Transport of ultracold Bose gases beyond the Gross-Pitaevskii description

Abstract

We explore atom-laser-like transport processes of ultracold Bose-condensed atomic vapors in mesoscopic waveguide structures beyond the Gross-Pitaevskii mean-field theory. Based on a microscopic description of the transport process in the presence of a coherent source that models the outcoupling from a reservoir of perfectly Bose-Einstein condensed atoms, we derive a system of coupled quantum evolution equations that describe the dynamics of a dilute condensed Bose gas in the framework of the Hartree-Fock-Bogoliubov approximation. We apply this method to study the transport of dilute Bose gases through an atomic quantum dot and through waveguides with disorder. Our numerical simulations reveal that the onset of an explicitly time-dependent flow corresponds to the appearance of strong depletion of the condensate on the microscopic level and leads to a loss of global phase coherence.

Effective Hamiltonian and excitation spectrum of harmonically trapped bosons

“…A gapeless modification was proposed in [23] for homogenous Bose-condensates. Analysis of transport properties of Bose-condensates in mesoscopic waveguides was given in [24]. Bosons in random potentials were studied in [25], see also [26] for a comprehensive review containing, in particular, analysis of the HFB approximation in the nonuniform case and its generalizations.…”

Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials

“…However, for an increased incoming particle current the scattering solution turns permanently time-dependent, and the condensate and non-condensate densities rapidly fluctuate. As conjectured in [47], the lack of a stationary scattering solution is associated with a large fraction of non-condensed atoms, which, in turn, implies the breakdown of the Hartree-Fock-Bogoliubov theory. In other words, in order to describe this scattering behavior more thoroughly, a theoretical description is needed which overcomes the limitations of the Hartree-Fock-Bogoliubov theory, and in particular allows for a realistic description of large non-condensate fractions.…”

“…Recently, matter wave scattering based on the Hartree-Fock Bogoliubov theory has been suggested [46,47]. The analysis in [47] revealed that for increasing interaction strength a strong depletion of the condensate sets in, which, in turn, outreaches the regime of validity of this model. Hence, the development of a proper theoretical description far from equilibrium and capable of describing the full transition from a condensate to a non-condensate is in order.…”

“…The introduction of the Møller operator (48) allows us to write down a Lippmann-Schwinger equation forΩ + (E) 18 by inserting the relation (47) 18 The same reasoning is true for Ω − (E).…”

“…Let us motivate our modus operandi with the help of the recent paper by Ernst et al [47]. Within this work, the authors treat an asymptotically noninteracting matter wave, see Section 2.1, which is guided by means of an optical potential towards, and then scattered off a one-dimensional disorder potential.…”