Inhomogeneous Light Shift Effects on Atomic Quantum State Evolution in   Non-Destructive Measurements
  Various parameters of a trapped collection of cold and ultracold atoms can be determined non--destructively by measuring the phase shift of an off--resonant probe beam, caused by the state dependent index of refraction of the atoms. The dispersive light--atom interaction, however, gives rise to a differential light shift (AC Stark shift) between the atomic states which, for a nonuniform probe intensity distribution, causes an inhomogeneous dephasing between the atoms. In this paper, we investigate the effects of this inhomogeneous light shift in non--destructive measurement schemes. We interpret our experimental data on dispersively probed Rabi oscillations and Ramsey fringes in terms of a simple light shift model which is shown to describe the observed behavior well. Furthermore, we show that by using spin echo techniques, the inhomogeneous phase shift distribution between the two clock levels can be reversed. 
Patrick Windpassinger, Daniel Oblak, Ulrich Busk Hoff, Juergen Appel,   Niels Kjaergaard, and Eugene S. Polzik