  We examine the spin current and the associated shot noise generated in a
quantum dot connected to normal leads with zero bias voltage across the dot.
The spin current is generated by spin flip transitions induced by a quantized
electromagnetic field inside a cavity with one of the Zeeman states lying below
the Fermi level of the leads and the other above. In the limit of strong
Coulomb blockade, this model is analogous to the Jaynes-Cummings model in
quantum optics. We also calculate the photon current and photon current shot
noise resulting from photons leaking out of the cavity. We show that the photon
current is equal to the spin current and that the spin current can be
significantly larger than for the case of a classical driving field as a result
of cavity losses. In addition to this, the frequency dependent spin (photon)
current shot noise show dips (peaks) that are a result of the discrete nature
of photons.
