Increasing Sensitivity of an Atom Interferometer to the Heisenberg Limit using Enhanced Quantum Noise

Abstract

In a conventional atomic interferometer employing N atoms, the phase sensitivity is at the standard quantum limit: 1/ √ N . Using spin-squeezing, the sensitivity can be increased, either by lowering the quantum noise or via phase amplification, or a combination thereof. Here, we show how to increase the sensitivity, to the Heisenberg limit of 1/N , while increasing the quantum noise by √ N , thereby suppressing by the same factor the effect of excess noise. The proposed protocol makes use of a Schrödinger Cat state representing a mesoscopic superposition of two collective states of N atoms, behaving as a single entity with an N -fold increase in Compton frequency. The resulting N -fold phase magnification is revealed by using atomic state detection instead of collective state detection. We also show how to realize an atomic clock based on such a Schrödinger Cat state, with an N -fold increase in the effective transition frequency. We also discuss potential experimental constraints for implementing this scheme, using one axis twist squeezing employing the cavity feedback scheme, and show that the effects of cavity decay and spontaneous emission are highly suppressed due to the N -fold phase magnification. We find that even for a modest value of the cavity cooperativity parameter that should be readily accessible experimentally, the maximum improvement in sensitivity is very close to the ideal limit, for as many as ten million atoms.PACS numbers: 06.30. Gv, 03.75.Dg, 37.25.+k Using the fact that Ȯ = tr(ρÔ) for any operatorÔ, it

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