Abstract
The exact factorization approach, originally developed for electron-nuclear dynamics, is extended to light-matter interactions within the dipole approximation. This allows for a Schrödinger equation for the photonic wavefunction, in which the potential contains exactly the effects on the photon field of its coupling to matter. We illustrate the formalism and potential for a two-level system representing the matter, coupled to an infinite number of photon modes in the Wigner-Weisskopf approximation, as well as to a single mode with various coupling strengths. Significant differences are found with the potential used in conventional approaches, especially for strong couplings. We discuss how our exact factorization approach for light-matter interactions can be used as a guideline to develop semiclassical trajectory methods for efficient simulations of light-matter dynamics.
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References
E. Orgiu, J. George, J.A. Hutchison, E. Devaux, J.F. Dayen, B. Doudin, F. Stellacci, C. Genet, J. Schachenmayer, C. Genes et al., Nat. Mater. 14, 1123 (2015)
A. Csehi, G.J. Halász, L.S. Cederbaum, A. Vibók, J. Phys. Chem. Lett. 8, 1624 (2017)
M. Gross, S. Haroche, Phys. Rep. 93, 301 (1982)
N.I. Gidopoulos, E.K.U. Gross, Philosophical Transactions of the R. Soc. Lond. A: Math., Phys. Eng. Sci. 372, 2011 2014
A. Abedi, N.T. Maitra, E.K.U. Gross, Phys. Rev. Lett. 105, 123002 (2010)
A. Abedi, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 137, 22A530 (2012)
G. Hunter, Int. J. Quantum Chem. 9, 237 (1975)
Y. Suzuki, A. Abedi, N.T. Maitra, K. Yamashita, E.K.U. Gross, Phys. Rev. A 89, 040501(R) (2014)
A. Maser, B. Gmeiner, T. Utikal, S. Götzinger, V. Sandoghdar, Nat. Photonics 10, 450 (2016)
C. Riek, D.V. Seletskiy, A.S. Moskalenko, J.F. Schmidt, P. Krauspe, S. Eckart, S. Eggert, G. Burkard, A. Leitenstorfer, Science 350, 420 (2015)
A.S. Moskalenko, C. Riek, D.V. Seletskiy, G. Burkard, A. Leitenstorfer, Phys. Rev. Lett. 115, 263601 (2015)
J. George, T. Chervy, A. Shalabney, E. Devaux, H. Hiura, C. Genet, T.W. Ebbesen, Phys. Rev. Lett. 117, 153601 (2016)
T. Byrnes, N.Y. Kim, Y. Yamamoto, Nat. Phys. 10, 803 (2014)
J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. Andre, J. Staehli et al., Nature 443, 409 (2006)
M.A. Sentef, M. Ruggenthaler, A. Rubio, arXiv:1802.09437 (2018)
S. Schmidt, Physica Scr. 91, 073006 (2016)
X. Zhong, T. Chervy, L. Zhang, A. Thomas, J. George, C. Genet, J. Hutchison, T.W. Ebbesen, Angew. Chem. Int. Ed. 56, 9034 (2017)
D.M. Coles, Y. Yang, Y. Wang, R.T. Grant, R.A. Taylor, S.K. Saikin, A. Aspuru-Guzik, D.G. Lidzey, J.K.H. Tang, J.M. Smith, Nat. Commun. 5, 5561 (2014)
J. Galego, F.J. Garcia-Vidal, J. Feist, Nat. Commun. 7, 13841 EP (2016)
J. Flick, M. Ruggenthaler, H. Appel, A. Rubio, Proc. Natl. Acad. Sci. 114, 3026 (2017)
T.W. Ebbesen, Acc. Chem. Res. 49, 2403 (2016)
A. Thomas, J. George, A. Shalabney, M. Dryzhakov, S.J. Varma, J. Moran, T. Chervy, X. Zhong, E. Devaux, C. Genet et al., Angew. Chem. 128, 11634 (2016)
B. Barnes, F. García Vidal, J. Aizpurua, ACS Photonics 5, 43 (2018)
F. Herrera, F.C. Spano, ACS Photonics 5, 65 (2018)
J. Feist, J. Galego, F.J. Garcia-Vidal, ACS Photonics 5, 205 (2018)
R.F. Ribeiro, L.A. Martínez-Martínez, M. Du, J. Campos-Gonzalez-Angulo, J. Yuen-Zhou, arXiv:1802.08681 (2018)
M. Ruggenthaler, N. Tancogne-Dejean, J. Flick, H. Appel, A. Rubio, Nat. Rev. Chem. 2, 0118 (2018)
K.E. Dorfman, F. Schlawin, S. Mukamel, J. Phys. Chem. Lett. 5, 2843 (2014)
