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Cavity enhanced light scattering off an ultracold gas in an optical latticeconstitutes a quantum measurement with a controllable form of the measurementback-action. Time-resolved counting of scattered photons alters the state ofthe atoms without particle loss implementing a quantum nondemolition (QND)measurement. The conditional dynamics is given by the interplay betweenphotodetection events (quantum jumps) and no-count processes. The class ofemerging atomic many-body states can be chosen via the optical geometry andlight frequencies. Light detection along the angle of a diffraction maximum(Bragg angle) creates an atom-number squeezed state, while light detection atdiffraction minima leads to the macroscopic superposition states (Schroedingercat states) of different atom numbers in the cavity mode. A measurement of thecavity transmission intensity can lead to atom-number squeezed or macroscopicsuperposition states depending on its outcome. We analyze the robustness of thesuperposition with respect to missed counts and find that a transmissionmeasurement yields more robust and controllable superposition states than theones obtained by scattering at a diffraction minimum.

Quantum optics with quantum gases: controlled state reduction by designed light scattering