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Journal of Physics B Atomic Molecular and Optical Physics

Self-consistent radiative backaction in dispersion interactions: a minimal mQED model

Johannes Fiedler

Published May 5, 2026• 1 citation
Publisher

Abstract

Abstract Dispersion interactions are usually derived assuming fixed internal spectra of the interacting quantum systems. Here, we relax this assumption and study how self-consistent electromagnetic backaction modifies van der Waals interactions when excitation energies and transition dipole moments are allowed to respond to the interaction itself. Within a macroscopic quantum electrodynamics framework, we formulate a self-consistent treatment that includes both self-energy corrections and mutual backaction. Using a minimal three-level model, we show that, while one-sided self-energy effects are short-ranged, fully self-consistent backaction can lead to substantial, long-ranged modifications of the effective van der Waals interaction. Our analysis demonstrates that these effects originate from the coherent accumulation of repeated photon-mediated scattering processes. The results highlight limitations of perturbative dispersion theories with fixed spectra and identify few-level systems as a clean platform for studying backaction in dispersion forces.

DOI
10.1088/1361-6455/ae68af

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Abstract Dispersion interactions are usually derived assuming fixed internal spectra of the interacting quantum systems. Here, we relax this assumption and study how self-consistent electromagnetic backaction modifies van der Waals interactions when excitation energies and transition dipole moments are allowed to respond to the interaction itself. Within a macroscopic quantum electrodynamics framework, we formulate a self-consistent treatment that includes both self-energy corrections and mutual backaction. Using a minimal three-level model, we show that, while one-sided self-energy effects are short-ranged, fully self-consistent backaction can lead to substantial, long-ranged modifications of the effective van der Waals interaction. Our analysis demonstrates that these effects originate from the coherent accumulation of repeated photon-mediated scattering processes. The results highlight limitations of perturbative dispersion theories with fixed spectra and identify few-level systems as a clean platform for studying backaction in dispersion forces.
Dispersion interactions are usually derived assuming fixed internal spectra of the interacting quantum systems. Here, we relax this assumption and study how self-consistent electromagnetic backaction modifies van der Waals interactions when excitation energies and transition dipole moments are allowed to respond to the interaction itself. Within a macroscopic quantum electrodynamics framework, we formulate a self-consistent treatment that includes both self-energy corrections and mutual backaction. Using a minimal three-level model, we show that, while one-sided self-energy effects are short-ranged, fully self-consistent backaction can lead to substantial, long-ranged modifications of the effective van der Waals interaction. Our analysis demonstrates that these effects originate from the coherent accumulation of repeated photon-mediated scattering processes. The results highlight limitations of perturbative dispersion theories with fixed spectra and identify few-level systems as a clean platform for studying backaction in dispersion forces.
Macroscopic quantum electrodynamics (MQED) provides a unified framework for describing quantum electromagnetic fields in arbitrary macroscopic environments. Central to this theory is the field correlation, which governs both radiative (e.g., Lamb shifts and the Purcell effect) and mechanical phenomena, such as van der Waals and Casimir forces. In this tutorial, we provide an overview of MQED and its extension to active media, highlighting fluctuation-induced forces as manifestations of gain-modified field correlations.
The van der Waals interaction between neutral atoms is typically studied using stationary perturbation theory for the short-distance (London) limit, while long-distance (Casimir-Polder) results are usually derived via semiclassical, time-dependent approaches. Here, we demonstrate that reformulating stationary perturbation theory calculations in terms of time-ordered correlation functions significantly simplifies the mathematical treatment. This reformulation is particularly advantageous for higher-order calculations required in the long-distance regime, where retardation effects become important. Our approach provides a unified framework connecting both limiting cases, and is intended as a bridge between advanced quantum mechanics and field-theoretic treatments of dispersion forces, suitable for graduate-level courses or specialized readers.
Abstract We consider the resonant van der Waals (vdW) interaction between two correlated identical two-level atoms (at least one of which being excited) within the framework of macroscopic cavity quantum electrodynamics in linear, dispersing and absorbing media. The interaction of both atoms with the body-assisted electromagnetic field of the cavity is assumed to be strong. Our time-independent evaluation is based on an extended Jaynes–Cummings model. For a system prepared in a superposition of its dressed states, we derive the general form of the vdW forces, using a Lorentzian single-mode approximation. We demonstrate the applicability of this approach by considering the case of a planar cavity and showing the position dependence of Rabi oscillations. We also show that in the limiting case of weak coupling, our results reproduce the perturbative ones for the case where the field is initially in vacuum state while the atomic state is in a superposition of two correlated states sharing one excitation.
van der Waals interactions, as a result of the exchange of photons between particles, can be altered by modifying the environment through which these photons propagate. As a consequence, phenomena such as the Rydberg blockade mechanism between highly excited atoms or excitons can be controlled by adding reflecting surfaces. We provide the quantum electrodynamic framework for the van der Waals interaction in the nonretarded limit that is relevant for long-wavelength transitions, such as those between Rydberg systems, and show its intimate connection with common static dipole-dipole interactions, thereby providing a generalization to include macroscopic bodies.
In this article, we review the principles of macroscopic quantum electrodynamics and discuss a variety of applications of this theory to medium-assisted atom-field coupling and dispersion forces. The theory generalises the standard mode expansion of the electromagnetic fields in free space to allow for the presence of absorbing bodies. We show that macroscopic quantum electrodynamics provides the link between isolated atomic systems and magnetoelectric bodies, and serves as an important tool for the understanding of surface-assisted atomic relaxation effects and the intimately connected position-dependent energy shifts which give rise to Casimir-Polder and van der Waals forces.