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From a quantum-electrodynamical light–matter description to novel spectroscopies

An Author Correction to this article was published on 12 September 2018

Abstract

Insights from spectroscopic experiments led to the development of quantum mechanics as the common theoretical framework for describing the physical and chemical properties of atoms, molecules and materials. Later, a full quantum description of charged particles, electromagnetic radiation and special relativity was developed, leading to quantum electrodynamics (QED). This is, to our current understanding, the most complete theory describing photon–matter interactions in correlated many–body systems. In the low-energy regime, simplified models of QED have been developed to describe and analyse spectra over a wide spatiotemporal range as well as physical systems. In this Review, we highlight the interrelations and limitations of such theoretical models, thereby showing that they arise from low-energy simplifications of the full QED formalism, in which antiparticles and the internal structure of the nuclei are neglected. Taking molecular systems as an example, we discuss how the breakdown of some simplifications of low-energy QED challenges our conventional understanding of light–matter interactions. In addition to high-precision atomic measurements and simulations of particle physics problems in solid-state systems, new theoretical features that account for collective QED effects in complex interacting many-particle systems could become a material-based route to further advance our current understanding of light–matter interactions.

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Figure 1: Schematic evolution of our understanding of quantized coupled light–matter systems.
Figure 2: Theoretical description of photon–matter interacting systems.
Figure 3: Schematic description of the different components of the light–matter QED Hamiltonian.
Figure 4: Numerical example for a QEDFT calculation: study of a 3D sodium dimer in an optical cavity.
Figure 5: Calculated spectra for a 1D model dimer.

References

  1. 1

    Zeilinger, A., Weihs, G., Jennewein, T. & Aspelmeyer, M. Happy centenary, photon. Nature 433, 230 (2005).

    CAS  PubMed  Article  Google Scholar 

  2. 2

    Sigrist, M. & Ueda, K. Phenomenological theory of unconventional superconductivity. Rev. Mod. Phys. 63, 239–311 (1991).

    CAS  Article  Google Scholar 

  3. 3

    Krausz, F. & Ivanov, M. Attosecond physics. Rev. Mod. Phys. 81, 163–234 (2009).

    Article  Google Scholar 

  4. 4

    Domcke, W. & Yarkony, D. R. Role of conical intersections in molecular spectroscopy and photoinduced chemical dynamics. Annu. Rev. Phys. Chem. 63, 325–352 (2012).

    CAS  PubMed  Article  Google Scholar 

  5. 5

    Wang, Y., Plummer, E. W. & Kempa, K. Foundations of plasmonics. Adv. Phys. 60, 799–898 (2011).

    CAS  Article  Google Scholar 

  6. 6

    Beenakker, C. W. J. Search for Majorana fermions in superconductors. Annu. Rev. Condens. Matter Phys. 4, 113–136 (2013).

    CAS  Article  Google Scholar 

  7. 7

    Endres, M. et al. Observation of correlated particle-hole pairs and string order in low-dimensional mott insulators. Science 334, 200–203 (2011).

    CAS  PubMed  Article  Google Scholar 

  8. 8

    Hübener, H., Sentef, M. A., De Giovannini, U., Kemper, A. F. & Rubio, A. Creating stable floquet–weyl semimetals by laser-driving of 3D dirac materials. Nat. Commun. 8, 13940 (2017).

    PubMed  PubMed Central  Article  CAS  Google Scholar 

  9. 9

    Mankowsky, R., Först, M. & Cavalleri, A. Non-equilibrium control of complex solids by non-linear phononics. Rep. Progress Phys. 79, 064503 (2016).

    Article  CAS  Google Scholar 

  10. 10

    Krausz, F. & Stockman, M. I. Attosecond metrology: from electron capture to future signal processing. Nat. Photon. 8, 205–213 (2014).

    CAS  Article  Google Scholar 

  11. 11

    Svanberg, S. Atomic and Molecular Spectroscopy: Basic Aspects and Practical Applications Vol. 6. (Springer Science & Business Media, Dordrecht, Netherlands, 2012).

    Google Scholar 

  12. 12

    Kuzmany, H. Solid-State Spectroscopy: An Introduction (Springer Science & Business Media, Dordrecht, Netherlands, 2009).

    Book  Google Scholar 

  13. 13

    Cowan, J. A. Inorganic Biochemistry: An Introduction (John Wiley & Sons, Hoboken, NJ, USA, 1997).

    Google Scholar 

  14. 14

    Byrnes, T., Kim, N. Y. & Yamamoto, Y. Exciton–polariton condensates. Nat. Phys. 10, 803–813 (2014).

    CAS  Article  Google Scholar 

  15. 15

    Hutchison, J. A., Schwartz, T., Genet, C., Devaux, E. & Ebbesen, T. W. Modifying chemical landscapes by coupling to vacuum fields. Angew. Chem. Int. Ed. 51, 1592–1596 (2012).

    CAS  Article  Google Scholar 

  16. 16

    Galego, J., Garcia-Vidal, F. J. & Feist, J. Cavity-induced modifications of molecular structure in the strong-coupling regime. Phys. Rev. X 5, 041022 (2015).

    Google Scholar 

  17. 17

    Flick, J., Ruggenthaler, M., Appel, H. & Rubio, A. Atoms and molecules in cavities, from weak to strong coupling in quantum-electrodynamics (QED) chemistry. Proc. Natl Acad. Sci. USA 114, 3026–3034 (2017).

    CAS  PubMed  Article  Google Scholar 

  18. 18

    Ebbesen, T. W. Hybrid light–matter states in a molecular and material science perspective. Acc. Chem. Res. 49, 2403–2412 (2016).

