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We describe a collective state atomic interferometer (COSAIN) with the signalfringe as a function of phase-difference or rotation narrowed by $\sqrt{N}$compared to a conventional interferometer - $N$ being the number of atoms -without entanglement. This effect arises from the interferences amongcollective states, and is a manifestation of interference at a Comptonfrequency of ten nonillion Hz, or a de Broglie wavelength of ten attometer, for$N=10^6$ and $v = 300 m/s$. The population of the collective state of interestis detected by a null measurement scheme, in which an event corresponding todetection of zero photons corresponds to the system being in that particularcollective state. The signal is detected by collecting fluorescence throughstimulated Raman scattering of Stokes photons, which are emitted predominantlyagainst the direction of the probe beam, for a high enough resonant opticaldensity. The sensitivity of the ideal COSAIN is found to be given by thestandard quantum limit. However, when detection efficiency and collectionefficiency are taken into account, the detection scheme of the COSAIN increasesthe quantum efficiency of detection significantly in comparison to a typicalconventional Raman atomic interferometer employing fluorescence detection,yielding a net improvement in stability by as much as a factor of $10$. Wediscuss how the inhomogeneities arising from the non-uniformity in experimentalparameters affect the COSAIN signal. We also describe an alternate experimentalscheme to enhance resonant optical density in a COSAIN by using cross-linearlypolarized counter-propagating Raman beams.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

An N-atom Collective State Atomic Interferometer with Ultra-High Compton  Frequency and Ultra-Short de Broglie Wavelength, with root-N Reduction in  Fringe Width