Optimal pulses for dipole moment estimation with coherent states

We investigate quantum sensing in spectroscopy by optimizing pulse shapes to maximize the quantum Fisher information (QFI) for estimating an atom’s dipole moment. Specifically, we provide the differential equations to compute the QFI of the light emitted from the interaction of coherent light with a two-level atom coupled to a waveguide and compute the optimal bandwidth for various families of standard pulses as a function of the average photon number. We provide intuition about the factors that maximize the QFI and show that the optimal pulse is a coherent state with frequency $omega{0}=delta pm frac{Gamma}{2}$ where $delta$ is the detuning and $Gamma$ is the spontaneous emission rate.