    CAS  Google Scholar 

  19. 19

    Coles, D. M. et al. Strong coupling between chlorosomes of photosynthetic bacteria and a confined optical cavity mode. Nat. Commun. 5, 5561 (2014).

    CAS  PubMed  Article  Google Scholar 

  20. 20

    Firstenberg, O. et al. Attractive photons in a quantum nonlinear medium. Nature 502, 71–75 (2013).

    CAS  PubMed  Article  Google Scholar 

  21. 21

    Upton, L. T. et al. Optically excited entangled states in organic molecules illuminate the dark. J. Phys. Chem. Lett. 4, 2046–2052 (2013).

    CAS  PubMed  Article  Google Scholar 

  22. 22

    Dorfman, K. E., Schlawin, F. & Mukamel, S. Nonlinear optical signals and spectroscopy with quantum light. Rev. Mod. Phys. 88, 045008 (2016).

    Article  Google Scholar 

  23. 23

    Grynberg, G., Aspect, A. & Fabre, C. Introduction to Quantum Optics: From the Semi-Classical Approach to Quantized Light (Cambridge Univ. Press, 2010).

    Book  Google Scholar 

  24. 24

    Venema, L. et al. The quasiparticle zoo. Nat. Phys. 12, 1085–1089 (2016).

    CAS  Article  Google Scholar 

  25. 25

    Bethe, H. A. & Salpeter, E. E. Quantum Mechanics of One- and Two-Electron Atoms (Springer Science & Business Media, Dordrecht, Netherlands, 2012).

    Google Scholar 

  26. 26

    Karshenboim, S. G. Precision Physics of Simple Atoms and Molecule Vol. 745 (Springer, Berlin, Heidelberg, 2007).

    Google Scholar 

  27. 27

    Sommer, A. et al. Attosecond nonlinear polarization and light–matter energy transfer in solids. Nature 534, 86–90 (2016).

    CAS  PubMed  Article  Google Scholar 

  28. 28

    Qi, X.-L., Hughes, T. L. & Zhang, S.-C. Topological field theory of time-reversal invariant insulators. Phys. Rev. B 78, 195424 (2008).

    Article  CAS  Google Scholar 

  29. 29

    Witczak-Krempa, W., Chen, G., Kim, Y. B. & Balents, L. Correlated quantum phenomena in the strong spin-orbit regime. Annu. Rev. Condens. Matter Phys. 5, 57–82 (2014).

    CAS  Article  Google Scholar 

  30. 30

    De Giovannini, U., Hübener, H. & Rubio, A. Monitoring electron-photon dressing in WSe2 . Nano Lett. 16, 7993–7998 (2016).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  31. 31

    Sie, E. J., Lui, C. H., Lee, Y.-H., Kong, J. & Gedik, N. Observation of intervalley biexcitonic optical stark effect in monolayer WS2 . Nano Lett. 16, 7421–7426 (2016).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  32. 32

    Kasprzak, J., et al. Bose–Einstein condensation of exciton polaritons. Nature 443, 409–414 (2006).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  33. 33

    Andrews, D. L. Physicality of the photon. J. Phys. Chem. Lett. 4, 3878–3884 (2013).

    CAS  Article  Google Scholar 

  34. 34

    Craig, D. P. & Thirunamachandran, T. Molecular Quantum Electrodynamics: An Introduction to Radiation-Molecule Interactions (Courier Corporation, 1984).

    Google Scholar 

  35. 35

    Woods, L. M. et al. Materials perspective on Casimir and van der Waals interactions. Rev. Mod. Phys. 88, 045003 (2016).

    Article  Google Scholar 

  36. 36

    Scholes, G. D. Long-range resonance energy transfer in molecular systems. Annu. Rev. Phys. Chem. 54, 57–87 (2003).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  37. 37

    Andrews, D. L. & Bradshaw, D. S. Virtual photons, dipole fields and energy transfer: a quantum electrodynamical approach. Eur. J. Phys. 25, 845 (2004).

    Article  Google Scholar 

  38. 38

    Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).

    Article  Google Scholar 

  39. 39

    Mahon, B. How Maxwell's equations came to light. Nat. Photon. 9, 2–4 (2015).

    CAS  Article  Google Scholar 

  40. 40

    Fermi, E. Quantum theory of radiation. Rev. Mod. Phys. 4, 87–132 (1932).

    CAS  Article  Google Scholar 

  41. 41

    Greiner, W. & Reinhardt, J. Field Quantization (Springer Science & Business Media, Dordrecht, Netherlands, 2013).

    Google Scholar 

  42. 42

    Cohen-Tannoudji, C., Dupont-Roc, J. & Grynberg, G. Photons and Atoms: Introduction to Quantum Electrodynamics (Wiley, Hoboken, NJ, USA, 1989).

    Google Scholar 

  43. 43

    Bethe, H. A. The electromagnetic shift of energy levels. Phys. Rev. 72, 339–341 (1947).

    CAS  Article  Google Scholar 

  44. 44

    [No authors listed.] Nobel prizes 1965. Phys. Today 18, 58–59 (1965).

  45. 45

    Pauli, W. & Fierz, M. Zur theorie der emission langwelliger lichtquanten [German]. Il Nuovo Cimento (1924–1942) 15, 167–188 (1938).

    CAS  Article  Google Scholar 

  46. 46

    Spohn, H. Dynamics of Charged Particles and their Radiation Field (Cambridge Univ. Press, 2004).

