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

Abstract

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. Here, 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)] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.

Authors:
 [1];  [1];  [2];  [3];  [1];  [1]
+ Show Author Affiliations
  1. Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Chemistry
  2. Arizona State Univ., Tempe, AZ (United States). Dept. of Physics; Arizona State Univ., Mesa, AZ (United States). College of Integrative Sciences and Arts
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States). Photon Ultrafast Laser Science and Engineering Inst. (PULSE), and Dept. of Chemistry
Publication Date:
Research Org.:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR)
OSTI Identifier:
1436986
Alternate Identifier(s):
OSTI ID: 1425531
Grant/Contract Number:  
AC02-76SF00515; FA9950-13-1-0157; FA9550-15-1-0189; 2014113; CHE1665291
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 97; Journal Issue: 3; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Li, Tao E., Nitzan, Abraham, Sukharev, Maxim, Martinez, Todd, Chen, Hsing-Ta, and Subotnik, Joseph E. Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy. United States: N. p., 2018. Web. doi:10.1103/physreva.97.032105.
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Li, Tao E., Nitzan, Abraham, Sukharev, Maxim, Martinez, Todd, Chen, Hsing-Ta, & Subotnik, Joseph E. Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy. United States. https://doi.org/10.1103/physreva.97.032105
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Li, Tao E., Nitzan, Abraham, Sukharev, Maxim, Martinez, Todd, Chen, Hsing-Ta, and Subotnik, Joseph E. Mon . "Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy". United States. https://doi.org/10.1103/physreva.97.032105. https://www.osti.gov/servlets/purl/1436986.
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@article{osti_1436986,
title = {Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy},
author = {Li, Tao E. and Nitzan, Abraham and Sukharev, Maxim and Martinez, Todd and Chen, Hsing-Ta and Subotnik, Joseph E.},
abstractNote = {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. Here, 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)] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.},
doi = {10.1103/physreva.97.032105},
journal = {Physical Review A},
number = 3,
volume = 97,
place = {United States},
year = {Mon Mar 12 00:00:00 EDT 2018},
month = {Mon Mar 12 00:00:00 EDT 2018}
}
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https://doi.org/10.1103/physreva.97.032105
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Works referenced in this record:

Nonlinear nanopolaritonics: Finite-difference time-domain Maxwell–Schrödinger simulation of molecule-assisted plasmon transfer
journal, July 2009

  • Lopata, Kenneth; Neuhauser, Daniel
  • The Journal of Chemical Physics, Vol. 131, Issue 1
  • DOI: 10.1063/1.3167407

A near linear-scaling smooth local coupled cluster algorithm for electronic structure
journal, August 2006

  • Subotnik, Joseph E.; Sodt, Alex; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 125, Issue 7
  • DOI: 10.1063/1.2336426

A classical analog for electronic degrees of freedom in nonadiabatic collision processes
journal, April 1979

  • Meyera), Hans‐Dieter; Miller, William H.
  • The Journal of Chemical Physics, Vol. 70, Issue 7
  • DOI: 10.1063/1.437910

Calculation and selective population of vibrational levels with the Multiconfiguration Time-Dependent Hartree (MCTDH) algorithm
journal, October 2006

Direct conversion of slow light into a stationary light pulse
journal, August 2012

Capturing Plasmon–Molecule Dynamics in Dye Monolayers on Metal Nanoparticles Using Classical Electrodynamics with Quantum Embedding
journal, July 2017

  • Smith, Holden T.; Karam, Tony E.; Haber, Louis H.
  • The Journal of Physical Chemistry C, Vol. 121, Issue 31
  • DOI: 10.1021/acs.jpcc.7b03440

Symmetrical windowing for quantum states in quasi-classical trajectory simulations: Application to electronically non-adiabatic processes
journal, December 2013

  • Cotton, Stephen J.; Miller, William H.
  • The Journal of Chemical Physics, Vol. 139, Issue 23
  • DOI: 10.1063/1.4845235

Vacuum Rabi splitting in semiconductors
journal, February 2006

  • Khitrova, G.; Gibbs, H. M.; Kira, M.
  • Nature Physics, Vol. 2, Issue 2
  • DOI: 10.1038/nphys227

Ab Initio Multiple Spawning Dynamics of Excited Butadiene: Role of Charge Transfer
journal, November 2009

  • Levine, Benjamin G.; Martínez, Todd J.
  • The Journal of Physical Chemistry A, Vol. 113, Issue 46
  • DOI: 10.1021/jp907111u

