Homodyne detection of matter-wave fields (shortened)
  A scheme is discussed that allows one for performing homodyne detection of the matter-wave field of ultracold bosonic atoms. It is based on a pump-probe lasers setup, that both illuminates a Bose-Einstein condensate, acting as reference system, and a second ultracold gas, composed by the same atoms but in a quantum phase to determine. Photon scattering outcouples atoms from both systems, which then propagate freely. Under appropriate conditions, when the same photon can either be scattered by the Bose-Einstein condensate or by the other quantum gas, both flux of outcoupled atoms and scattered photons exhibit oscillations, whose amplitude is proportional to the condensate fraction of the quantum gas. The setup can be extended to measure the first-order correlation function of a quantum gas. The dynamics here discussed make use of the entanglement between atoms and photons which is established by the scattering process in order to access detailed information on the quantum state of matter. 
Stefan Rist and Giovanna Morigi
cond-mat.quant-gas quant-ph