  The light force on particles trapped in the field of a high-Q cavity mode
depends on the quantum state of field and particle. Different photon numbers
generate different optical potentials anddifferent motional states induce
different field evolution. Even for weak saturation and linear polarizability
the induced particle motion leads to nonlinear field dynamics. We derive a
corresponding effective field Hamiltonian containing all the powers of the
photon number operator, which predicts nonlinear phase shifts and squeezing
even at the few-photon level. Wave-function simulations of the full
particle-field dynamics confirm this and show significant particle-field
entanglement in addition.
