Nonlinear transport of Bose-Einstein condensates through mesoscopic waveguides

Abstract

We study the coherent flow of interacting Bose-condensed atoms in mesoscopic waveguide geometries. Analytical and numerical methods, based on the mean-field description of the condensate, are developed to study both stationary as well as time-dependent propagation processes. We apply these methods to the propagation of a condensate through an atomic quantum dot in a waveguide, discuss the nonlinear transmission spectrum and show that resonant transport is generally suppressed due to an interaction-induced bistability phenomenon. Finally, we establish a link between the nonlinear features of the transmission spectrum and the self-consistent quasibound states of the quantum dot.

Elastic and inelastic transmission in guided atom lasers: A truncated Wigner approach

“…This curve has been obtained by solving the stationary GP equation in the same way as it was done in Ref. [22]. The dashed black curves correspond to solutions of the stationary GP equation that are unstable (middle branch of the resonance peak) or inaccessible through a time-dependent loading of the waveguide at constant chemical potential (upper branch of the resonance peak).…”

“…A full many-body treatment of such an open system is very complex and impossible to solve exactly in practice. During last years, these scattering processes have been studied in the mean-field approximation described by a nonlinear Gross-Pitaevskii (GP) equation [21][22][23]. While this description gives satisfactory results for a weak nonlinearity, the question of validity arises rapidly in the case of strong nonlinear dynamics [23] where dynamical instabilities occur.…”

Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials

“…Conversely, the stationary scattering scenario has been extensively studied also on the basis of the Gross-Pitaevskii equation [42][43][44][45] by neglecting the non-condensate fraction. Recently, matter wave scattering based on the Hartree-Fock Bogoliubov theory has been suggested [46,47].…”

“…The factor 1/2 arises due to the indistinguishability of the two-particle scenario considered in detail in Appendix B.1. The value of the chemical potential µ is determined by the source term -an incident matter wave in a scattering setup -where ψ(r) takes the role of the scattering amplitude, see e. g. [43,44]. Consequently, a diagrammatic representation of the scattering process described by (139) can be developed [62], where now single particles propagate in a nonlinear medium.…”

Quantum Transport in the Black‐Hole Configuration of an Atom Condensate Outcoupled Through an Optical Lattice

“…Besides the clear gravitational analogue, the study of such quasi-stationary scenarios is of general interest for the investigation of atom quantum transport [30][31][32][33][34][35][36][37], within the emergent field of atomtronics [38,39]. For instance, the considered setup can be used to provide a quasi-stationary supersonic current, with a well controlled atom velocity.…”