Two-photon interaction between trapped ions and cavity fields
Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, 13083 São Paulo, Brazil
Corresponding author: a firstname.lastname@example.org
Revised: 6 October 2006
Published online: 10 November 2006
In this paper, we generalize the ordinary two-photon Jaynes-Cummings model (TPJCM) by considering the atom (or ion) to be trapped in a simple harmonic well. A typical setup would be an optical cavity containing a single ion in a Paul trap. Due to the inclusion of atomic vibrational motion, the atom-field coupling becomes highly nonlinear what brings out quite different behaviours for the system dynamics when compared to the ordinary TPJCM. In particular, we derive an effective two-photon Hamiltonian with dependence on the number operator of the ion's center-of-mass motion. This dependence occurs both in the cavity induced Stark-shifts and in the ion-field coupling, and its role in the dynamics is illustrated by showing the time evolution of the probability of occupation of the electronic levels for simple initial preparations of the state of the system.
PACS: 42.50.-p – Quantum optics / 32.80.Qk – Coherent control of atomic interactions with photons / 32.80.Wr – Other multiphoton processes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006