Eur. Phys. J. D (2013) 67: 120
https://doi.org/10.1140/epjd/e2013-30649-9

Regular Article

Quantum dynamics of a three-level trapped ion under a time-dependent interaction with laser beams

¹ Department of Physics, Afyon Kocatepe University, 03200 Afyonkarahisar, Turkey
² Department of Electrical and Computer Engineering, Michigan Technological University, Houghton, 49931 Michigan, USA

^a e-mail: dermez@aku.edu.tr

Received: 22 October 2012
Received in final form: 12 April 2013
Published online: 25 June 2013

Abstract

We solved time-dependent Hamiltonian of a three-level ion interacting with two-laser beams in Λ scheme using a unitary transformation method which transform the Λ scheme to a cascade Ξ scheme for the vibrational phonon transitions. Our analytical results for the probability amplitudes become precise after a certain period of time when the Lamb-Dicke regime is reached. We analyzed the entanglement created in the system.