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arXiv:cond-mat/9811129 · Physical Review Letters

Self-Consistent Effects of Continuous Wave Output Coupling of Atoms from a Bose-Einstein Condensate

David A. W. Hutchinson

Published Jan 4, 1999• 22 citations
arXivHTMLPDF

Abstract

We present a self-consistent mean field model of the extraction of atoms from a Bose-Einstein condensate to form a cw atom laser. The model is based upon the Hartree-Fock-Bogoliubov equations within the Popov approximation, modified by the inclusion of spatially dependent source and sink terms, which lead to current flow within the condensate. The effects of this current flow are investigated for traps containing rubidium (repulsive effective interaction) and lithium (attractive interaction) atoms. The extra kinetic energy associated with this flow is shown to be able to stabilize the condensate in the attractive case against mechanical instability.

DOI
10.1103/physrevlett.82.6

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We present a self-consistent mean field model of the extraction of atoms from a Bose-Einstein condensate to form a cw atom laser. The model is based upon the Hartree-Fock-Bogoliubov equations within the Popov approximation, modified by the inclusion of spatially dependent source and sink terms, which lead to current flow within the condensate. The effects of this current flow are investigated for traps containing rubidium (repulsive effective interaction) and lithium (attractive interaction) atoms. The extra kinetic energy associated with this flow is shown to be able to stabilize the condensate in the attractive case against mechanical instability.
Summary form only given.Our treatment is based on a straightforward application of the quantum-field theory of atoms. Although the key result is obtained within the Hartree-Fock-Bogoliubov-Popov (HFB-Popov) approximation we believe it will be found to be valid in a wider context. The essential aspects of this result are as follows. First, current BEC systems are produced in atom traps, and so they are intrinsically inhomogeneous. Second, the condensed and noncondensed (thermal) fractions of the atomic gas are distributed differently over the trap, and they make separate and distinct contributions to the local coherence function.
We demonstrate a continuous output coupler for magnetically trapped atoms. Over a period of up to 100 ms, a collimated and monoenergetic beam of atoms is continuously extracted from a Bose-Einstein condensate. The intensity and kinetic energy of the output beam of this atom laser are controlled by a weak rf field that induces spin flips between trapped and untrapped states. Furthermore, the output coupler is used to perform a spectroscopic measurement of the condensate, which reveals the spatial distribution of the magnetically trapped condensate and allows manipulation of the condensate on a micrometer scale.
We study the stability of vortices in trapped single-component Bose–Einstein condensates within self-consistent mean-field theories; in particular, we consider the Hartree–Fock–Bogoliubov–Popov theory and its recently proposed gapless extensions. It is shown that for sufficiently repulsively interacting systems the anomalous negative-energy modes related to vortex instabilities are lifted to positive energies due to partial filling of the vortex core with noncondensed gas. Such behaviour implies that within these theories the vortex states are eventually stable against the transfer of condensate matter to the anomalous core modes. This self-stabilization of vortices, shown to occur under very general circumstances, is contrasted to the predictions of the non-self-consistent Bogoliubov approximation, which is known to exhibit anomalous modes for all vortex configurations and thus implying instability of these states. In addition, the shortcomings of these approximations in describing the properties of vortices are analysed, and the need for a self-consistent theory taking properly into account the coupled dynamics of the condensate and the noncondensate atoms is emphasized.
A self-consistent quantum theory is developed for an atomic laser utilizing cooling of atoms in a trap by the method of stimulated evaporation. The model describes the pumping and extraction of the atomic field from a trap upon its interaction with independent atomic reservoirs. The stimulated collisions between atoms in the trap, which produce a Bose condensate in the lower state of the trap, are considered. The interaction of atoms with a phonon field causes spontaneous transitions between the discrete states of the trap. Calculations performed for the three-and four-level models of the trap showed the possibility of generation of a strongly squeezed sub-Poisson Bose condensate.
We present two gapless mean-field theories for trapped Bose-Einstein condensates, and compare them to the better known Hartree-Fock-Bogoliubov (HFB)-Popov approach. The proposed theories are based on suitable inclusion of the simplest anomalous average of the Bose field operator. This leads to an effective interaction between two atoms which is both temperature and density dependent, as opposed to the HFB-Popov approach, for which it is constant. These theories are compared to the HFB-Popov approach for a trapped one-dimensional condensate of 2000 atoms. The density profiles and excitation frequencies of the proposed theories differ from the corresponding HFB-Popov ones by at most a few percent.