Geometric phase assisted detection of Lorentz-invariance violation from modified dispersion at high energies

TL;DR

This paper proposes using the geometric phase of an inertial atomic detector to detect Lorentz-invariance violations caused by modified dispersion relations at high energies, potentially observable at accessible energy scales.

Contribution

It introduces a novel method leveraging geometric phase sensitivity to weak Lorentz-violating effects, enabling detection at lower energies than traditional approaches.

Findings

Geometric phase depends on detector velocity in Lorentz-violating theories.

Low-energy Lorentz violation can be detected via geometric phase shifts.

Detectable geometric phase signals are achievable below current collider rapidities.

Abstract

Many theories of quantum gravity propose Lorentz-violating dispersion relations of the form $\omega_{|\mathbf{k}|}=|\mathbf{k}|f(|\mathbf{k}|/M_\star)$, which approximately recover to the Lorentz invariance, $\omega_{|\mathbf{k}|}\approx|\mathbf{k}|$, at the energy scales much below $M_\star$. However, usually such a scale is assumed to be near the Planck scale, thus the feature of the Lorentz-violating theory is weak and its experimental test becomes extremely challenging. Since the geometric phase (GP) is of accumulative and sensitive nature to weak effects, here we explore the GP acquired by an inertial atomic detector that is coupled to a quantum field with this kind of Lorentz-violating dispersion. We show that for the Lorentz-violating field theory case the GP depends on the velocity of the detector, which is quite different from the Lorentz symmetry case where the GP is independent of the detector's velocity. In particular, we show that the GP may present a drastic low-energy Lorentz violation for any $f$ that dips below unity somewhere. We apply our analysis to detecting the polymer quantization motivated by loop quantum gravity, and show the detector acquires an experimentally detectable GP with the assist of detector's velocity that below current ion collider rapidities. Furthermore, the accumulative nature of GP might facilitate the relevant detection significantly.