2023/06/17 by Erik Orvehed Hiltunen, Joseph Kraisler, Hiltunen, Erik Orvehed +5 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2306.10431
openalex publication_date 2023/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We consider the quantum optics of a single photon interacting with a system of two level atoms. This leads to the study of a nonlinear eigenproblem for a system of nonlocal partial differential equations. Two classes of solutions to these equations are studied. Bound states correspond to negative eigenvalues and resonances to eigenvalues with positive real parts. We have found necessary and sufficient conditions for the existence of bound states, along with an upper bound on the number of such states. We have also considered the eigenproblem for atomic models with small high contrast inclusions. In this setting, we have derived asymptotic formulas for the eigenvalues. Our results are illustrated with numerical computations.