Quantum limit for the atom-light interferometer

Abstract

The standard quantum limit is calculated for the atom-light interferometer. It is shown that the smallest detectable phase is

$$\delta \phi _{\min } = \frac{1}{2}[N_{atoms} + 4N_{photons} )/N_{atoms} N_{photons} ]^{1/2} .$$

Therefore, in practical experiments, the accuracy is limited by the square root of the number of atoms. We propose a novel correlated atom-photon state interferometer which makes a transition to the Heisenberg limit, δφ_min ∝ 1/N _atoms, as the atoms approach a Bose condensate. Such an interferometer may serve as a sensitive probe of the onset of Bose condensation. Finally, we point out that the correlated atom-photon state preparation scheme we propose may be used in a different way to approach the Heisenberg limit for non-Bose-condensed atoms.