Time-frequency metrology with two single-photon states: phase space picture and the Hong-Ou-Mandel interferometer

TL;DR

This paper explores time-frequency continuous variables in quantum optics, analyzing the Hong-Ou-Mandel interferometer's precision limits and optimality for various transformations in phase space.

Contribution

It adapts phase space methods to time-frequency variables and provides a general formula for coincidence probability in generalized Hong-Ou-Mandel experiments.

Findings

Derived a general formula for coincidence probability.

Analyzed optimality of measurement settings for arbitrary transformations.

Discussed specific transformations as translations and rotations in phase space.

Abstract

We use time-frequency continuous variables as the standard framework to describe states of light in the subspace of individual photons occupying distinguishable auxiliary modes. We adapt to this setting the interplay between metrological properties and the phase space picture already extensively studied for quadrature variables. We also discuss in details the Hong-Ou-Mandel interferometer, which was previously shown to saturate precision limits, and provide a general formula for the coincidence probability of a generalized version of this experiment. From the obtained expression, we systematically analyze the optimality of this measurement setting for arbitrary unitary transformations applied to each one of the input photons. As concrete examples, we discuss transformations which can be represented as translations and rotations in time-frequency phase space for some specific states.