    Book  Google Scholar 

  47. 47

    Derezinski, J. & Jakšic, V. Spectral theory of Pauli–Fierz operators. J. Funct. Analysis 180, 243–327 (2001).

    Article  Google Scholar 

  48. 48

    Bach, V., Fröhlich, J. & Sigal, I. M. Spectral analysis for systems of atoms and molecules coupled to the quantized radiation field. Commun. Math. Phys. 207, 249–290 (1999).

    Article  Google Scholar 

  49. 49

    Hidaka, T. & Hiroshima, F. Pauli–Fierz model with kato-class potentials and exponential decays. Rev. Math. Phys. 22, 1181–1208 (2010).

    Article  Google Scholar 

  50. 50

    Rokaj, V., Welakuh, D. M., Ruggenthaler, M. & Rubio, A. Light-matter interaction in the long-wavelength limit: no ground-state without dipole self-energy. J. Phys. B Atom. Mol. Opt. Phys. 51, 034005 (2017).

    Article  CAS  Google Scholar 

  51. 51

    Nelson, E. Interaction of nonrelativistic particles with a quantized scalar field. J. Math. Phys. 5, 1190–1197 (1964).

    CAS  Article  Google Scholar 

  52. 52

    Greiner, W., Müller, B. & Rafelski, J. Quantum Electrodynamics of Strong Fields (Springer-Verlag, Berlin, Heiderlberg, 2013).

    Google Scholar 

  53. 53

    Di Piazza, A., Müller, C., Hatsagortsyan, K. Z. & Keitel, C. H. Extremely high-intensity laser interactions with fundamental quantum systems. Rev. Mod. Phys. 84, 1177 (2012).

    CAS  Article  Google Scholar 

  54. 54

    The ALEPH Collaboration et al. Precision electroweak measurements on the Z resonance. Phys. Rep. 427, 257–454 (2006).

    Google Scholar 

  55. 55

    Marklund, M. & Shukla, P. K. Nonlinear collective effects in photon-photon and photon-plasma interactions. Rev. Mod. Phys. 78, 591 (2006).

    CAS  Article  Google Scholar 

  56. 56

    Gooth, J. et al. Experimental signatures of the mixed axial-gravitational anomaly in the weyl semimetal NbP. Nature 547, 324 (2017).

    CAS  PubMed  Article  Google Scholar 

  57. 57

    Reich, E. S., Higgs physics on the cheap. Nature 495, 422–423 (2013).

    CAS  PubMed  Article  Google Scholar 

  58. 58

    Alicea, J. New directions in the pursuit of majorana fermions in solid state systems. Rep. Progress Phys. 75, 076501 (2012).

    Article  Google Scholar 

  59. 59

    Rundong, L., Jing, W., Xiao-Liang, Q. & Shou-Cheng, Z. Dynamical axion field in topological magnetic insulators. Nat. Phys. 6, 284–288 (2010).

    Article  CAS  Google Scholar 

  60. 60

    Walther, H., Varcoe, B. T. H., Englert, B.-G. & Becker, T. Cavity quantum electrodynamics. Rep. Progress Phys. 69, 1325 (2006).

    Article  Google Scholar 

  61. 61

    Saleh, B. E. A., Teich, M. C. & Saleh, B. E. Fundamentals of Photonics, Vol. 22 (Wiley New York, 1991).

    Book  Google Scholar 

  62. 62

    Maier, S. A. Plasmonics: Fundamentals and Applications, (Springer Science & Business Media, Dordrecht, Netherlands, 2007).

    Book  Google Scholar 

  63. 63

    Szabo, A. & Ostlund, N. S. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Dover Publications, 2012).

    Google Scholar 

  64. 64

    Haroche, S. Nobel lecture: Controlling photons in a box and exploring the quantum to classical boundary. Rev. Mod. Phys. 85, 1083 (2013).

    CAS  Article  Google Scholar 

  65. 65

    Vahala, K. J. Optical microcavities. Nature 424, 839–846 (2003).

    CAS  PubMed  Article  Google Scholar 

  66. 66

    Miller, R. et al. Trapped atoms in cavity qed: coupling quantized light and matter. J. Phys. B Atom. Mol. Opt. Phys. 38, S551 (2005).

    CAS  Google Scholar 

  67. 67

    Hadfield, R. H. Single-photon detectors for optical quantum information applications. Nat. Photon. 3, 696–705 (2009).

    CAS  Article  Google Scholar 

  68. 68

    Fleischhauer, M., Imamoglu, A. & Marangos, J. P. Electromagnetically induced transparency: optics in coherent media. Rev. Mod. Phys. 77, 633–673 (2005).

    CAS  Article  Google Scholar 

  69. 69

    Mu, Y. & Savage, C. M. One-atom lasers. Phys. Rev. A 46, 5944–5954 (1992).

    CAS  PubMed  Article  Google Scholar 

  70. 70

    Pellizzari, T. & Ritsch, H. Preparation of stationary Fock states in a one-atom Raman laser. Phys. Rev. Lett. 72, 3973–3976 (1994).

    CAS  PubMed  Article  Google Scholar 

  71. 71

    McKeever, J., Boca, A., Boozer, A. D., Buck, J. R. & Kimble, H. J. Experimental realization of a one-atom laser in the regime of strong coupling. Nature 425, 268–271 (2003).

    CAS  PubMed  Article  Google Scholar 

  72. 72

    Breuer, H.-P. & Petruccione, F. The Theory of Open Quantum Systems (Oxford Univ. Press, 2002).

