Kavli Affiliate: Birgitta Whaley
| First 5 Authors: Robert L. Cook, Liwen Ko, K. Birgitta Whaley, ,
| Summary:
We study the connection between exceptional points (EPs) and optimal
parameter estimation, in a simple system consisting of two counter-propagating
traveling wave modes in a microring resonator. The unknown parameter to be
estimated is the strength of a perturbing cross-coupling between the two modes.
Partially reflecting the output of one mode into the other creates a
non-Hermitian Hamiltonian which exhibits a family of EPs, creating an
exceptional surface (ES). We use a fully quantum treatment of field inputs and
noise sources to obtain a quantitative bound on the estimation error by
calculating the quantum Fisher information (QFI) in the output fields, whose
inverse gives the Cram’er-Rao lower bound on the mean-squared-error of any
unbiased estimator. We determine the bounds for two input states, namely, a
semiclassical coherent state and a highly nonclassical NOON state. We find that
the QFI is enhanced in the presence of an EP for both of these input states and
that both states can saturate the Cram’er-Rao bound. We then identify
idealized yet experimentally feasible measurements that achieve the minimum
bound for these two input states. We also investigate how the QFI changes for
parameter values that do not lie on the ES, finding that these can have a
larger QFI, suggesting alternative routes to optimize the parameter estimation
for this problem.
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