Kohn-Sham Approach to Quantum Electrodynamical Density Functional Theory: Exact Time-Dependent Effective Potentials in Real Space

Proceedings Of The National Academy Of Sciences Of The United States Of America 112, 15285 - 15290 (2015)

Kohn-Sham Approach to Quantum Electrodynamical Density Functional Theory: Exact Time-Dependent Effective Potentials in Real Space

Johannes Flick,Michael Ruggenthaler,Heiko Appel, Angel Rubio

The density-functional approach to quantum electrodynamics is extending traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system which consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. While the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential which mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light, i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real-space in order to take the quantum nature of the electromagnetic field fully into account.

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http://dx.doi.org/10.1073/pnas.1518224112
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We acknowledges financial support from the European Research Council Advanced Grant DYNamo (ERC- 2010- AdG-267374), Spanish Grant (FIS2013-46159-C3-1-P), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), COST Actions CM1204 (XLIC), MP1306 (EUSpec) and the Austrian Science Fund (FWF P25739-N27).

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