Strong Light–Matter Interaction in Quantum Emitter/Metal Hybrid Nanostructures
journal, October 2017

The formulation of quantum statistical mechanics based on the Feynman path centroid density. I. Equilibrium properties
journal, April 1994

  • Cao, Jianshu; Voth, Gregory A.
  • The Journal of Chemical Physics, Vol. 100, Issue 7
  • DOI: 10.1063/1.467175

Wave packet interferometry for short-time electronic energy transfer: Multidimensional optical spectroscopy in the time domain
journal, January 2003

  • Cina, Jeffrey A.; Kilin, Dmitri S.; Humble, Travis S.
  • The Journal of Chemical Physics, Vol. 118, Issue 1
  • DOI: 10.1063/1.1519259

Recall and Creation of Spatial Excitation Distributions in Dielectric Media
journal, October 1997

Mixed quantum-classical equilibrium
journal, March 2005

  • Parandekar, Priya V.; Tully, John C.
  • The Journal of Chemical Physics, Vol. 122, Issue 9
  • DOI: 10.1063/1.1856460

Understanding the Surface Hopping View of Electronic Transitions and Decoherence
journal, May 2016

Semiclassical Description of Nonadiabatic Quantum Dynamics
journal, January 1997

Quantum-classical Liouville dynamics in the mapping basis
journal, August 2008

  • Kim, Hyojoon; Nassimi, Ali; Kapral, Raymond
  • The Journal of Chemical Physics, Vol. 129, Issue 8
  • DOI: 10.1063/1.2971041

Mixed quantum-classical surface hopping dynamics
journal, April 2000

  • Nielsen, Steve; Kapral, Raymond; Ciccotti, Giovanni
  • The Journal of Chemical Physics, Vol. 112, Issue 15
  • DOI: 10.1063/1.481225

Ring-Polymer Molecular Dynamics: Quantum Effects in Chemical Dynamics from Classical Trajectories in an Extended Phase Space
journal, April 2013

A new symmetrical quasi-classical model for electronically non-adiabatic processes: Application to the case of weak non-adiabatic coupling
journal, October 2016

  • Cotton, Stephen J.; Miller, William H.
  • The Journal of Chemical Physics, Vol. 145, Issue 14
  • DOI: 10.1063/1.4963914

A local correlation model that yields intrinsically smooth potential-energy surfaces
journal, August 2005

  • Subotnik, Joseph E.; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 123, Issue 6
  • DOI: 10.1063/1.2000252

Classical description of nonadiabatic photoisomerization processes and their real‐time detection via femtosecond spectroscopy
journal, December 1995

  • Stock, Gerhard
  • The Journal of Chemical Physics, Vol. 103, Issue 23
  • DOI: 10.1063/1.469905

Ab initio Ehrenfest dynamics
journal, August 2005

  • Li, Xiaosong; Tully, John C.; Schlegel, H. Bernhard
  • The Journal of Chemical Physics, Vol. 123, Issue 8
  • DOI: 10.1063/1.2008258

Chemical Reaction Rates from Ring Polymer Molecular Dynamics: Zero Point Energy Conservation in Mu + H 2 → MuH + H
journal, January 2012

  • Pérez de Tudela, Ricardo; Aoiz, F. J.; Suleimanov, Yury V.
  • The Journal of Physical Chemistry Letters, Vol. 3, Issue 4
  • DOI: 10.1021/jz201702q

On generalising Abraham-Lorentz equation
journal, November 1974

  • Daboul, Jamil
  • International Journal of Theoretical Physics, Vol. 11, Issue 3
  • DOI: 10.1007/BF01809564

A multiple spawning approach to tunneling dynamics
journal, April 2000

  • Ben-Nun, M.; Martı́nez, Todd J.
  • The Journal of Chemical Physics, Vol. 112, Issue 14
  • DOI: 10.1063/1.481213

Mixed quantum-classical equilibrium: Surface hopping
journal, July 2008

  • Schmidt, J. R.; Parandekar, Priya V.; Tully, John C.
  • The Journal of Chemical Physics, Vol. 129, Issue 4
  • DOI: 10.1063/1.2955564

Exciton–polariton light–semiconductor coupling effects
journal, March 2011

Ab Initio Multiple Spawning:  Photochemistry from First Principles Quantum Molecular Dynamics
journal, June 2000

  • Ben-Nun, M.; Quenneville, Jason; Martínez, Todd J.
  • The Journal of Physical Chemistry A, Vol. 104, Issue 22
  • DOI: 10.1021/jp994174i

Exact time‐dependent wave packet propagation: Application to the photodissociation of methyl iodide
journal, March 1982

