Phase Fluctuations in Bose-Einstein Condensates
  We demonstrate the existence of phase fluctuations in elongated Bose-Einstein Condensates (BECs) and study the dependence of those fluctuations on the system parameters. A strong dependence on temperature, atom number, and trapping geometry is observed. Phase fluctuations directly affect the coherence properties of BECs. In particular, we observe instances where the phase coherence length is significantly smaller than the condensate size. Our method of detecting phase fluctuations is based on their transformation into density modulations after ballistic expansion. An analytic theory describing this transformation is developed. 
D. Hellweg, S. Dettmer, P. Ryytty, J. J. Arlt, W. Ertmer, K.   Sengstock, D. S. Petrov, G. V. Shlyapnikov, H. Kreutzmann, L....