  We propose a theoretical scheme to deterministically generate Fock states in
a Kerr cavity thorough adiabatic variation of the driving field strength and
the cavity detuning. We show that the required time to generate a $n$-photon
Fock state scales as the square root of $n$. Requirements for the Kerr
coefficient relative to the system decoherence rate are provided as a function
of desired state fidelity, indicating that the scheme is potentially realizable
with the present state of the art in microwave superconducting circuits.
