Collective excitations of atoms and field modes in coupled cavities

The exact solution for the system formed from two or three q-bits doped in coupled cavities is discussed. The problem of indistinguishability between the excited radiators and the 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 new polariton excitations. The exact solution of the Schrodinger equation is obtained for single and two excitations in each cavity considering the indistinguishability principle. This approach opens new possibilities for the interpretation of quantum entangled states in comparison with the traditional distinct situation (see e. g. Napoli and Messina 2001 Fortschr. Phys. 49 1059; Enaki and Bazgan 2013 Phys. Scr. T153 014022) due to the decrease in the number of degrees of freedom in the system. Considering that the energy of coupling between the radiators and the photons is larger than that of the coupling with an external vacuum field, we have found the master equation for the dumping of collective excitations. The time dependence of the population for new dressed quasi-levels of energy is obtained by solving the master equation analytically and numerically.