Exactly solvable three-level two-mode model with multiphoton transitions

The Jaynes-Cummings Model

“…Analytic solutions to the general interaction R=(at)m(a) (108) have been presented by Kochetov (1987) . Other discussions of multiphoton interactions in the JCM include Zubairy and Yeh (1980), Shumovsky et al . (1985), Buzek and Jex (1989b), Drobny and Jex (1992), Meng et al (1992), and Zhou et al .…”

The general formalism for a three-level atom interacting with a two-mode cavity field

“…The JCM is generalized in several directions; some of this generalizations are based on considering the multiphotons transitions [2], the atom-field coupling in intensity dependent [3] and the Kerr-like medium [4]. Recently, the three-level two-mode system has been discussed [5] and the statistical properties of the photons interacting with the three-level has been investigated [6]. Also, the sub-Poissonian statistics [7] have been predicted.…”

The dynamics of a four-level three-mode system. Operator solution

“…A number of recent papers have been devoted to studies of the dynamics of a three-level atom interacting with two modes of classical [3][4][5][6] or quantized [7][8][9][10][11][12] electromagnetic field. In papers [7,8], exact Schrodinger wave functions have been obtained for some special initial states.…”

“…Moreover, the strict operator solutions for lambda configuration of the levels in the case when the two lower levels are coupled to the upper one by multiphoton transitions have been obtained [12]. An interesting review of the dynamical theory of J-Ctype models has been given by Yoo and Eberly [13].…”

“…Formally, the solutions (17)-(18) resemble those for the three-level two-mode system [10,11] ; due to the configuration of levels assumed, the four-level atom preserves the two Rabi frequency branches nand 2 â of the three-level atom [9][10][11][12]. However, the amplitude operators are different and their form is as follows :…”