  A superconducting single-electron transistor (SSET) coupled to an anharmonic
oscillator, e.g., a Josephson junction-L-C circuit, can drive the latter to a
nonequilibrium photon number state. By biasing the SSET in a regime where the
current is carried by a combination of inelastic quasiparticle tunneling and
coherent Cooper-pair tunneling (Josephson quasiparticle cycle), cooling of the
oscillator as well as a laser like enhancement of the photon number can be
achieved. Here we show, that the cut-off in the quasiparticle tunneling rate
due to the superconducting gap, in combination with the anharmonicity of the
oscillator, may create strongly squeezed photon number distributions. For low
dissipation in the oscillator nearly pure Fock states can be produced.
