Adaptive estimation of a time-varying phase with power-law spectrum
Hossein T. Dinani, Howard M. Wiseman, Dominic W. Berry · arXiv (Cornell University) · 2016
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 $p=2$. For the coherent state case we derive the achievable mean-square error analytically for even $p$, and compare it to the standard quantum limit as found previously.