Quantum measurement of collective atomic position in optical lattice

A quantum-mechanical analysis of an indirect measurement of a collective atomic position in an optical standing wave is presented. Depending on the atom–field interaction and the time of measurement two different measurement regimes are identified. The first one reveals the semiclassical result [V.I. Balykin, V.G. Minogin, V.S. Letokhov, Rep. Prog. Phys. 13 (2000) 1429, I.Sh. Averbukh, Yehiam Prior, Phys. Rev. Lett. 94 (2005) 153002]. The second regime, however, is shown to measure a quantity different from that predicted by the semiclassical analysis. This quantity, being a specific function of the atomic coordinates, is what is required for the optimal implementation of the feedback cooling scheme [I.Sh. Averbukh, Yehiam Prior, Phys. Rev. Lett. 94 (2005) 153002].