Collective excitations of atoms and field modes in coupled cavities

TL;DR

This paper provides an exact analytical solution for the collective excitations in coupled cavity systems with atoms and field modes, highlighting the use of polariton excitations to simplify the analysis and interpret quantum entanglement.

Contribution

It introduces a novel approach using polariton excitations to simplify the solution of coupled cavity systems with multiple atoms and photons, advancing understanding of quantum entangled states.

Findings

Exact solutions for single and two excitations in coupled cavities.

Master equation describing the decay of collective excitations.

Analytical and numerical results on population dynamics of dressed energy levels.

Abstract

The exact solution of the system consisted from two or three q-bits doped in coupled cavities is discussed. The problem of indistinguishable between the excited radiators and photons is analyzed using the intrinsic symmetry of the system. It is demonstrated that the solution is drastically simplified when the radiators and photons are considered as a new polariton excitations. The exact solution of Schrodinger equation is obtained for single and two excitations in each cavity taking into consideration the indistinguishable principle. This approach opens new possibilities in the interpretation of quantum entangled states in comparison with the traditional distinctive situation (see for example [1,2]) due to the decreasing of the number of degrees of freedoms in the system. Considering that the energies of coupling between the radiators and photons is larger than the coupling with external vacuum field, we have found the master equation for the dumping of collective excitations of the system of coupled radiators through the cavity fields. The time-dependence of population for new dressed quasi-levels of energy is obtained solving analytically and numerically the master equation.