    Google Scholar 

  73. 73

    Schröter, M. et al. Exciton–vibrational coupling in the dynamics and spectroscopy of Frenkel excitons in molecular aggregates. Phys. Rep. 567, 1–78 (2015).

    Article  CAS  Google Scholar 

  74. 74

    Vandersypen, L. M. K. & Chuang, I. L. NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037–1069 (2005).

    Article  Google Scholar 

  75. 75

    Kiffner, M., Evers, J. & Keitel, C. H. Breakdown of the few-level approximation in collective systems. Phys. Rev. A 76, 013807 (2007).

    Article  CAS  Google Scholar 

  76. 76

    George, J. et al. Multiple Rabi splittings under ultrastrong vibrational coupling. Phys. Rev. Lett. 117, 153601 (2016).

    PubMed  Article  CAS  Google Scholar 

  77. 77

    Vukics, A. & Domokos, P. Adequacy of the Dicke model in cavity QED: A counter-no-go statement. Phys. Rev. A 86, 053807 (2012).

    Article  CAS  Google Scholar 

  78. 78

    Demtröder, W. Laser Spectroscopy: Basic Concepts and Instrumentation (Springer Science & Business Media, Dordrecht, Netherlands, 2013).

    Google Scholar 

  79. 79

    Yabana, K., Sugiyama, T., Shinohara, Y., Otobe, T. & Bertsch, G. F. Time-dependent density functional theory for strong electromagnetic fields in crystalline solids. Phys. Rev. B 85, 045134 (2012).

    Article  CAS  Google Scholar 

  80. 80

    Lucchini, M. et al. Attosecond dynamical franz-keldysh effect in polycrystalline diamond. Science 353, 916–919 (2016).

    CAS  PubMed  Article  Google Scholar 

  81. 81

    Fratalocchi, A. & Ruocco, G. Single-molecule imaging with x-ray free-electron lasers: dream or reality? Phys. Rev. Lett. 106, 105504 (2011).

    CAS  PubMed  Article  Google Scholar 

  82. 82

    Lopata, K. & Neuhauser, D. Multiscale Maxwell–Schrödinger modeling: a split field finite-difference time-domain approach to molecular nanopolaritonics. J. Chem. Phys. 130, 104707 (2009).

    PubMed  Article  CAS  Google Scholar 

  83. 83

    Agrawal, G. P. Nonlinear Fiber Optics (Academic press, 2007).

    Google Scholar 

  84. 84

    Novotny, L. & Van Hulst, N. Antennas for light. Nat. Photon. 5, 83–90 (2011).

    CAS  Article  Google Scholar 

  85. 85

    Keller, O. Quantum Theory of Near-Field Electrodynamics (Springer, 2012).

    Google Scholar 

  86. 86

    Fercher, A. F., Drexler, W., Hitzenberger, C. K. & Lasser, T. Optical coherence tomography principles and applications. Rep. Progress Phys. 66, 239 (2003).

    Article  Google Scholar 

  87. 87

    Born, M. & Wolf, E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. (Elsevier, 2013).

    Google Scholar 

  88. 88

    Collier, R. Optical Holography (Elsevier, 2013).

    Google Scholar 

  89. 89

    Gray, S. K. Theory and modeling of plasmonic structures. J. Phys. Chem. C 117, 1983–1994 (2012).

    Article  CAS  Google Scholar 

  90. 90

    Ramsey, N. F. Experiments with separated oscillatory fields and hydrogen masers. Rev. Mod. Phys. 62, 541–552 (1990).

    CAS  Article  Google Scholar 

  91. 91

    Jones, K. M., Tiesinga, E., Lett, P. D. & Julienne, P. S. Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering. Rev. Mod. Phys. 78, 483–535 (2006).

    CAS  Article  Google Scholar 

  92. 92

    Korobov, V. I., Koelemeij, J. C. J., Hilico, L. & Karr, J.-P. Theoretical hyperfine structure of the molecular hydrogen ion at the 1 ppm level. Phys. Rev. Lett. 116, 053003 (2016).

    PubMed  Article  CAS  Google Scholar 

  93. 93

    Edelhoch, H., Brand, L. & Wilchek, M. Fluorescence studies with tryptophyl peptides. Biochemistry 6, 547–559 (1967).

    CAS  PubMed  Article  Google Scholar 

  94. 94

    Engel, E. & Dreizler, R. M. Density Functional Theory: An Advanced Course (Springer Science & Business Media, Dordrecht, Netherlands, 2011).

    Book  Google Scholar 

  95. 95

    Stefanucci, G. & Van Leeuwen, R. Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction (Cambridge Univ. Press, 2013).

    Book  Google Scholar 

  96. 96

    Ruggenthaler, M. et al. Quantum-electrodynamical density-functional theory: bridging quantum optics and electronic-structure theory. Phys. Rev. A 90, 012508 (2014).

    Article  CAS  Google Scholar 

  97. 97

    de Melo, P. M. M. C. & Marini, A. Unified theory of quantized electrons, phonons, and photons out of equilibrium: a simplified ab initio approach based on the generalized Baym-Kadanoff ansatz. Phys. Rev. B 93, 155102 (2016).

    Article  CAS  Google Scholar 

  98. 98

    Almbladh, C.-O. & Hedin, L. in Handbook on Synchrotron Radiation (ed. Koch, E. E. ) 607–904 (North Holland, Amsterdam, 1983).

    Google Scholar 

  99. 99

    Flick, J., Ruggenthaler, M., Appel, H. & Rubio, A. Kohn–Sham approach to quantum electrodynamical density-functional theory: exact time-dependent effective potentials in real space. Proc. Natl Acad. Sci. USA 112, 15285–15290 (2015).

