Externally induced metastability of an electron in a Penning trap: Analytical results - art. no. 063405

The effect of a driving held on the cyclotron mode of a relativistic electr on in a Penning trap is studied analytically. The Hamiltonian dynamics of t his driven nonlinear oscillator is analyzed by using linearization techniqu es and displaced squeezed-state formalism. With the approximate analytical expressions obtained for the eigenstates in this approach. a simplified tre atment of the dissipative dynamics is carried out and some of the nontrivia l features found in a recent numerical study [D. Enzer and G. Gabrielse, Ph ys. Rev. Lett, 78, 1211 (1997)] are unraveled. The emergence of different t ime scales and the generation of a metastable statistical mixture are under stood in terms of the changes induced in the structure of the master equati on by the nonuniform characteristics of the eigenstates: the partial reviva ls of specific coherent states are accounted for by the evolution of partic ular coherences. The control of these effects by a proper choice of the dri ving parameters is discussed.