Nonlinear squeezing in the motion of a trapped atom

We study a Raman-driven two-quantum interaction in the motion of a trapped atom, which in the Lamb-Dicke limit corresponds to a classically driven parametric interaction known from nonlinear optics. When the Lamb-Dicke approximation fails, interference effects between the driving laser waves and the spatially extended motional wave function of the atom lead to nonlinear modifications of the motional dynamics. Destructive interferences occur for particular values of the motional amplitude. They lead to a partitioning of the motional phase space accompanied by interesting dynamical effects. Starting the dynamics in the motional ground state of the atom, a quadrature-squeezed state emerges for short interaction times, in agreement with recent experiments [D. M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)]. For longer interaction times the phase-space partitioning gives rise to a reduction of the variance of the motional excitation number and to phase-locking effects leading to a partial revival of the state towards the origin of the phase space.