    CAS  PubMed  Article  Google Scholar 

  100. 100

    Pellegrini, C., Flick, J., Tokatly, I. V., Appel, H. & Rubio, A. Optimized effective potential for quantum electrodynamical time-dependent density functional theory. Phys. Rev. Lett. 115, 093001 (2015).

    PubMed  Article  CAS  Google Scholar 

  101. 101

    Truppe, S. et al. A search for varying fundamental constants using hertz-level frequency measurements of cold CH molecules. Nat. Commun. 4, 2600 (2013).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  102. 102

    Jansen, P., Bethlem, H. L. & Ubachs, W. Perspective: Tipping the scales: search for drifting constants from molecular spectra. J. Chem. Phys. 140, 010901 (2014).

    PubMed  Article  CAS  Google Scholar 

  103. 103

    Biesheuvel, J. et al. Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD+. Nat. Commun. 7, 10385 (2016).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  104. 104

    Mohr, P. J., Newell, D. B. & Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2014. Rev. Mod. Phys. 88, 035009 (2016).

    Article  Google Scholar 

  105. 105

    Pople, J. A. Nobel lecture: quantum chemical models. Rev. Mod. Phys. 71, 1267 (1999).

    CAS  Article  Google Scholar 

  106. 106

    Bonitz, M. Quantum Kinetic Theory (Springer, 1998).

    Google Scholar 

  107. 107

    Shankar, R. Renormalization-group approach to interacting fermions. Rev. Mod. Phys. 66, 129–192 (1994).

    Article  Google Scholar 

  108. 108

    Schollwöck, U. The density-matrix renormalization group. Rev. Mod. Phys. 77, 259–315 (2005).

    Article  CAS  Google Scholar 

  109. 109

    Schollwöck, U. Time-dependent density-matrix renormalization-group methods. J. Phys. Soc. Japan 74, 246–255 (2005).

    Article  Google Scholar 

  110. 110

    Tanimura, Y. Stochastic Liouville, Langevin, Fokker–Planck, and master equation approaches to quantum dissipative systems. J. Phys. Soc. Japan 75, 082001 (2006).

    Article  CAS  Google Scholar 

  111. 111

    Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors 5th edn (World Scientific Publishing Co, 2009).

    Book  Google Scholar 

  112. 112

    Axt, V. M. & Mukamel, S. Nonlinear optics of semiconductor and molecular nanostructures; a common perspective. Rev. Mod. Phys. 70, 145 (1998).

    CAS  Article  Google Scholar 

  113. 113

    Essler, F. H. L., Frahm, H., Göhmann, F., Klümper, A. & Korepin, V. E. The One-Dimensional Hubbard Model (Cambridge Univ. Press, 2005).

    Book  Google Scholar 

  114. 114

    Hewson, A. C. The Kondo Problem to Heavy Fermions Vol. 2 (Cambridge Univ. Press, 1997).

    Google Scholar 

  115. 115

    Minguzzi, A., Succi, S., Toschi, F., Tosi, M. P. & Vignolo, P. Numerical methods for atomic quantum gases with applications to Bose–Einstein condensates and to ultracold fermions. Phys. Rep. 395, 223–355 (2004).

    CAS  Article  Google Scholar 

  116. 116

    Spuntarelli, A., Pieri, P. & Calvanese Strinati, G. Solution of the Bogoliubov–de Gennes equations at zero temperature throughout the BCS–BEC crossover: Josephson and related effects. Phys. Rep. 488, 111–167 (2010).

    CAS  Article  Google Scholar 

  117. 117

    Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957).

    CAS  Article  Google Scholar 

  118. 118

    Mulser, P. & Bauer, D. High Power Laser–Matter Interaction Vol. 238 (Springer Science & Business Media, Dordrecht, Netherlands, 2010).

    Book  Google Scholar 

  119. 119

    Bertsch, G. F., Iwata, J.-I., Rubio, A. & Yabana, K. Real-space, real-time method for the dielectric function. Phys. Rev. B 62, 7998 (2000).

    CAS  Article  Google Scholar 

  120. 120

    Hedin, L. & Lee, J. D. Sudden approximation in photoemission and beyond. J. Electron. Spectrosc. Related Phenomena 124, 289–315 (2002).

    CAS  Article  Google Scholar 

  121. 121

    Onida, Gi., Reining, L. & Rubio, A. Electronic excitations: density-functional versus many-body Green's-function approaches. Rev. Mod. Phys. 74, 601–659 (2002).

    Article  CAS  Google Scholar 

  122. 122

    Ehrenreich, H. in The Optical Properties of Solids (ed. Tauc, J. ) 106 (Academic Press, 1966).

    Google Scholar 

  123. 123

    Mochán, W. L. & Barrera, R. G. Electromagnetic response of systems with spatial fluctuations. I. general formalism. Phys. Rev. B 32, 4984 (1985).

    Article  Google Scholar 

  124. 124

    Maki, J. J., Malcuit, M. S., Sipe, J. E. & Boyd, R. W. Linear and nonlinear optical measurements of the Lorentz local field. Phys. Rev. Lett. 67, 972 (1991).

    CAS  PubMed  Article  Google Scholar 

  125. 125

    Luppi, E., Hübener, H. & Véniard, V. Ab initio second-order nonlinear optics in solids: Second-harmonic generation spectroscopy from time-dependent density-functional theory. Phys. Rev. B 82, 235201 (2010).

    Article  CAS  Google Scholar 

  126. 126

    Reiher, M. & Wolf, A. Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science (John Wiley & Sons, 2014).

