Dispersive vacuum as a decoherence amplifier of an Unruh-DeWitt detector

TL;DR

This paper explores how a dispersive vacuum, modeled through modified dispersion relations from theories like doubly special relativity and Hořava-Lifshitz gravity, accelerates decoherence in an Unruh-DeWitt detector, especially at high accelerations and interaction times.

Contribution

It demonstrates that dispersive vacuum effects, derived from advanced quantum gravity theories, significantly enhance decoherence in a quantum detector, revealing observable consequences of spacetime discreteness.

Findings

Decoherence occurs faster with increased vacuum dispersion.

Higher dispersion order amplifies quantum fluctuations affecting decoherence.

Dispersive vacuum effects are more pronounced at high accelerations.

Abstract

Recently, interest has been growing in studies on discrete or "pixelated" space-time that, through modifications in the dispersion relation, can treat the vacuum as a dispersive medium. Discrete spacetime considers that spacetime has a cellular structure on the order of the Planck length, and if this is true we should certainly have observable effects. In this paper, we investigated the effects caused by the dispersive vacuum on the decoherence process of an Unruh-DeWitt detector, our setup consists of a uniformly accelerated detector, initially in a qubit state, which interacts with a massless scalar field during a time interval finite. We use dispersion relations drawn from doubly special relativity and Ho\v{r}ava-Lifshitz gravity, with these modifications the vacuum becomes dispersive and has a corresponding refractive index. We calculate the probability transition rates, the probability of finding the detector in the ground state, and the quantum coherence variation. Our results indicate that the decoherence process occurs more quickly in cases with changes in the dispersion relation in the regime of high accelerations and interaction time. Additionally, the decoherence increases as the vacuum becomes more dispersive due to the increase in the order of modification in the dispersion relation, and this happens because the dispersive vacuum amplifies the effects of quantum fluctuations that are captured by the detector when interacting with the field.