# Exclusive Hong-Ou-Mandel zero-coincidence point

## TL;DR

This paper introduces a generalized multi-parameter Hong-Ou-Mandel interferometer capable of detecting multiple simultaneous time-delays using a symmetric biphoton source, with explicit examples for certain cases.

## Contribution

It extends the traditional Hong-Ou-Mandel setup to monitor multiple time-delays simultaneously with a novel multi-parameter configuration and analyzes its sensitivity to fluctuations.

## Key findings

- Zero coincidence counts correspond to absence of all time-delays for k=1,2,4.
- The method cannot be extended to k=3.
- Interferometer sensitivity is affected by time-scale fluctuations of delays.

## Abstract

A generalized multi-parameter Hong-Ou-Mandel interferometer is presented which extends the conventional "Mandel dip" configuration to the case where a symmetric biphoton source is used to monitor the contemporary presence of k independent time-delays. Our construction results in a two-input/two-output setup, obtained by concatenating 50:50 beam splitters with a collection of adjustable achromatic wave-plates. For k=1,2 and k=4 explicit examples can be exhibited that prove the possibility of uniquely linking the zero value of the coincidence counts registered at the output of the interferometer, with the contemporary absence of all the time-delays. Interestingly enough the same result cannot be extended to k=3. Besides, the sensitivity of the interferometer is analyzed when the time-delays are affected by the fluctuations over time-scales that are larger than the inverse of the frequency of the pump used to generate the biphoton state.