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NATO ASI series. Series B : Physics

Interferometric Measurements Beyond the Shot-Noise Limit

Philippe Grangier, Richard E. Slusher, Bernard Yurke, Arthur La Porta

Published Jan 1, 1989• 1 citation
Publisher
DOI
10.1007/978-1-4757-6574-8_19

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An interferometric detection scheme to measure optical phase shift with sensitivity beyond the shot noise limit is proposed. The theoretical calculation shows that using the quantum correlated twin beams produced from an optical parametric amplifier as the input fields of a Mach-Zehnder interferometer, the minimum detectable phase shift will exceed the shot noise limit N-1/2 and approach the Heisenberg limit N-1. The parametric dependences of the minimum detectable phase shift on the nonlinear interaction, input photon number, and detection efficiency are shown.
Interferometers with atomic ensembles are an integral part of modern precision metrology. However, these interferometers are fundamentally restricted by the shot noise limit, which can only be overcome by creating quantum entanglement among the atoms. We used spin dynamics in Bose-Einstein condensates to create large ensembles of up to 10(4) pair-correlated atoms with an interferometric sensitivity -1.61(-1.1)(+0.98) decibels beyond the shot noise limit. Our proof-of-principle results point the way toward a new generation of atom interferometers.
We critically analyze the commonly maintained statement that entanglement is necessary to beat the shot-noise limit or standard quantum limit (SQL) in the sensitivity with which certain parameters can be measured in interferometric experiments. We consider in detail three different physical realizations of a beam splitter and a Mach-Zehnder interferometer using photons, massive bosons, and distinguishable spins or qubits. We study several input states and the corresponding definitions of entanglement. We show that mode entanglement is not required for photons or massive bosons for beating the SQL. In particular, with a fluctuating number of two-mode bosons, the shot-noise limit can be beaten by nonentangled bosonic states with all bosons in one mode. As a consequence, the trivially present entanglement due to symmetrization that appears when writing bosonic states in terms of individual particles is a useful resource for precision measurements.