Supersymmetry breaking and the Jaynes-Cummings model

We describe models with equal numbers of bosonic and fermionic degrees and find their nontrivial spectra. At certain critical couplings the ground states become highly degenerate and odd operators get nonzero ground state expectation values. We comment on the field theory limit too. Physically these models provide a simple explanation for coherence of radiation in interaction with matter. We furthermore show that they describe particles in a QHE device with an electric field parallel to the magnetic one, where the coupling is given by the spin-orbit term. (orig.)