The Fermi Problem in Discrete Systems

TL;DR

This paper demonstrates that the Fermi two-atom problem, which involves causality issues in quantum field theory, can be simulated in discrete systems like trapped ions, allowing for experimental investigation of the effect.

Contribution

The study introduces a simulation framework for the Fermi problem in discrete systems, enabling experimental exploration of causality violations in quantum settings.

Findings

Discrete systems can mimic the Fermi problem's causal structure

Distinguishing trivial causality effects from Fermi-related effects is feasible

Fermi effects could be observed using trapped ions

Abstract

The Fermi two-atom problem illustrates an apparent causality violation in Quantum Field Theory which has to do with the nature of the built in correlations in the vacuum. It has been a constant subject of theoretical debate and discussions during the last few decades. Nevertheless, although the issues at hand could in principle be tested experimentally, the smallness of such apparent violations of causality in Quantum Electrodynamics prevented the observation of the predicted effect. In the present paper we show that the problem can be simulated within the framework of discrete systems that can be manifested, for instance, by trapped atoms in optical lattices or trapped ions. Unlike the original continuum case, the causal structure is no longer sharp. Nevertheless, as we show, it is possible to distinguish between "trivial" effects due to "direct" causality violations, and the effects associated with Fermi's problem, even in such discrete settings. The ability to control externally the strength of the atom-field interactions, enables us also to study both the original Fermi problem with "bare atoms", as well as correction in the scenario that involves "dressed" atoms. Finally, we show that in principle, the Fermi effect can be detected using trapped ions.