---
_id: '294'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
arxiv: 1
author:
- first_name: Filippo
  full_name: Fratini, Filippo
  last_name: Fratini
- first_name: Laleh
  full_name: Safari, Laleh
  id: 3C325E5E-F248-11E8-B48F-1D18A9856A87
  last_name: Safari
- first_name: Pedro
  full_name: Amaro, Pedro
  last_name: Amaro
- first_name: José
  full_name: Santos, José
  last_name: Santos
citation:
  ama: Fratini F, Safari L, Amaro P, Santos J. Two-photon processes based on quantum
    commutators. <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>.
    2018;97(4). doi:<a href="https://doi.org/10.1103/PhysRevA.97.043842">10.1103/PhysRevA.97.043842</a>
  apa: Fratini, F., Safari, L., Amaro, P., &#38; Santos, J. (2018). Two-photon processes
    based on quantum commutators. <i>Physical Review A - Atomic, Molecular, and Optical
    Physics</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevA.97.043842">https://doi.org/10.1103/PhysRevA.97.043842</a>
  chicago: Fratini, Filippo, Laleh Safari, Pedro Amaro, and José Santos. “Two-Photon
    Processes Based on Quantum Commutators.” <i>Physical Review A - Atomic, Molecular,
    and Optical Physics</i>. American Physical Society, 2018. <a href="https://doi.org/10.1103/PhysRevA.97.043842">https://doi.org/10.1103/PhysRevA.97.043842</a>.
  ieee: F. Fratini, L. Safari, P. Amaro, and J. Santos, “Two-photon processes based
    on quantum commutators,” <i>Physical Review A - Atomic, Molecular, and Optical
    Physics</i>, vol. 97, no. 4. American Physical Society, 2018.
  ista: Fratini F, Safari L, Amaro P, Santos J. 2018. Two-photon processes based on
    quantum commutators. Physical Review A - Atomic, Molecular, and Optical Physics.
    97(4).
  mla: Fratini, Filippo, et al. “Two-Photon Processes Based on Quantum Commutators.”
    <i>Physical Review A - Atomic, Molecular, and Optical Physics</i>, vol. 97, no.
    4, American Physical Society, 2018, doi:<a href="https://doi.org/10.1103/PhysRevA.97.043842">10.1103/PhysRevA.97.043842</a>.
  short: F. Fratini, L. Safari, P. Amaro, J. Santos, Physical Review A - Atomic, Molecular,
    and Optical Physics 97 (2018).
date_created: 2018-12-11T11:45:40Z
date_published: 2018-04-18T00:00:00Z
date_updated: 2025-04-15T06:50:21Z
day: '18'
department:
- _id: MiLe
doi: 10.1103/PhysRevA.97.043842
ec_funded: 1
external_id:
  arxiv:
  - '1801.06892'
  isi:
  - '000430296800008'
intvolume: '        97'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1801.06892
month: '04'
oa: 1
oa_version: Submitted Version
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Physical Review A - Atomic, Molecular, and Optical Physics
publication_status: published
publisher: American Physical Society
publist_id: '7587'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Two-photon processes based on quantum commutators
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 97
year: '2018'
...