Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy

Tao E. Li, Abraham Nitzan, Maxim Sukharev, Todd Martinez, Hsing Ta Chen, Joseph E. Subotnik

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one- and three-dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. We consider three flavors of mixed quantum-classical dynamics: (i) the classical path approximation (CPA), (ii) Ehrenfest dynamics, and (iii) symmetrical quasiclassical (SQC) dynamics. Our findings are as follows: (i) The CPA fails to recover a consistent description of spontaneous emission, (ii) a consistent "spontaneous" emission can be obtained from Ehrenfest dynamics, provided that one starts in an electronic superposition state, and (iii) spontaneous emission is always obtained using SQC dynamics. Using the SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by Miller [J. Chem. Phys. 69, 2188 (1978)JCPSA60021-960610.1063/1.436793] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.

Original languageEnglish
Article number032105
JournalPhysical Review A
Issue number3
StatePublished - 12 Mar 2018
Externally publishedYes


FundersFunder number
Chemical Sciences, Geosciences, and Biosciences Division
US Department of Energy
US National Science FoundationCHE1665291
National Science Foundation1665291
Air Force Office of Scientific ResearchFA9550-15-1-0189, FA9950-13-1-0157
Office of Science
Basic Energy Sciences
United States-Israel Binational Science Foundation2014113


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