  • Lee, Soo‐Y.; Heller, Eric J.
  • The Journal of Chemical Physics, Vol. 76, Issue 6
  • DOI: 10.1063/1.443342

Classical path methods in line broadening. I. The classical path approximation
journal, July 1969

  • Smith, Earl W.; Vidal, C. R.; Cooper, J.
  • Journal of Research of the National Bureau of Standards Section A: Physics and Chemistry, Vol. 73A, Issue 4
  • DOI: 10.6028/jres.073A.030

Theoretical analysis of dipole-induced electromagnetic transparency
journal, April 2015

Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation
journal, December 2012

  • Huo, Pengfei; Coker, David F.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4748316

Strong coupling between surface plasmon polaritons and emitters: a review
journal, December 2014

Detailed Balance in Ehrenfest Mixed Quantum-Classical Dynamics
journal, January 2006

  • Parandekar, Priya V.; Tully, John C.
  • Journal of Chemical Theory and Computation, Vol. 2, Issue 2
  • DOI: 10.1021/ct050213k

Ab Initio Multiple Spawning Dynamics Using Multi-State Second-Order Perturbation Theory
journal, December 2009

  • Tao, Hongli; Levine, Benjamin G.; Martínez, Todd J.
  • The Journal of Physical Chemistry A, Vol. 113, Issue 49
  • DOI: 10.1021/jp9063565

Interfacing single photons and single quantum dots with photonic nanostructures
journal, May 2015

  • Lodahl, Peter; Mahmoodian, Sahand; Stobbe, Søren
  • Reviews of Modern Physics, Vol. 87, Issue 2
  • DOI: 10.1103/RevModPhys.87.347

Multilayer formulation of the multiconfiguration time-dependent Hartree theory
journal, July 2003

  • Wang, Haobin; Thoss, Michael
  • The Journal of Chemical Physics, Vol. 119, Issue 3
  • DOI: 10.1063/1.1580111

Semiclassical initial value representation for electronically nonadiabatic molecular dynamics
journal, April 1997

  • Sun, Xiong; Miller, William H.
  • The Journal of Chemical Physics, Vol. 106, Issue 15
  • DOI: 10.1063/1.473624

Self-Referenced Coherent Diffraction X-Ray Movie of Ångstrom- and Femtosecond-Scale Atomic Motion
journal, October 2016

Symmetrical Windowing for Quantum States in Quasi-Classical Trajectory Simulations
journal, March 2013

  • Cotton, Stephen J.; Miller, William H.
  • The Journal of Physical Chemistry A, Vol. 117, Issue 32
  • DOI: 10.1021/jp401078u

Molecular dynamics with electronic transitions
journal, July 1990

  • Tully, John C.
  • The Journal of Chemical Physics, Vol. 93, Issue 2
  • DOI: 10.1063/1.459170

Communication: Note on detailed balance in symmetrical quasi-classical models for electronically non-adiabatic dynamics
journal, April 2015

  • Miller, William H.; Cotton, Stephen J.
  • The Journal of Chemical Physics, Vol. 142, Issue 13
  • DOI: 10.1063/1.4916945

Ab initio multiple spawning on laser-dressed states: a study of 1,3-cyclohexadiene photoisomerization via light-induced conical intersections
journal, July 2015

  • Kim, Jaehee; Tao, Hongli; Martinez, Todd J.
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 48, Issue 16
  • DOI: 10.1088/0953-4075/48/16/164003

An effective thermal-parametrization theory for the slow-light dynamics in a Doppler-broadened electromagnetically induced transparency medium
journal, July 2011

  • Su, Shih-Wei; Chen, Yi-Hsin; Gou, Shih-Chuan
  • Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 44, Issue 16
  • DOI: 10.1088/0953-4075/44/16/165504

A classical/semiclassical theory for the interaction of infrared radiation with molecular systems
journal, September 1978

  • Miller, William H.
  • The Journal of Chemical Physics, Vol. 69, Issue 5
  • DOI: 10.1063/1.436793

An assessment of mean-field mixed semiclassical approaches: Equilibrium populations and algorithm stability
journal, April 2016

  • Bellonzi, Nicole; Jain, Amber; Subotnik, Joseph E.
  • The Journal of Chemical Physics, Vol. 144, Issue 15
  • DOI: 10.1063/1.4946810

Dynamics of an atomic electron and its electromagnetic field in a cavity
journal, March 2005

Quantum-Classical Liouville Dynamics in the Mapping Basis
text, January 2009

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