K.E. Dorfman, F. Schlawin, S. Mukamel, Rev. Mod. Phys. 88, 045008 (2016)
Z. Ficek, P.D. Drummond, Phys. Today 50, 34 (1997)
D.N. Matsukevich, A. Kuzmich, Science 306, 663 (2004)
E.J. Heller, J. Chem. Phys. 65, 1289 (1976)
F.H. Faisal, Theory of Multiphoton Processes (Springer, Berlin, 1987)
J. Flick, H. Appel, M. Ruggenthaler, A. Rubio, J. Chem. Theory Comput. 13, 1616 (2017)
I.V. Tokatly, Phys. Rev. Lett. 110, 233001 (2013)
C. Pellegrini, J. Flick, I.V. Tokatly, H. Appel, A. Rubio, Phys. Rev. Lett. 115, 093001 (2015)
J. Flick, M. Ruggenthaler, H. Appel, A. Rubio, Proc. Natl. Acad. Sci. 50, 15285 (2015)
D.P. Craig, T. Thirunamachandran, Molecular Quantum Electrodynamics: An Introduction to Radiation-molecule Interactions (Dover Publications, 1998)
M. Ruggenthaler, J. Flick, C. Pellegrini, H. Appel, I.V. Tokatly, A. Rubio, Phys. Rev. A 90, 012508 (2014)
V. Rokaj, D.M. Welakuh, M. Ruggenthaler, A. Rubio, J. Phys. B: Atomic, Molecular and Optical Physics 51, 034005 (2017)
G. Hunter, Int. J. Quantum Chem. 19, 755 (1981)
A. Abedi, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 139, 087102 (2013)
J.L. Alonso, J. Clemente-Gallardo, P. Echenique-Robba, J.A. Jover-Galtier, J. Chem. Phys. 139, 087101 (2013)
S.K. Min, A. Abedi, K.S. Kim, E.K.U. Gross, Phys. Rev. Lett. 113, 263004 (2014)
R. Requist, F. Tandetzky, E.K.U. Gross, Phys. Rev. A 93, 042108 (2016)
R. Requist, C.R. Proetto, E.K.U. Gross, Phys. Rev. A 96, 062503 (2017)
Y.C. Chiang, S. Klaiman, F. Otto, L.S. Cederbaum, J. Chem. Phys. 140, 054104 (2014)
J. Galego, F.J. Garcia-Vidal, J. Feist, Phys. Rev. X 5, 041022 (2015)
Y. Suzuki, A. Abedi, N. Maitra, E.K.U. Gross, Phys. Chem. Chem. Phys. 17, 29271 (2015)
E. Khosravi, A. Abedi, N.T. Maitra, Phys. Rev. Lett. 115, 263002 (2015)
T. Fiedlschuster, J. Handt, E.K.U. Gross, R. Schmidt, Phys. Rev. A 95, 063424 (2017)
A. Schild, E. Gross, Phys. Rev. Lett. 118, 163202 (2017)
A. Abedi, F. Agostini, Y. Suzuki, E.K.U. Gross, Phys. Rev. Lett. 110, 263001 (2013)
F. Agostini, A. Abedi, Y. Suzuki, S.K. Min, N.T. Maitra, E.K.U. Gross, J. Chem. Phys. 142, 084303 (2015)
B.F.E. Curchod, F. Agostini, E.K.U. Gross, J. Chem. Phys. 145, 034103 (2016)
A. Scherrer, F. Agostini, D. Sebastiani, E.K.U. Gross, R. Vuilleumier, Phys. Rev. X 7, 031035 (2017)
A. Scherrer, F. Agostini, D. Sebastiani, E.K.U. Gross, R. Vuilleumier, J. Chem. Phys. 143, 074106 (2015)
K. Hader, J. Albert, E.K.U. Gross, V. Engel, J. Chem. Phys. 146, 074304 (2017)
B.F.E. Curchod, F. Agostini, J. Phys. Chem. Lett. 8, 831 (2017)
M. Scully, A. Zubairy, Quantum Optics (Cambridge University Press, 1997)
H.I. Yoo, J. Eberly, Phys. Rep. 118, 239 (1985)
S.K. Min, F. Agostini, I. Tavernelli, E.K.U. Gross, J. Phys. Chem. Lett. 8, 3048 (2017)
F. Agostini, S.K. Min, A. Abedi, E.K.U. Gross, J. Chem. Theory Comput. 12, 2127 (2016)
S.K. Min, F. Agostini, E.K.U. Gross, Phys. Rev. Lett. 115, 073001 (2015)
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Contribution to the Topical Issue “Topical issue: Special issue in honor of Hardy Gross”, edited by C.A. Ullrich, F.M.S. Nogueira, A. Rubio, and M.A.L. Marques.
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Hoffmann, N.M., Appel, H., Rubio, A. et al. Light-matter interactions via the exact factorization approach. Eur. Phys. J. B 91, 180 (2018). https://doi.org/10.1140/epjb/e2018-90177-6
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DOI: https://doi.org/10.1140/epjb/e2018-90177-6