Abstract
Differential interferometry (DI) with two coupled sensors is a most powerful approach for precision measurements in the presence of strong phase noise. However, DI has been studied and implemented only with classical resources. Here we generalize the theory of differential interferometry to the case of entangled probe states. We demonstrate that, for perfectly correlated interferometers and in the presence of arbitrary large phase noise, sub-shot noise sensitivities—up to the Heisenberg limit—are still possible with a special class of entangled states in the ideal lossless scenario. These states belong to a decoherence free subspace where entanglement is passively protected. Our work paves the way to the full exploitation of entanglement in precision measurements.
Highlights
Atom interferometers [1] offer nowadays unprecedented precision in the measurement of gravity [2], inertial forces [3], atomic properties [4] and fundamental constants [5]
In order to overcome this limitation, many experiments aiming at precision measurements adopt a differential scheme: two interferometers operating in parallel are affected by the same phase noise and accumulate a different phase shift induced by the measured field
We demonstrate that the Heisenberg limit (HL), which is believed to be only achievable in noiseless quantum interferometers [25, 26, 27, 28], is preserved by the lossless differential scheme as long as relative noise fluctuations are at the HL
Summary
Atom interferometers [1] offer nowadays unprecedented precision in the measurement of gravity [2], inertial forces [3], atomic properties [4] and fundamental constants [5]. The analysis of a single interferometer has emphasized [25, 26, 27, 28, 29] that sub-SN cannot be reached in presence of strong phase noise Is it possible to exploit DI with highly entangled states to overcome the SN [30] in such a noisy environment?. Equation (1) takes into account the full quantum correlations of the interferometers outcomes and provides the lowest possible phase uncertainty, given the conditional probability distribution P (μ|θ). It can be saturated for large m by the maximumlikelihood estimator [32].
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