Unitary transformation method for solving generalized Jaynes-Cummings models

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

“…But all the existing revivals obey the condition for times predicted by (50). The unitary transformation method presented here [21] has the unique advantage that it not only solves the time dependent problem but also permits a determination of the eigensolutions of the interacting Hamiltonian at the same time.…”

“…The occurrence of the transformed state |a, n 1 , n 2 corresponds to no interaction whereas the occurrence of the state |b, n 1 + 1, n 2 + 1 admit of interaction in which one photon of mode ω 1 is emitted along with another photon of mode ω 2 , resulting in two-mode process. It is easy to see from (12) that the transition probability and hence the energy emitted depends upon √ (n 1 + 1)(n 2 + 1) in place of √ (n + 1) in J-C model [13] and √ (n + 1)(n + 2) in the two photon single mode J-C model [12,21].…”

“…For an intensity dependent coupling two-mode multiphoton interaction model the Hamiltonian is obtained from (18) as [20][21][22] …”

“…The paper aims to show that a straightforward method , that of unitary transformation in quantum mechanics by Sudha Singh [21] can be conveniently used to obtain the eigenfunctions and eigenvalues of the Hamiltonian of the interacting system. The method, besides being general is mathematically simpler.…”

Exact Solutions for Two-Channel Cavity QED Model by Unitary Transformation Method

“…In this paper solutions have also been obtained for the case when the intensity dependent coupling in both the channels is taken into consideration. The paper intends to show that the technique used by [8] can be avoided and instead a straightforward method, that of Unitary Transformation in Quantum Mechanics by [11] can be used to find out the eigenvalues and eigenfunctions of the Hamiltonian of the interacting system. The method, besides being general, is mathematically simpler.…”