Signature of electromagnetic quantum fluctuations in exciton physics

Abstract: Quantum fluctuations of the electromagnetic field are known to produce the atomic Lamb shift. We here reveal their iconic signature in semiconductor physics, through the blue-shift they produce to optically bright excitons, thus lifting the energy of these excitons above their dark counterparts. The electromagnetic field here acts in its full complexity: in addition to the longitudinal part via interband \textit{virtual Coulomb} processes, the transverse part -- which has been missed up to now -- also acts via resonant and nonresonant \textit{virtual photons}. These two parts beautifully combine to produce a bright exciton blue-shift independent of the exciton wave-vector direction. Our work readily leads to a striking prediction: long-lived excitons must have a small bright-dark splitting. Although the analogy between exciton and hydrogen atom could lead us to see the bright exciton shift as a Lamb shift, this is not fully so: the atom shift entirely comes from virtual photons, whereas the Coulomb interaction also contributes to the exciton shift through the so-called "electron-hole exchange".