Time-ordering in Heisenberg’s equation of motion as related to spontaneous radiation

Abstract Despite many years of research into Raman phenomena, the problem of how to include both spontaneous and stimulated Raman scattering into a unified set of partial differential equations persists. The issue is solved by formulating the quantum dynamics in the Heisenberg picture with a rigorou...

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Autor principal:	Benjamin D. Strycker
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/13c3961760134e44b78da35652617ca8
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spelling	oai:doaj.org-article:13c3961760134e44b78da35652617ca82021-11-14T12:17:46ZTime-ordering in Heisenberg’s equation of motion as related to spontaneous radiation10.1038/s41598-021-01781-72045-2322https://doaj.org/article/13c3961760134e44b78da35652617ca82021-11-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-01781-7https://doaj.org/toc/2045-2322Abstract Despite many years of research into Raman phenomena, the problem of how to include both spontaneous and stimulated Raman scattering into a unified set of partial differential equations persists. The issue is solved by formulating the quantum dynamics in the Heisenberg picture with a rigorous accounting for both time- and normal-ordering of the operators. It is shown how this can be done in a simple, straightforward way. Firstly, the technique is applied to a two-level Raman system, and comparison of analytical and numerical results verifies the approach. A connection to a fully time-dependent Langevin operator method is made for the spontaneous initiation of stimulated Raman scattering. Secondly, the technique is demonstrated for the much-studied two-level atom both in vacuum and in a lossy dielectric medium. It is shown to be fully consistent with accepted theories: using the rotating wave approximation, the Einstein A coefficient for the rate of spontaneous emission from a two-level atom can be derived in a manner parallel to the Weisskopf–Wigner approximation. The Lamb frequency shift is also calculated. It is shown throughout that field operators corresponding to spontaneous radiative terms do not commute with atomic/molecular operators. The approach may prove useful in many areas, including modeling the propagation of next-generation high-energy, high-intensity ultrafast laser pulses as well as spontaneous radiative processes in lossy media.Benjamin D. StryckerNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-13 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Benjamin D. Strycker Time-ordering in Heisenberg’s equation of motion as related to spontaneous radiation
description	Abstract Despite many years of research into Raman phenomena, the problem of how to include both spontaneous and stimulated Raman scattering into a unified set of partial differential equations persists. The issue is solved by formulating the quantum dynamics in the Heisenberg picture with a rigorous accounting for both time- and normal-ordering of the operators. It is shown how this can be done in a simple, straightforward way. Firstly, the technique is applied to a two-level Raman system, and comparison of analytical and numerical results verifies the approach. A connection to a fully time-dependent Langevin operator method is made for the spontaneous initiation of stimulated Raman scattering. Secondly, the technique is demonstrated for the much-studied two-level atom both in vacuum and in a lossy dielectric medium. It is shown to be fully consistent with accepted theories: using the rotating wave approximation, the Einstein A coefficient for the rate of spontaneous emission from a two-level atom can be derived in a manner parallel to the Weisskopf–Wigner approximation. The Lamb frequency shift is also calculated. It is shown throughout that field operators corresponding to spontaneous radiative terms do not commute with atomic/molecular operators. The approach may prove useful in many areas, including modeling the propagation of next-generation high-energy, high-intensity ultrafast laser pulses as well as spontaneous radiative processes in lossy media.
format	article
author	Benjamin D. Strycker
author_facet	Benjamin D. Strycker
author_sort	Benjamin D. Strycker
title	Time-ordering in Heisenberg’s equation of motion as related to spontaneous radiation
title_short	Time-ordering in Heisenberg’s equation of motion as related to spontaneous radiation
title_full	Time-ordering in Heisenberg’s equation of motion as related to spontaneous radiation
title_fullStr	Time-ordering in Heisenberg’s equation of motion as related to spontaneous radiation
title_full_unstemmed	Time-ordering in Heisenberg’s equation of motion as related to spontaneous radiation
title_sort	time-ordering in heisenberg’s equation of motion as related to spontaneous radiation
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/13c3961760134e44b78da35652617ca8
work_keys_str_mv	AT benjamindstrycker timeorderinginheisenbergsequationofmotionasrelatedtospontaneousradiation
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Time-ordering in Heisenberg’s equation of motion as related to spontaneous radiation

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