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We consider the quantum optics of a single photon interacting with a systemof two level atoms. This leads to the study of a nonlinear eigenproblem for asystem of nonlocal partial differential equations. Two classes of solutions tothese equations are studied. Bound states correspond to negative eigenvaluesand resonances to eigenvalues with positive real parts. We have found necessaryand sufficient conditions for the existence of bound states, along with anupper bound on the number of such states. We have also considered theeigenproblem for atomic models with small high contrast inclusions. In thissetting, we have derived asymptotic formulas for the eigenvalues. Our resultsare illustrated with numerical computations.

Nonlocal PDEs and Quantum Optics: Bound States and Resonances