    Google Scholar 

  127. 127

    Bishop, R. F., Brandes, T., Gernoth, K. A., Walet, N. R. & Xian, Y. Recent Progress in Many-Body Theories (World Scientific Publishing Co, 2002).

    Book  Google Scholar 

  128. 128

    Bartlett, R. J. & Musiał, M. Coupled-cluster theory in quantum chemistry. Rev. Mod. Phys. 79, 291–352 (2007).

    CAS  Article  Google Scholar 

  129. 129

    Gubernatis, J., Kawashima, N. & Werner, P. Quantum Monte Carlo Methods (Cambridge Univ. Press, 2016).

    Book  Google Scholar 

  130. 130

    Schollwöck, U. The density-matrix renormalization group in the age of matrix product states. Ann. Phys. 326, 96–192 (2011).

    Article  CAS  Google Scholar 

  131. 131

    Kotliar, G. et al. Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys 78, 865–951 (2006).

    CAS  Article  Google Scholar 

  132. 132

    Li, Z. H. et al. Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems. Phys. Rev. Lett. 109, 266403 (2012).

    PubMed  Article  CAS  Google Scholar 

  133. 133

    Härtle, R., Cohen, G., Reichman, D. R. & Millis, A. J. Decoherence and lead-induced interdot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach. Phys. Rev. B 88, 235426 (2013).

    Article  CAS  Google Scholar 

  134. 134

    Ye, L. Z. et al. HEOM-QUICK: a program for accurate, efficient, and universal characterization of strongly correlated quantum impurity systems. Wiley Interdiscip. Rev. Comput. Mol. Sci. 6, 608–638 (2016).

    Article  Google Scholar 

  135. 135

    Kong, L., Bischoff, F. A. & Valeev, E. F. Explicitly correlated R12/F12 methods for electronic structure. Chem. Rev. 112, 75–107 (2012).

    CAS  PubMed  Article  Google Scholar 

  136. 136

    Metzner, W., Salmhofer, M., Honerkamp, C., Meden, V. & Schönhammer, K. Functional renormalization group approach to correlated fermion systems. Rev. Mod. Phys. 84, 299–352 (2012).

    Article  Google Scholar 

  137. 137

    Knecht, S., Legeza, Ö. & Reiher, M. Communication: Four-component density matrix renormalization group. J. Chem. Phys. 140, 041101 (2014).

    PubMed  Article  CAS  Google Scholar 

  138. 138

    Liu, W. Handbook of Relativistic Quantum Chemistry (Springer, Berlin, Heidelberg, 2016).

    Google Scholar 

  139. 139

    Pašteka, L. F., Eliav, E., Borschevsky, A., Kaldor, U. & Schwerdtfeger, P. Relativistic coupled cluster calculations with variational quantum electrodynamics resolve the discrepancy between experiment and theory concerning the electron affinity and ionization potential of gold. Phys. Rev. Lett. 118, 023002 (2017).

    PubMed  Article  Google Scholar 

  140. 140

    Hagen, G., Papenbrock, T., Hjorth-Jensen, M. & Dean, D. J. Coupled-cluster computations of atomic nuclei. Rep. Progress Phys. 77, 096302 (2014).

    CAS  Article  Google Scholar 

  141. 141

    Manthe, U. Wavepacket dynamics and the multiconfigurational time-dependent Hartree approach. J. Phys. Condens. Matter (2017).

  142. 142

    Culver, R. et al., Collective strong coupling of cold potassium atoms in a ring cavity. New J.Phys. 18, 113043 (2016).

    Article  CAS  Google Scholar 

  143. 143

    Hood, J. D. et al. Atom–atom interactions around the band edge of a photonic crystal waveguide. Proc. Natl Acad. Sci. USA 113, 10507–10512 (2016).

    CAS  PubMed  Article  Google Scholar 

  144. 144

    Zhong, X. Energy transfer between spatially separated entangled molecules. Angew. Chem. Int. Ed. (2017).

  145. 145

    Coles, D., et al. A nanophotonic structure containing living photosynthetic bacteria. Small 13, 1701777 (2017).

    Article  CAS  Google Scholar 

  146. 146

    Blanchet, V., Zgierski, M. Z., Seideman, T. & Stolow, A. Discerning vibronic molecular dynamics using time-resolved photoelectron spectroscopy. Nature 401, 52–54 (1999).

    CAS  Article  Google Scholar 

  147. 147

    Tavernelli, I. Nonadiabatic molecular dynamics simulations: synergies between theory and experiments. Acc. Chem. Res. 48, 792–800 (2015).

    CAS  PubMed  Article  Google Scholar 

  148. 148

    Shalabney, A., et al. Coherent coupling of molecular resonators with a microcavity mode. Nat. Commun. 6, 5981 (2015).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  149. 149

    Shalabney, A. et al. Enhanced Raman scattering from vibro-polariton hybrid states. Angew. Chem. Int. Ed. 54, 7971–7975 (2015).

    CAS  Article  Google Scholar 

  150. 150

    Thomas, A. et al. Ground-state chemical reactivity under vibrational coupling to the vacuum electromagnetic field. Angew. Chem. Int. Ed. 55, 11462–11466 (2016).

    CAS  Article  Google Scholar 

  151. 151

    Wagner, R. E., Su, Q. & Grobe, R. Computational renormalization scheme for quantum field theories. Phys. Rev. A 88, 012113 (2013).

    Article  CAS  Google Scholar 

  152. 152

    Dicke, R. H., Coherence in spontaneous radiation processes. Phys. Rev. 93, 99–110 (1954).

