Martin Damyanov

Project Title: Fisher Information Analysis Based Approach to Modified Hong-Ou-Mandel Interferometry

The Hong-Ou-Mandel (HOM) effect is a two-photon interference effect that was first demonstrated in 1987. It has a wide variety of applications within quantum science. It has been recently demonstrated experimentally that this interference effect can be combined with methods from statistical estimation theory to yield attosecond-precision time measurements. These methods are based on Fisher information optimisation and maximum-likelihood estimation. As a result of these findings, HOM interferometry can enable single-photon characterisation of small biological samples, which is relevant to the field of cell biology.

Up to now, this approach has only been used to perform single-parameter estimations. The goal of this project was to see if this methodology can be used in the context of a nested interferometer to simultaneously measure phase and group velocities of single photons, i.e. a multi-parameter estimation. The nested interferometer analysed is a combination of HOM and Mach-Zehnder interferometers. During the project, a full theoretical analysis was produced and the probabilities of experimentally measurable events were obtained. After that, a lot of work was dedicated towards investigating ways to efficiently optimise the Fisher information. Python 3 and SageMath were used to perform numerical analysis and calculations.

It was found that the Fisher information exhibits an interesting and complicated behaviour. It was concluded that a maximum-likelihood based approach could be problematic and the analysis indicated that Bayesian-like protocols could be more adequate. The theoretical findings sparked interesting and important questions regarding the measurement efficiency, in terms of gain of information per photon, when performing simultaneous measurements. Continuing theoretical investigation is being conducted by a research team at Heriot-Watt university, building upon the findings from this summer project.