Exact Solutions for Jaynes-Cummings Models with Non-degenerate Two-Photon Transitions in the Ladder Configuration

Abstract

In the present paper, the eigenfunctions and eigenvalues of the Hamiltonian of the interacting system have been obtained in two generalized Jaynes Cummings models separately, one in which the transition are mediated by two different modes of photon in the ladder configuration and the other involving two mode multi-photon interaction between the field and the atom. Effect of intensity dependent coupling between the field and the atom in both the above-mentioned cases have been investigated. Graphical features of the time dependence of population inversion have been analyzed when one of the field modes is prepared initially in a coherent state while the other one in a vacuum state.The unitary transformation method presented here for the special case of exact resonance not only solves the time-dependent problem but also provides the eigensolutions of the interacting Hamiltonian at the same time.Keywords Jaynes-Cummings (J-C) model · Rotating wave approximation (RWA) · Unitary operatorT · Two-mode ladder model · Two-mode k-photon interaction (2k interaction) ladder model · Intensity dependent coupling · Atomic population inversion W (t)

Dynamics for two atoms interacting with intensity-dependent two-mode quantized cavity fields in the ladder configuration

“…(8) (11) where the relabeling of the A coefficients from Eqs. (10) and 11is obvious. The coefficients of |0,n 1 ,n 2 , |1,n 1 + 1,n 2 + 1 , and |2,n 1 + 2,n 2 + 2 in the state vector are the probability amplitudes A n 1 ,n 2 a,a (t), A n 1 ,n 2 a,b (t), and…”

“…The intensity-dependent two-atom two-mode two-photon Jaynes-Cummings model is obtained from Eq. 1as [7][8][9][10][15][16][17][18]…”

“…Taking this into consideration Napoli and Messina [9] generalized the intensity-dependent Jaynes-Cummings model (JCM) to a two-mode cavity field with a two-photon process based upon the dressed-atom states. Singh and Amrita [10] studied the dynamic properties of the intensity-dependent Jaynes-Cummings model for a two-mode cavity field.…”

Time-dependent interaction between a two-level atom and a su(1,1) Lie algebra quantum system

“…Also, it is interesting to refer to the work by authors of Ref. 19 where they introduced a generalized model for (JC) closely related to the present work in the absence of the time dependence.…”

“…To do this, we use Eqs. (19) and (24) to construct the density operatorρ = |ψ(t) ψ(t)|, from which we can calculate the expectation values for discussion of some physical properties. In the following section, we will discuss atomic inversion, where we can discuss the collapse and revival phenomenon.…”