    CAS  Article  Google Scholar 

  153. 153

    Scheibner, M. et al. Superradiance of quantum dots, Nat. Phys. 3, 106–110 (2007).

    CAS  Article  Google Scholar 

  154. 154

    Chang, D. E., Vuletic´, V. & Lukin, M. D. Quantum nonlinear optics–photon by photon. Nat. Photon. 8, 685–694 (2014).

    CAS  Article  Google Scholar 

  155. 155

    Flick, J., Appel, H., Ruggenthaler, M. & Rubio, A. Cavity Born–Oppenheimer approximation for correlated electron–nuclear–photon systems. J. Chem. Theory Comput. 13, 1616–1625 (2017).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  156. 156

    Chikkaraddy, R. et al. Single-molecule strong coupling at room temperature in plasmonic nanocavities. Nature 535, 127–130 (2016).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  157. 157

    Galego, J., Garcia-Vidal, F. J. & Feist, J. Suppressing photochemical reactions with quantized light fields. Nat. Commun. 7, 13841 (2016).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  158. 158

    Ficek, Z. & Drummond, P. D. Nonclassical excitation in spectroscopy with squeezed light. Phys. Today 50, 34 (1997).

    CAS  Article  Google Scholar 

  159. 159

    Matsukevich, D. N. & Kuzmich, A. Quantum state transfer between matter and light. Science 306, 663–666 (2004).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  160. 160

    Kippenberg, T. J. & Vahala, K. J. Cavity optomechanics: back-action at the mesoscale. Science 321, 1172–1176 (2008).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  161. 161

    Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014).

    Article  Google Scholar 

  162. 162

    Andersen, M. L., Stobbe, S., Sørensen, A. S. & Lodahl, P. Strongly modified plasmon–matter interaction with mesoscopic quantum emitters. Nat. Phys. 7, 215–218 (2011).

    CAS  Article  Google Scholar 

  163. 163

    Fernández-Domínguez, A. I., GarcíaVidal, F. J. & Martín-Moreno, L. Unrelenting plasmons. Nat. Photon. 11, 8–10 (2017).

    Article  CAS  Google Scholar 

  164. 164

    Sukharev, M. & Nitzan, A. Optics of exciton–plasmon nanomaterials. J. Phys. Condens. Matter 29, 443003 (2017).

    PubMed  Article  Google Scholar 

  165. 165

    Yamamoto, Y. S., Ozaki, Y. & Itoh, T. Recent progress and frontiers in the electromagnetic mechanism of surface-enhanced Raman scattering. J. Photochem. Photobiol. C Photochem. Rev. 21, 81–104 (2014).

    CAS  Article  Google Scholar 

  166. 166

    Hell, S. W. Nanoscopy with focused light. Annalen Physik 527, 423–445 (2015).

    CAS  Article  Google Scholar 

  167. 167

    Maier, S. A. in Photonics Society Summer Topical Meeting Series, 2010 IEEE 66–67 (Playa del Carmen, 2010).

    Book  Google Scholar 

  168. 168

    Ludwig, A. et al. Breakdown of the dipole approximation in strong-field ionization. Phys. Rev. Lett. 113, 243001 (2014).

    CAS  PubMed  Article  Google Scholar 

  169. 169

    Tang, Y. & Cohen, A. E. Enhanced enantioselectivity in excitation of chiral molecules by superchiral light. Science 332, 333–336 (2011).

    CAS  PubMed  Article  PubMed Central  Google Scholar 

  170. 170

    Schmiegelow, C. T. et al. Transfer of optical orbital angular momentum to a bound electron. Nat. Commun. 7, 12998 (2016).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  171. 171

    Taminiau, T. H., Karaveli, S., Van Hulst, N. F. & Zia, R. Quantifying the magnetic nature of light emission. Nat. Commun. 3, 979 (2012).

    PubMed  Article  CAS  Google Scholar 

  172. 172

    Lindle, D. W. & Hemmers, O. Breakdown of the dipole approximation in soft-x-ray photoemission. J. Electron. Spectrosc. Related Phenomena 100, 297–311 (1999).

    CAS  Article  Google Scholar 

  173. 173

    Klimchitskaya, G. L., Mohideen, U. & Mostepanenko, V. M. The Casimir force between real materials: experiment and theory. Rev. Mod. Phys. 81, 1827 (2009).

    Article  Google Scholar 

  174. 174

    Derezinski, J. & Gérard, C. Mathematics of Quantization and Quantum Fields (Cambridge Univ. Press, 2013).

    Book  Google Scholar 

  175. 175

    Thirring, W. Quantum Mathematical Physics: Atoms, Molecules and Large (Springer Science & Business Media, Dordrecht, Netherlands, 2013).

    Google Scholar 

  176. 176

    Giesbertz, K. J. H. & Ruggenthaler, C. One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures. Preprint at https://arxiv.org/abs/1710.08805 (2017).

  177. 177

    European X-ray Free-Electron Laser. The European XFEL in international comparison. European XFELhttps://www.xfel.eu/facility/comparison/index_eng.html (2018).

  178. 178

    Bressler, C. & Chergui, M. Ultrafast x-ray absorption spectroscopy. Chem. Rev. 104, 1781–1812 (2004).

    CAS  PubMed  Article  Google Scholar 

  179. 179

    Chen, L. X., Zhang, X. & Shelby, M. L. Recent advances on ultrafast x-ray spectroscopy in the chemical sciences. Chem. Sci. 5, 4136–4152 (2014).

