Noisy quantum metrology enhanced by continuous nondemolition measurement

TL;DR

This paper demonstrates that continuous quantum nondemolition measurement can enhance frequency estimation precision in atomic ensembles, achieving superclassical scaling despite dephasing, through spin squeezing and optimized measurements.

Contribution

It introduces a protocol utilizing continuous QND measurement to improve quantum metrology, showing superclassical scaling and near-optimal measurement strategies in noisy environments.

Findings

Superclassical scaling of information with atom number N

Effective spin squeezing generated by continuous measurement

Near-optimal precision achieved with projective measurements

Abstract

We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N = 150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical scaling holds for different values of dephasing and monitoring efficiency. We moreover calculate the extra information obtainable via a final strong measurement on the conditional states generated during the dynamics and show that the corresponding ultimate limit is nearly achieved via a projective measurement of the spin-squeezed collective spin operator. We also briefly discuss the difference between our protocol and standard estimation schemes, where the state preparation time is neglected.