Adaptive estimation of a time-varying phase with a power-law spectrum via continuous squeezed states

TL;DR

This paper demonstrates that adaptive measurements on squeezed states can achieve the Heisenberg scaling for estimating a time-varying phase with a power-law spectrum, extending previous results to a broader class of spectral exponents.

Contribution

The paper introduces an adaptive measurement scheme that attains the generalized Heisenberg limit for phase estimation with power-law spectra, generalizing prior work limited to p=2.

Findings

Achieves Heisenberg scaling with adaptive measurements on squeezed states.

Provides analytical predictions and numerical validation of optimal parameters.

Extends phase estimation results to a range of spectral exponents p>1.

Abstract

When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum $1/|\omega|^p$ with $p>1$, then the generalized standard quantum limit and Heisenberg limit have recently been found to have scalings of $1/{\cal N}^{(p-1)/p}$ and $1/{\cal N}^{2(p-1)/(p+1)}$, respectively, where ${\cal N}$ is the mean photon flux. We show that this Heisenberg scaling can be achieved via adaptive measurements on squeezed states. We predict the experimental parameters analytically, and test them with numerical simulations. Previous work had considered the special case of $p=2$.