Dynamic generation of light states with discrete symmetries
Sergio Cordero, Eduardo Nahmad-Achar, Octavio Castaños, Ramón López–Peña · Physical Review A · 2018
A dynamic procedure is established within the generalized Tavis--Cummings model to generate light states with discrete point symmetries, given by the cyclic group ${\mathcal{C}}_{n}$. 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 three-level atoms. An initial state constituted by the superposition of two states with definite total excitation numbers, ${|\ensuremath{\psi}\ensuremath{\rangle}}_{{M}_{1}}$, and ${|\ensuremath{\psi}\ensuremath{\rangle}}_{{M}_{2}}$, 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 $n=|{M}_{1}\ensuremath{-}{M}_{2}|$.