downstream density, which brings about the entry into the Tonks-Girardeau regime.