Dynamical Casimir-Polder force on a partially dressed atom near a conducting wall

We study the time evolution of the Casimir-Polder force acting on a neutral atom in front of a perfectly conducting plate, when the system starts its unitary evolution from a partially dressed state. We solve the Heisenberg equations for both atomic and field quantum operators, exploiting a series expansion with respect to the electric charge and an iterative technique. After discussing the behavior of the time-dependent force on an initially partially dressed atom, we analyze a possible experimental scheme to prepare the partially dressed state and the observability of this new dynamical effect.

Figure 1

Time evolution of the atom-wall force for $t<2d$ ($c=1$). We have chosen $k_0=1$, $k_0^{\prime }=2$, and $d=10$, so the back-reaction time is $t=20$. The red (solid) line corresponds to the case of an initial partially dressed state, while the blue (dashed) line is for the case of an initially bare ground state. Time is in units of $d/c$. The force is in arbitrary units.

Figure 2

Time evolution of the atom-wall force for $t>2d$, with the same values and units of Fig. 1.

Figure 3

Time evolution of the relative difference between the force for an initially partially dressed state and the stationary value for $t\to +\infty$. We have chosen $k_0=1$, $k_0^{\prime }=2$, and $d=10$ (and $c=1$). Time is in units of $d/c$.