  A quantum dot interacting with two resonant cavity modes is described by a
two-mode Jaynes-Cummings model. Depending on the quantum dot energy level
scheme, the interaction of a singly doped quantum dot with a cavity photon
generates entanglement of electron spin and cavity states or allows one to
implement a SWAP gate for spin and photon states. An undoped quantum dot in the
same structure generates pairs of polarization entangled photons from an
initial photon product state. For realistic cavity loss rates, the fidelity of
these operations is of order 80%.
