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Communications in Mathematical Physics

Resonant decay of a two state atom interacting with a massless non-relativistic quantised scalar field

Christopher King

Published Oct 1, 1994• 14 citations
Publisher
DOI
10.1007/bf02099424

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Abstract We consider a two-atom system uniformly moving through a circular ring at an ultra-relativistic speed and weakly interacting with the common quantum fields. Two kinds of fields are introduced here: a massive free scalar field and electromagnetic (EM) vector fields. The vacuum fluctuations of the quantum fields give rise to the resonance Casimir–Polder interaction (RCPI) in the system. Using the quantum master equation formalism, we calculate the second-order energy shift of the entangled states of the system. We find two major aspects of RCPI in a circular trajectory. The first one is the presence of the centripetal acceleration, which gives rise to non-thermality in the system, and secondly, due to the interaction with the above fields, the energy shift for RCPI is retarded in comparison with the massless scalar field. The retardation effect can die out by decreasing the centripetal acceleration and increasing the Zeeman frequency of the atoms. We also show that this phenomenon can be observed via the polarization transfer technique. The coherence time for the polarization transfer is calculated, which is different for the different fields.
Using spacetime Gaussian test functions, we find closed-form expressions for the smeared Wightman function, Feynman propagator, retarded and advanced Green's functions, causal propagator, and symmetric propagator of a massless scalar field in the vacuum of Minkowski spacetime. We apply our results to localized quantum systems that interact with a quantum field in Gaussian spacetime regions and study different relativistic quantum information protocols. In the protocol of entanglement harvesting, we find a closed-form expression for the entanglement that can be acquired by probes that interact in Gaussian spacetime regions and obtain asymptotic results for the protocol. We also revisit the case of two gapless detectors and show that the detectors can become entangled if there is two-way signalling between their interaction regions, providing closed-form expressions for the detectors' final state.