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Quantum Electronics and Laser Science Conference

The excitation spectrum of a Bose-Einstein condensate

Jeff Steinhauer, Roee Ozeri, Nadav Y. Katz, Nir Davidson

Published Jan 1, 2002• 32 citations
Publisher

Abstract

Summary form only given. The excitation spectrum of a Bose-Einstein condensate should give much insight into this system. For wavelengths much shorter than the radius of the condensate, the excitation spectrum is an essentially continuous function, which characterizes the intrinsic bulk properties of the condensate Previously, isolated points on the excitation spectrum and their dependence on the chemical potential were measured We report the first measurement of the excitation spectrum, as well as the static structure factor.

DOI
10.1109/qels.2002.1031264

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Summary form only given. The excitation spectrum of a Bose-Einstein condensate should give much insight into this system. For wavelengths much shorter than the radius of the condensate, the excitation spectrum is an essentially continuous function, which characterizes the intrinsic bulk properties of the condensate Previously, isolated points on the excitation spectrum and their dependence on the chemical potential were measured We report the first measurement of the excitation spectrum, as well as the static structure factor.
We report a measurement of the excitation spectrum omega(k) and the static structure factor S(k) of a Bose-Einstein condensate. The excitation spectrum displays a linear phonon regime, as well as a parabolic single-particle regime. The linear regime provides an upper limit for the superfluid critical velocity, by the Landau criterion. The excitation spectrum agrees well with the Bogoliubov spectrum in the local density approximation, even close to the long-wavelength limit of the region of applicability. Feynman's relation between omega(k) and S(k) is verified, within an overall constant.
The elementary excitation spectrum of a two-component Bose—Einstein condensate in different hyperfine states is obtained by Green's function method. It is found to have two branches. In the long wave-length limit, the two branches of the excitation spectrum are reduced to one phonon excitation and one single-particle excitation. The single-particle one has an energy gap. When the energy gap exists, we study the Landau critical velocity and the depletion of the condensate. With the obtained Green's functions, we calculate the structure factor of a two-component condensate. It is found that the static structure factor comprises only the branch of the phonon excitation and the single-particle excitation makes no contribution to the structure factor.
We calculate the two-photon $1S\ensuremath{-}2S$ spectrum of an atomic hydrogen Bose-Einstein condensate in the regime where the cold collision frequency shift dominates the line shape. Wentzel-Kramers-Brillouin and static phase approximations are made to find the intensities for transitions from the condensate to motional eigenstates for 2S2S2S atoms. The excited-state wave functions are found using a mean field potential, which includes the effects of collisions with condensate atoms. Results agree well with experimental data. This formalism can be used to find condensate spectra for a wide range of excitation schemes.
We investigate theoretically the properties of a Bose-Einstein condensate located in a spatially periodic potential. The excitations of the condensate are obtained from linear equations involving the periodic potential and the periodic condensate density. The Bloch ansatz therefore applies and the excitation spectrum exhibits band structure. If the periodic potential is accelerated, the condensate may undergo Bloch oscillations in the accelerated frame, corresponding to an acceleration without spreading of the entire condensate.