Two and k-Photon Jaynes–Cummings Models and Dirac Oscillator Problem in Bargmann–Segal Representation

Matrix diagonalization and exact solution of the k-photon Jaynes–Cummings model

“…This energy spectrum of the k-photon Jaynes-Cummings model matches perfectly with that presented in reference [37], obtained by means of the Bargmann-Segal representation. Also, it is important to note that for k = 1, this energy spectrum is adequately reduced to that of the Jaynes-Cummings model.…”

“…Therefore, we have obtained the eigenfunctions and energy spectrum of the two-photon Jaynes-Cummings model by using the tilting transformation and the SU(2) realization of the Pauli matrices. The energy spectrum of equation (35) coincides with the previously obtained in reference [37] by means of the Bargmann-Segal representation.…”

“…The Hamiltonian of two-photon Jaynes-Cummings model with rotating wave approximation (RWA) is given by [36,37]…”

“…In this Section, we shall use the same formalism developed in Section 2 to obtain the general solution of the k-photon Jaynes-Cummings model. In the rotating wave approximation (RWA), the k-photon Jaynes-Cummings model is given by the expression [36,37]…”

“…In these works, the authors showed that these models exhibit periodic decay and revival of atomic coherence. The k-photon Jaynes-Cummings model has been extensively studied, as can be seen in references [33][34][35][36][37].…”