  We propose a mechanism for producing Fock states on demand leaking from a
single mode optical cavity interacting with a single atom and a laser pulse.
The number of photons can be chosen, as it is determined by the Zeeman
substructure of the ground state of the atom and its initial state. The
deterministic generation of a free-propagating Fock state of $1\leq n\leq2F$
photons is achieved, when a circularly polarized laser pulse completely
transfers the atomic population between Zeeman sublevels of the ground
hyperfine state $F$ through far-detuned Raman scattering thus producing
linearly polarized cavity photons. We describe analytically the evolution of
optical field taking into account the spontaneous losses and the cavity
damping. We demonstrate the possibility of production of Fock-state with
different numbers of photons by using different transitions of the same atom.
We show also that this technique provides a deterministic source of a train of
identical multiphoton Fock-states, if a sequence of left- and right-circularly
polarized laser pulses is applied. The resulting states have potential
applications in quantum computation and simulation.
