Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

DERIVATION OF THE STATIONARY FLUORESCENCE SPECTRUM FORMULA FOR MOLECULAR SYSTEMS FROM THE PERSPECTIVE OF QUANTUM ELECTRODYNAMICS
Yakov Braver^a,b, Leonas Valkunas^a,b, and Andrius Gelzinis^a,b
^aInstitute of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio 9, 10222 Vilnius, Lithuania
^bDepartment of Molecular Compound Physics, Center for Physical Sciences and Technology, Saulėtekio 3, 10257 Vilnius,
Lithuania
Email: andrius.gelzinis@ff.vu.lt

Received 6 January 2021; revised 5 February 2021; accepted 8 February 2021

Numerical simulations of stationary fluorescence spectra of molecular systems usually rely on the relation between the photon emission rate and the system’s dipole–dipole correlation function. However, research papers usually take this relation for granted, and standard textbook expositions of the theory of fluorescence spectra also tend to leave out this important relation. In order to help researchers with less theoretical training gain a deeper understanding of the emission process, we perform a step-by-step derivation of the expression for the fluorescence spectrum, focusing on rigorous mathematical treatment and the underlying physical content. Right from the start, we employ quantum description of the electromagnetic field, which provides a clear picture of emission that goes beyond the phenomenological treatment in terms of the Einstein A coefficient. Having obtained the final expression, we discuss the relation of the latter to the present level of theory by studying a simple two-level system. From the technical perspective, the present work also aims at familiarizing the reader with the density matrix formalism and with the application of the double-sided Feynman diagrams.

Keywords: quantum molecular electrodynamics, dipole–dipole correlation function, Einstein coefficients, Feynman diagrams

MOLEKULINIŲ SISTEMŲ STACIONARIOSIOS FLUORESCENCIJOS SPEKTRO FORMULĖS IŠVEDIMAS NAUDOJANT KVANTINĘ ELEKTRODINAMIKĄ
Jakov Braver^a,b, Leonas Valkūnas^a,b, Andrius Gelžinis^a,b

^aVilniaus universiteto Fizikos fakulteto Cheminės fizikos institutas, Vilnius, Lietuva
^bFizinių ir technologijos mokslų centro Molekulinių darinių fizikos skyrius, Vilnius, Lietuva

Molekulinių sistemų stacionarių fluorescencijos spektrų skaitinis modeliavimas dažniausiai remiasi tam tikru sąryšiu tarp fotonų emisijos spartos ir sistemos dipolių koreliacinės funkcijos. Mokslo darbuose ši išraiška paprastai laikoma savaime suprantamu dalyku, o fluorescencijos spektrų teorijos vadovėliuose šis svarbus sąryšis nėra aptariamas. Norėdami padėti mokslininkams giliau suprasti emisijos procesą, šiame darbe, išlaikydami matematinį griežtumą ir akcentuodami formulių fizikinį turinį, pateikiame nuoseklų fluorescencijos spektro išraiškos išvedimą. Naudojame kvantinį elektromagnetinio lauko aprašymą, suteikiantį aiškesnį emisijos proceso vaizdinį, negu fenomenologinis aprašymas taikant Einšteino koeficientą A. Gavę galutinę išraišką, pateikiame pavyzdinį jos panaudojimą, pritaikydami ją paprastai dviejų lygmenų sistemai nagrinėti. Be to, šiuo darbu siekiame supažindinti skaitytoją su tankio matricos formalizmu ir dvigubujų Feynmano diagramų taikymu.

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