  The striking nonlinear effects exhibited by cavity QED systems make them a
powerful tool in modern condensed matter and atomic physics. A recently
discovered example is the quantized pumping of energy into a cavity by a
strongly-coupled, periodically-driven spin. We uncover a remarkable feature of
these energy pumps: they coherently translate, or boost, a quantum state of the
cavity in the Fock basis. Current optical cavity and circuit QED experiments
can realize the required Hamiltonian in a rotating frame. Boosting thus enables
the preparation of highly-excited non-classical cavity states in near-term
experiments.
