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Physical Review A

Spontaneous and stimulated combination scattering from alkali-metal Bose-Einstein condensates

Y. B. Band

Published Aug 1, 1996• 2 citations
Publisher

Abstract

We calculate the spontaneous and stimulated nonresonant combination scattering cross sections from a finite-size trapped alkali-metal Bose-Einstein condensate (BEC). The probabilities for scattered radiation at frequencies which differ from the incident frequency by elementary vibrational-rotational-spin excitations of the BEC are thereby determined. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.1500

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We calculate the spontaneous and stimulated nonresonant combination scattering cross sections from a finite-size trapped alkali-metal Bose-Einstein condensate (BEC). The probabilities for scattered radiation at frequencies which differ from the incident frequency by elementary vibrational-rotational-spin excitations of the BEC are thereby determined. \textcopyright{} 1996 The American Physical Society.
The scattering of an incident electron by a pure Bose-Einstein condensate of alkali-metal atoms confined to a three-dimensional harmonic-oscillator potential is investigated to give the corresponding differential cross section. It is shown that for the elastic scattering process the differential cross section is proportional to the square of the number of condensed atoms, and hence can be called the ``coherent scattering.'' For the inelastic scattering process, the stopping power is obtained by considering the state of the center of mass and the internal electronic state of the condensed atom being excited separately and simultaneously, which is found to be proportional to the 75\frac{7}{5}57​ power of the number of condensed atoms when the binary collision interaction between atoms is taken into account.
We describe a method for finding the excitation frequencies of a Bosecondensed collection of trapped, neutral atoms. These excitations are the equivalents of the collisionless phonons in a homogeneous gas. Numerical results for a small assembly of trapped atoms are also presented. We discuss how one may be able to use these excitations as diagnostics of Bose condensates formed, for example, in evaporative cooling of alkali atoms. I. INTRODUCTION Now that Bose-Einstein condensation (BEC) has been achieved in a magnetic, alkalivapor trap [1], we soon hope to be able to look at its dynamical behavior. The approach used to produce this condensate combined laser- and evaporative-cooling techniques [2,3]. By the standards of most condensed-matter experiments, however, the trap used in this experiment was very small and the condensate formed in it correspondingly very inhomogeneous. Planning and analyzing experiments to probe this novel condensate requires a theory of how it responds to ext...
We present a Thomas-Fermi treatment of resonant incoherent scattering of low-intensity light by a dilute spatially confined Bose-Einstein condensate. The description gives simple analytical results and allows scattering data from finite-size condensates to be interpreted in terms of the properties of the homogeneous BEC-system. As an example, we show how the energy dispersion of the elementary excitations can be measured from scattering by a finite-size atomic-trap condensate. As a second example, we point out that a near-resonant scattering experiment can observe quasi-particle creation caused by particle annihilation.
Considering the Fermi gases of alkali-metal atoms that are trapped in a harmonic potential, we study theoretically the elastic and inelastic scattering of the electrons by the trapped Fermi atoms and present the corresponding differential cross sections. We also obtain the stopping power for the cases that the electronic state as well as the center-of-mass state are excited both separately and simultaneously. It is shown that the elastic scattering process is no longer coherent in contrast to the electron scattering by the atomic Bose-Einstein condensate (BEC). For the inelastic scattering process, on the other hand, the differential cross section is found to be proportional to the 2/3 power of the number of the trapped atoms. In particular, the trapped fermionic atoms display the effect of ``Fermi surface,'' that is, only the energy levels near the Fermi energy have dominant contributions to the scattering process. Moreover, it is found that the stopping power scales as the 7/6 power of the atomic number. These results are fundamentally different from those of the electron scattering by the atomic BEC, mainly due to the different statistics obeyed by the trapped atomic systems.