# Dynamic Generation of Light States with Discrete Symmetries

## TL;DR

This paper presents a method to dynamically generate light states with discrete cyclic symmetries using the generalized Tavis-Cummings model, leveraging matter-field entanglement and initial superposition states.

## Contribution

It introduces a novel dynamic procedure for creating light states with specific discrete symmetries in a cavity QED system, applicable to any number of three-level atoms.

## Key findings

- Husimi function invariance under cyclic transformations
- Generation of light states with ${
m C}_n$ symmetry
- Method applicable to arbitrary dipolar couplings

## Abstract

A dynamic procedure is established within the generalised Tavis-Cummings model to generate light states with discrete point symmetries, given by the cyclic group ${\cal C}_n$. We consider arbitrary dipolar coupling strengths of the atoms with a one-mode electromagnetic field in a cavity. The method uses mainly the matter-field entanglement properties of the system, which can be extended to any number of $3$-level atoms. An initial state constituted by the superposition of two states with definite total excitation numbers, $\vert \psi \rangle_{M_1}$, and $\vert \psi \rangle_{M_2}$, is considered. It can be generated by the proper selection of the time-of-flight of an atom passing through the cavity. We demonstrate that the resulting Husimi function of the light is invariant under cyclic point transformations of order $n=\vert M_1-M_2\vert$.