Causality and Atomic Dynamics in the Fermi Problem

J. Ben-Benjamin

Peter Holland

Erez Zohar, Benni Reznik

The Fermi two-atom problem illustrates an apparent causality violation in quantum field theory that has to do with the nature of the built-in correlations in the vacuum. It has been a constant subject of theoretical debate and discussion in 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 have prevented the observation of the predicted effect. In this 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’ and correction in the scenario that involves ‘dressed’ atoms. Finally, we show that, in principle, the Fermi effect can be detected using trapped ions.

Massimo Borrelli, Carlos Sabín, Gerardo Adesso +2 more

We present a detailed perturbative study of the dynamics of several types of atom–atom correlations in the famous Fermi problem. This is an archetypal model to study micro-causality in the quantum domain, where two atoms, one initially excited and the other prepared in its ground state, interact with the vacuum electromagnetic field. The excitation can be transferred to the second atom via a flying photon, and various kinds of quantum correlations between the two are generated during this process. Among these, prominent examples are given by entanglement, quantum discord and non-local correlations. The aim of this paper is to analyze the role of the light cone in the emergence of such correlations.

Carlos Sabín, Marco del Rey, Juan José García‐Ripoll +1 more

We propose a feasible experimental test of a 1D version of the Fermi problem using superconducting qubits. We give an explicit nonperturbative proof of strict causality in this model, showing that the probability of excitation of a two-level artificial atom with a dipolar coupling to a quantum field is completely independent of the other qubit until signals from it may arrive. We explain why this is in perfect agreement with the existence of nonlocal correlations and previous results which were used to claim apparent causality problems for Fermi's two-atom system.