Bragg Spectroscopy of a Bose-Einstein Condensate

Abstract

Properties of a Bose-Einstein condensate were studied by stimulated, two-photon Bragg scattering. The high momentum and energy resolution of this method allowed a spectroscopic measurement of the mean-field energy and of the intrinsic momentum uncertainty of the condensate. The coherence length of the condensate was shown to be equal to its size. Bragg spectroscopy can be used to determine the dynamic structure factor over a wide range of energy and momentum transfers.[S0031-9007(99)

Spinor Condensates and Light Scattering from Bose-Einstein Condensates

“…The above treatments, in which we considered the effects of each of these shifts separately, are valid predictions in two limiting cases: for large condensates so that µ/ ≫ q/mx c one can neglect Doppler broadening, while for small condensates where µ/ ≪ q/mx c one can neglect mean-field broadening. However, in our experiments on Bragg scattering in the free-particle regime [10], the Doppler and mean-field widths were comparable, and one must consider both effects simultaneously. We now show with the aid of simple sum rules that it is correct to add the Doppler broadening (Eq.…”

“…In our first experimental study of Bragg scattering, excitations in the free-particle regime were studied by using two counter-propagating Bragg beams [10]. As shown in Table 1, the recoil velocity and energy for an excitation with a momentum of two photon recoils ( q = 2 k) were clearly in the free-particle regime.…”

“…The Bragg resonance is shifted upwards by the chemical potential ∆ω ≃ µ/ , and the line strength tends to S( q) → 1 − µ/ ω 0 q . Thus, by measuring the frequency shift of the Bragg scattering resonance in the free-particle regime, one can directly measure the chemical potential [10]. For small wavevectors (q ≪ ξ −1 ), the Bose-Einstein condensate responds to optical excitation collectively with the creation of phonons.…”

“…This has been studied separately using stimulated Rayleigh scattering (or Bragg spectroscopy) [10], where the linewidth of the Bragg resonance resulted from Doppler and mean-field broadening. The observed FWHM of approximately 5 kHz yields a decoherence time of 32 µs, in good agreement with the value shown above.…”

“…In this paper, we describe two applications of Bragg spectroscopy to study excitations of a Bose-Einstein condensate in either the free-particle [10] (large momentum transfer) or the phonon [11] (small momentum transfer) regime. The discussion includes a description of the dynamic structure factor of a Bose-Einstein condensate which leads to the interpretation of our measurements as an observation of the zero-point momentum distribution of trapped condensates, as a measurement of the energies of free-particle and phonon excitations, and as evidence for correlations in the many-body condensate wavefunction introduced by interatomic interactions.…”