Eur. Phys. J. D (2015) 69: 278
https://doi.org/10.1140/epjd/e2015-60403-2

Regular Article

Controlling instability and phase hops of a kicked two-level ion in Lamb-Dicke regime

Department of Physics and Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081, P.R. China

^a e-mail: whhai2005@gmail.com

Received: 14 July 2015
Received in final form: 27 September 2015
Published online: 15 December 2015

Abstract

Nonlinearity and singularity lead to lack of quantum exact solution of a kicked rotor. We here study quantum motion of a laser-kicked two-level ion in the Lamb-Dicke regime and obtain a set of exact solutions of the generalized coherent states. A new stability region of parameter space where classical stability criterion fully agrees with fidelity treatment of quantum ground-state stability is found, which unusually contains the resonance frequency for a weak kick and the larger kick strength for a far-off-resonance frequency. When the field parameters in the stability region are applied, the ion’s wave-packet trains continuously oscillate in the Lamb-Dicke regime, while for the parameters in the instability region, they collapse and spread to far away from the Lamb-Dicke regime, resulting in the crossover from linearity to nonlinearity. Meanwhile the laser kicks bring hopping phases of the exact solutions, and lead to stable or unstable hops of the expected momentum and energy. The exact results provide a transparent scheme for using periodic kicks with wider parameter region to localize ions in the Lamb-Dicke regime and for suppressing the instability-induced decoherence in laser-ion interactions, which can be observed in the existing experimental setups and possess potential applications.