Algebraic treatment of the time-dependent Jaynes–Cummings Hamiltonian including nonlinear terms
Sergio Cordero, J. Récamier · Journal of Physics A Mathematical and Theoretical · 2012
A generalization of the time-dependent Jaynes–Cummings Hamiltonian is considered including nonlinear terms in the field and/or an intensity-dependent coupling term. Using algebraic methods we find the corresponding time evolution operator of the problem as a product of exponential operators. Also, we study the effect of the atomic motion in the cavity on its quantum state. We found that, when the atom is vibrating classically with a small amplitude A0 (in comparison with the effective length of the cavity L), i.e. A0 ≪ L, the effects of the atom’s motion are negligible but when A0 ∼ L/4, the state of the atom changes drastically. Our study is devoted to a Jaynes–Cummings Hamiltonian with an additional Kerr medium.