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.
Highlights
The interaction of light with matter involves the correlated dynamics of photons, electrons, and nuclei
We have introduced an extension of the exact– factorization approach, originally derived for coupled electron-nuclear systems, to light-matter systems in the non- relativistic limit within the dipole approximation
We have presented different possible choices for the factorization but in this work have focussed on the one where the marginal is chosen as the photonic system and the matter system is conditionally-dependent on this
Summary
The interaction of light with matter involves the correlated dynamics of photons, electrons, and nuclei. Rapid experimental and theoretical advances have drawn attention to fascinating phenomena that depend on the quantization of the light field in its interaction with matter This includes few-photon coherent nonlinear optics with single molecules [9], direct experimental sampling of electric-field vacuum fluctuations [10,11], multiple Rabi splittings under ultrastrong vibrational coupling [12], exciton-polariton condensates [13,14], polaritonically enhanced superconductivity in cavities [15], or frustrated polaritons [16] among others. Coupling to matter within the dipole approximation where the coupling operator is linear in the photonic variable preserves the quadratic nature of the Hamiltonian, and one might think that again a classical Wigner treatment would be exact.
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