    CAS  Article  Google Scholar 

  180. 180

    Smith, J. W. & Saykally, R. J. Soft x-ray absorption spectroscopy of liquids and solutions. Chem. Rev. 117, 13909–13934 (2017).

    CAS  PubMed  Article  Google Scholar 

  181. 181

    Schiff, L. I. Quantum Mechanics (McGraw-Hill, 1949).

    Google Scholar 

  182. 182

    Wacker, O.-J., Kümmel, R. & Gross, E. K. U. Time-dependent density-functional theory for superconductors. Phys. Rev. Lett. 73, 2915 (1994).

    CAS  PubMed  Article  Google Scholar 

  183. 183

    Vignale, G. & Rasolt, M. Density-functional theory in strong magnetic fields. Phys. Rev. Lett. 59, 2360 (1987).

    CAS  PubMed  Article  Google Scholar 

  184. 184

    Vignale, G. Mapping from current densities to vector potentials in time-dependent current density functional theory. Phys. Rev. B 70, 201102 (2004).

    Article  CAS  Google Scholar 

  185. 185

    Rajagopal, A. K. Time-dependent functional theory of coupled electron and electromagnetic fields in condensed-matter systems. Phys. Rev. A 50, 3759–3765 (1994).

    CAS  PubMed  Article  Google Scholar 

  186. 186

    Ruggenthaler, M., Mackenroth, F. & Bauer, D. Time-dependent Kohn–Sham approach to quantum electrodynamics. Phys. Rev. A 84, 042107 (2011).

    Article  CAS  Google Scholar 

  187. 187

    Tokatly, I. V. Time-dependent density functional theory for many-electron systems interacting with cavity photons. Phys. Rev. Lett. 110, 233001 (2013).

    CAS  PubMed  Article  Google Scholar 

  188. 188

    Ruggenthaler, M. Ground-state quantum-electrodynamical density-functional theory. Preprint at https://arxiv.org/abs/1509.01417 (2015).

  189. 189

    Strubbe, D. A., Lehtovaara, L., Rubio, A., Marques, M. A. L. & Louie, S. G. in Fundamentals of Time-Dependent Density Functional Theory (eds Marques, M. A. L., Maitra, N. T., Nogueira, F. M. S. Gross, E. K. U. & Rubio, A. ) 139–166 (Springer, Berlin, Heidelberg, 2012).

    Book  Google Scholar 

  190. 190

    Kleemann, M.-E. et al. Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature. Nature 8, 1296 (2017).

    Google Scholar 

  191. 191

    Schlawin, F. & Mukamel, S. Two-photon spectroscopy of excitons with entangled photons. J. Chem. Phys. 139, 244110 (2013).

    PubMed  Article  CAS  Google Scholar 

  192. 192

    Dorfman, K. E., Schlawin, F. & Mukamel, S. Stimulated Raman spectroscopy with entangled light: Enhanced resolution and path-way selection. J. Phys. Chem. Lett. 5, 2843–2849 (2014).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  193. 193

    Flick, J., Schaefer, C., Ruggenthaler, M., Appel, H. & Rubio, A. Ab-initio optimized effective potentials for real molecules in optical cavities: photon contributions to the molecular ground state. ACS Photon.https://doi.org/10.1021/acsphotonics.7b01279 (2018).

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  194. 194

    Kummel, S., Brack, M. & Reinhard, P.-G. Ionic and electronic structure of sodium clusters up to N = 59. Phys. Rev. B 62, 7602 (2000).

    CAS  Article  Google Scholar 

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Acknowledgements

The authors acknowledge financial support from the European Research Council (ERC- 2015-AdG-694097). The authors thank Arunangshu Debnath, Klaas Giesbertz, Christian Schäfer and Martin Ruggenthaler for fruitful discussions.

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Correspondence to Michael Ruggenthaler, Nicolas Tancogne-Dejean, Johannes Flick, Heiko Appel or Angel Rubio.

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Glossary

Polariton

A polariton is a bosonic quasi-particle formed by an excitation, such as an exciton or plasmon coupled (‘dressed’) with photons.

Polaritonic chemistry

Molecular systems strongly coupled to light show the emergence of polaritonic states, which can change the chemical properties of the molecules.

Electromagnetic vacuum

If all harmonic oscillators of the quantized electromagnetic field are in their ground state, the number of photons is zero, corresponding to the bare electromagnetic vacuum. However, when coupled to a matter system, the vacuum fluctuations induce changes in the matter system, which lead to the Lamb shift. This coupling forms the basis of vacuum-mediated (‘dark’) polaritonic chemistry.

Pauli Hamiltonian

The Pauli Hamiltonian comprises the standard Schrödinger Hamiltonian and the Pauli (Stern–Gerlach) term σ ·B(r), which describes the coupling between the electron spin (characterized by a vector of the usual Pauli matrices σ) and the magnetic field B(r).

Spinor representation

To represent the spin of a quantum particle a vector of wavefunctions can be used, in which each entry corresponds to a specific spin state of the particle. A spin one-half particle has two such entries, that is, spin up and spin down.

External fields

Fields that are externally controlled, fixed perturbations, such as pump and probe pulses or in the clamped nuclei approximation the nuclear attractive potential, whose sources are not included in theoretical description. These fields are usually classical but can also be of quantum nature.

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Ruggenthaler, M., Tancogne-Dejean, N., Flick, J. et al. From a quantum-electrodynamical light–matter description to novel spectroscopies. Nat Rev Chem 2, 0118 (2018). https://doi.org/10.1038/s41570-018-0118

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