Exact solution of quantum dynamics of a cantilever coupling to a single trapped ultracold ion

The quantum behavior of a precooled cantilever can be probed highly efficiently by coupling to a trapped ultracold ion, in which a fast cooling of the cantilever down to the ground vibrational state is possible. We solve the dynamics of the coupling system by a squeezed-state expansion technique, and can in principle obtain the exact solution of the time-evolution of the coupling system. Compared to the treatment under rotating-wave approximation, we can present a more accurate description of the quantum behavior of the cantilever.