# Quantum state of a frequency comb

## TL;DR

This paper develops a formalism to describe the mixed quantum state of a frequency comb laser, accounting for uncertainties in frequency parameters and including both particle-number and temporal degrees of freedom.

## Contribution

It introduces a new formalism for representing the quantum state of a frequency comb laser with uncertainties, integrating spectral density calculations.

## Key findings

- Derived a formalism for mixed quantum states of frequency combs.
- Computed power spectral density considering frequency uncertainties.
- Provided a framework for quantum state analysis of frequency combs.

## Abstract

Uncertainties in the frequency parameters of a frequency comb laser, causes it to represent a mixed quantum state. The formulation of such a quantum state is compounded by the fact that it contains both particle-number degrees of freedom and temporal degrees of freedom. Here we develop a formalism in terms of which such a mixed quantum state can be expressed. For this purpose we also need to compute the expression for the power spectral density of the frequency comb laser. We do so by taking the uncertainties in the frequency parameters into account.