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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


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.


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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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All authors contributed equally to the preparation of this manuscript.

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

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PowerPoint slides



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).

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