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arXiv:cond-mat/9901109 · Physical Review Letters

Bragg Spectroscopy of a Bose-Einstein Condensate

J. Stenger, S. Inouye, A. P. Chikkatur, Dan Stamper-Kurn, David E. Pritchard, Wolfgang Ketterle

Published Jun 7, 1999• 764 citations
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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.

DOI
10.1103/physrevlett.82.4569

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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.
We study the properties of an atomic Bose--Einstein condensate produced in an optical-box potential, using high-resolution Bragg spectroscopy. For a range of box sizes, up to $70\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}$m, we directly observe Heisenberg-limited momentum uncertainty of the condensed atoms. We measure the condensate interaction energy with a precision of ${k}_{\mathrm{B}}\ifmmode\times\else\texttimes\fi{}100$ pK and study, both experimentally and numerically, the dynamics of its free expansion upon release from the box potential. All our measurements are in good agreement with theoretical expectations for a perfectly homogeneous condensate of spatial extent equal to the size of the box, which also establishes the uniformity of our optical-box system on a sub-nK energy scale.
Bose-Einstein condensates (BEC) serve as a model system for the study of the dynamic and spectroscopic response of a quantum system to momentum excitation. However, high -resolution spectroscopy of BEC has suffered from various finite-size (Doppler broadening) and inhomogeneous density effects [1]. We propose and demonstrate experimentally [2] a momentum space echo method using two and four -photon Bragg pulses, in order to overcome these broadening mechanisms. This method is pre sented in Fig. 1, where the excitation scheme and resulting populations in momentum space are shown. We demonstrate this scheme experimentally by using a four -photon echo pulse to reflect the initi ally populated excitations. The spectroscopic response of t he echo pulse is narrower than that of a regular Bragg pulse, as shown in Fig. 2.