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arXiv:0810.5687 · Physical Review A

Incoherence of Bose-Einstein condensates at supersonic speeds due to quantum noise

R. G. Scott, David A. W. Hutchinson

Published Dec 18, 2008• 14 citations
arXivHTMLPDF

Abstract

We calculate the effect of quantum noise in supersonic transport of Bose-Einstein condensates. When an obstacle obstructs the flow of atoms, quantum fluctuations cause atoms to be scattered incoherently into random directions. This suppresses the propagation of Cherenkov radiation, creating quantum turbulence and a crescent of incoherent atoms around the obstacle. We observe similar dynamics if the BEC is stirred by a laser beam: crescents of incoherent atoms are emitted from the laser's turning points. Finally, we investigate supersonic flow through a disordered potential, and find that the quantum fluctuations generate an accumulation of incoherent atoms as the condensate enters the disorder.

DOI
10.1103/physreva.78.063614

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Journal of Physics B Atomic Molecular and Optical Physics•Aug 7, 2008•25 citations
We calculate the effect of quantum noise in supersonic transport of Bose-Einstein condensates. When an obstacle obstructs the flow of atoms, quantum fluctuations cause atoms to be scattered incoherently into random directions. This suppresses the propagation of Cherenkov radiation, creating quantum turbulence and a crescent of incoherent atoms around the obstacle. We observe similar dynamics if the BEC is stirred by a laser beam: crescents of incoherent atoms are emitted from the laser's turning points. Finally, we investigate supersonic flow through a disordered potential, and find that the quantum fluctuations generate an accumulation of incoherent atoms as the condensate enters the disorder.
This thesis presents investigations on the interplay of coherence and many-body effects in the quasi one-dimensional transport of Bose-Einstein condensates (BEC) through scattering potentials. Such configurations can be realized with guided atom lasers that provide a coherent atomic beam. An exact theoretical description of the dynamics is out of reach due to the presence atom-atom interactions. Different levels of approximations are nevertheless possible with their strengths and weaknesses. The mean-field approximation, where the dynamics of the BEC is governed by the Gross-Pitaevskii equation, is most commonly used in the field of ultracold atoms. In this thesis the truncated Wigner method is used to go beyond the standard Gross-Pitaevskii description. This method is adapted in order to study the scattering of Bose-Einstein condensates in one-dimensional waveguides where atom-atom interactions and external potentials are nonvanishing only in a finite region of space. In this case, the truncated Wigner method is combined with the smooth exterior complex scaling method and incorporates quantum noise that originate from the vacuum fluctuations in the waveguide. Inelastic scattering is shown to play a major role in the resonant transport of BEC through a symmetric double potential barrier effectively forming an atomic quantum dot. Indeed, fully resonant transmission is prohibited and incoherent atoms as well as collective oscillations are detected in the transmitted beam. It is also shown that inelastic scattering destroys Anderson localization in the case of transport through disordered potentials. The classical (incoherent) ohmic transmission is recovered for finite atom-atom interactions. The validity of the truncated Wigner method is then assessed using the semiclassical van Vleck-Gutzwiller propagator in the Fock space of the many-body system. It is shown that the truncated Wigner method corresponds to the so-called diagonal approximation, and it is possible to identify the leading correction to the truncated Wigner results, which is provided by the so-called coherent backscattering (CBS) contribution. Coherent basckattering in Fock space is a genuine quantum many-body effect that lies beyond the reach of any mean-field approach. For the case of closed Bose-Hubbard models, the relevance of CBS is confirmed by numerically comparing the (classical) truncated Wigner evolution probabilities to the exact quantum probabilities in Bose-Hubbard models: While a CBS-induced enhancement of the return probability to the initial state is clearly seen in the exact quantum simulations of the bosonic many-body system, this enhancement is absent in the classical calculations. The magnitude and dependence of the CBS contribution on gauge fields, which break time-reversal invariance, is numerically confirmed. For the case of disordered open systems, it can be shown that this contribution as well as next-to leading order contributions vanish thereby confirming the validity of the truncated Wigner method.
A paper presents a theoretical investigation of subsonic and supersonic effects in a Bose-Einstein condensate (BEC). The BEC is represented by a time-dependent, nonlinear Schroedinger equation that includes terms for an external confining potential term and a weak interatomic repulsive potential proportional to the number density of atoms. From this model are derived Madelung equations, which relate the quantum phase with the number density, and which are used to represent excitations propagating through the BEC. These equations are shown to be analogous to the classical equations of flow of an inviscid, compressible fluid characterized by a speed of sound (g/Po)1/2, where g is the coefficient of the repulsive potential and Po is the unperturbed mass density of the BEC. The equations are used to study the effects of a region of perturbation moving through the BEC. The excitations created by a perturbation moving at subsonic speed are found to be described by a Laplace equation and to propagate at infinite speed. For a supersonically moving perturbation, the excitations are found to be described by a wave equation and to propagate at finite speed inside a Mach cone.
We report the experimental generation of two-dimensional quantum turbulence in dilute-gas Bose-Einstein condensates by stirring the condensate with a laser beam, and the decay of the turbulent state to a large-scale flow in the form of a persistent current in a toroidal trap geometry. From numerical simulations of the stirring process, we characterize the dynamics of the quantized vortices in the condensate, and analyze the kinetic energy spectrum. Our observations are consistent with basic features of two-dimensional turbulence in classical incompressible fluids.
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The theory of stationary linear wave patterns generated in a supersonic flow of a Bose–Einstein condensate past a point-like obstacle is developed. It is shown that they are located mainly outside the Mach cone corresponding to infinitely long wavelengths. The shape of wave crests and dependence of amplitude on coordinates far enough from the obstacle are calculated. The results are in good agreement with the results of numerical simulations. The theory gives a qualitative description of experiments with Bose–Einstein condensate flow past an obstacle after the condensate's release from a trap.