# Complementarity Analysis of Interference between Frequency-Displaced Photonic Wave-Packets

## TL;DR

This paper investigates the complementarity between spectral distinguishability and visibility in frequency-displaced photonic wave-packets using a Hong-Ou-Mandel interferometer, providing experimental validation of the complementarity relation.

## Contribution

It introduces an experimental definition of the distinguishability parameter K and tests the K^2 + V^2 ≤ 1 inequality for frequency-displaced photonic wave-packets.

## Key findings

- Spectral distinguishability is complementary to visibility.
- The complementarity relation holds for frequency-displaced wave-packets.
- Quantum interference can be examined with weak-coherent states.

## Abstract

The complementarity relation between the visibility and the spectral distinguishability of frequency-displaced photonic wave-packets in a Hong-Ou-Mandel interferometer is studied. An experimental definition of $K$, the distinguishability parameter, is proposed and tested for the $K^2+\mathcal{V}^2\leq 1$ complementarity inequality when a consistent visibility parameter is defined. The results show that the spectral distinguishability is, indeed, complementary to the visibility and that the quantum aspect of the two-photon interference phenomenon can be examined by employing weak-coherent states.