Quantum gravity corrections to the spontaneous excitation of an accelerated atom interacting with a quantum scalar field

TL;DR

This paper investigates how the Generalized Uncertainty Principle (GUP) alters spontaneous atomic processes for a two-level atom coupled to a real massless scalar field, using the Dalibard–Dupont‑Roc/Cohen‑Tannoudji (DDC) formalism. By adopting the Kempf GUP and deriving the corresponding Green's functions, it computes the GUP-induced corrections to vacuum fluctuations and radiation reaction for inertial, uniformly accelerated, and uniform circular motions, yielding analytic expressions for the transition rates and an effective temperature where applicable. The key finding is that GUP introduces β-dependent corrections that can be dramatically amplified by acceleration, while preserving qualitative features such as ground-state stability for inertial motion and the Unruh-temperature behavior for linear acceleration; circular motion, however, exhibits nonthermal, acceleration‑dependent GUP effects that can significantly enhance transition rates. These results suggest that atomic systems in high-acceleration regimes could serve as laboratory probes of quantum-gravity corrections, and motivate future work with multilevel atoms and electromagnetic fields. $A_{ ext{up}}$ and $A_{ ext{down}}$ acquire terms such as $\beta a^2$, $\beta \omega_0^2$, and $\beta a^3$, reflecting the interplay between GUP and noninertial motion across different trajectories.

Abstract

The Generalized Uncertainty Principle (GUP) extends the Heisenberg Uncertainty Principle (HUP) by suggesting a minimum observable scale that includes the effects of quantum gravity, which is supposed to potentially result in observable effects far below the Planck energy scale, providing us the opportunity to explore the theory of quantum gravity through physical processes at low energy scale. In present work, we study the corrections induced by the GUP to the spontaneous radiation properties of a two-level atom interacting with a real massless scalar quantum field based on the DDC formalism. The GUP alters the correlation function of the scalar field, consequently affecting the radiative properties of atoms. We calculate the rate of change in the mean atomic energy for an atom undergoing inertial motion, uniform acceleration, and uniform circular motion. We show that the GUP can modify the spontaneous emission rate of an excited-state atom in inertial motion; however, it does not alter the stability of the ground-state atom in vacuum. For an atom in uniformly accelerated and uniformly circular motions, the GUP can change both its spontaneous emission and excitation rates; moreover, the corrections caused by the GUP contains the terms proportional to $βa^2$ or $βa^3$, suggesting that the proper acceleration $a$ of an atom in non-inertial motions could significantly amplify the effect of the GUP on the spontaneous transition rates of the atom.

Figures (4)

• Figure 1: The behaviors of $\frac{A^{\mathrm{GUP}}_ \uparrow}{\gamma_{0}}$ (Left) and $\frac{A^{\mathrm{GUP}}_ \downarrow}{\gamma_{0}}$ (Right) for a uniformly accelerating atom with the increase of $\frac{a}{\omega _0}$. The solid, dashed, and dot-dashed lines refer to the cases for $\beta\omega _0^2=0.1$, $0.2$ and $0.3$, respectively.
• Figure 2: The GUP-modified effective temperature $T_{\mathrm{eff}}$ for the two-level atom undergoing the uniform circular motion as a function of the atomic acceleration (Left) and as a function of GUP parameter $\beta$ (Right).
• Figure 3: The behavior of $\frac{A^{\mathrm{GUP}}_ \uparrow}{\gamma_{0}}$ (Left) and $\frac{A^{\mathrm{GUP}}_ \downarrow}{\gamma_{0}}$ (Right) for a uniformly circulating atom with the growth of $\frac{a}{\omega _0}$. The solid, dashed, and dot-dashed lines refer to the cases for $\beta\omega _0^2=0.1$, $0.2$ and $0.3$, respectively.
• Figure A1: The Poles and integration paths.