Nonlinear Jaynes-Cummings dynamics of a trapped ion

q-Boson in Quantum Integrable Systems

“…have been verified in maser and laser experiments. However, for describing physical situations more accurately generalizations of these basic models, like q-deformed BS and JC model [7,8,29,30], q-boson model interacting with q-spins [31] or its classical variant [32], trapped ion (TI) with nonlinear coupling, multi-atom models [33,34] etc. have been proposed.…”

Self-organization effects and light amplification of collective atomic recoil motion in a harmonic trap

“…Our modification by this configuration produces a very different laser gain profile illustrated by Fig.2 [10]. Fig.2 displays a discrete spectral structure which is very similar to that of a nonlinear Jaynes-Cummings model of one atom in a high-Q cavity [12]. When the pump-probe detuning satisfies a Raman condition ∆ 21 = nν, where n is an arbitrary integer and ν is the effective axial trapping frequency, a distinct light amplification process occurs for certain n as displayed by Fig.2.…”

A new perturbative expansion of the time evolution operator associated with a quantum system

“…Another natural choice of the functions g, f is provided by a more accurate approximation of the interaction term H (t) of the ion trap Hamiltonian, approximation which is adopted by some authors (see, for instance, refs. [23,24,25]). Indeed, it turns out that we have:…”