Chain-mapping methods for relativistic light-matter interactions

Robert H. Jonsson1,2 and Johannes Knörzer3

1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
2Nordita, Stockholm University and KTH Royal Institute of Technology, Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden
3Institute for Theoretical Studies, ETH Zurich, 8092 Zurich, Switzerland

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The interaction between localized emitters and quantum fields, both in relativistic settings and in the case of ultra-strong couplings, requires non-perturbative methods beyond the rotating-wave approximation. In this work we employ chain-mapping methods to achieve a numerically exact treatment of the interaction between a localized emitter and a scalar quantum field. We extend the application range of these methods beyond emitter observables and apply them to study field observables. We first provide an overview of chain-mapping methods and their physical interpretation, and discuss the thermal double construction for systems coupled to thermal field states. Modelling the emitter as an Unruh-DeWitt particle detector, we then calculate the energy density emitted by a detector coupling strongly to the field. As a stimulating demonstration of the approach's potential, we calculate the radiation emitted from an accelerated detector in the Unruh effect, which is closely related to the thermal double construction as we discuss. We comment on prospects and challenges of the method.

Quantum systems coupled strongly to their environment are often challenging to treat, even with advanced numerical methods. Many such open quantum systems can be modeled by a linear coupling between the system of interest and independent, harmonic bath modes.
The paper studies this type of theoretical model and explores computational methods to study the interactions between localized emitters and quantum fields, especially in relativistic and ultra-strong coupling scenarios. Utilizing so-called chain-mapping techniques, a numerically exact treatment of the problem is achieved. The paper advances computational techniques for light-matter interactions by extending these methods to both emitter and field observables. As an intriguing demonstration, the radiation emitted by an accelerated particle detector in the Unruh effect is calculated.
In the numerical findings, the errors introduced by numerical implementations of the chain-mapping can be carefully monitored. This contributes to a rich numerical toolbox for studying strong-coupling regimes in relativistic quantum information and quantum optics.

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