Two-photon processes based on quantum commutators Journal Article

Author(s): Fratini, Filippo ; Safari, Laleh; Amaro, Pedro; Santos, José P
Article Title: Two-photon processes based on quantum commutators
Affiliation IST Austria
Abstract: We developed a method to calculate two-photon processes in quantum mechanics that replaces the infinite summation over the intermediate states by a perturbation expansion. This latter consists of a series of commutators that involve position, momentum, and Hamiltonian quantum operators. We analyzed several single- and many-particle cases for which a closed-form solution to the perturbation expansion exists, as well as more complicated cases for which a solution is found by convergence. Throughout the article, Rayleigh and Raman scattering are taken as examples of two-photon processes. The present method provides a clear distinction between the Thomson scattering, regarded as classical scattering, and quantum contributions. Such a distinction lets us derive general results concerning light scattering. Finally, possible extensions to the developed formalism are discussed.
Keywords: Photons; Closed form solutions; Light scattering; Classical scatterings; Intermediate state; Perturbation expansions; Quantum commutators; Quantum operators; Rayleigh; Thomson scattering; Two photon processes
Journal Title: Physical Review A - Atomic, Molecular, and Optical Physics
Volume: 97
Issue 4
ISSN: 1094-1622
Publisher: American Physical Society  
Date Published: 2018-04-18
Start Page: Article number 043842
DOI: 10.1103/PhysRevA.97.043842
Notes: P.A. acknowledges the support of the FCT, under Contract No. SFRH/BPD/92329/2013. This work was supported in part by the research center Grant No. UID/FIS/04559/2013 to LIBPhys-UNL from the FCT/MCTES/PIDDAC. L.S. acknowledges financial support from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA Grant Agreement No. [291734]. F.F. acknowledges partial support from the University of Applied Sciences BFI, Vienna.
Open access: yes (repository)