GUP Corrections to the Jaynes-Cummings Model

TL;DR

This paper explores how the Generalized Uncertainty Principle modifies the Jaynes-Cummings Model, providing analytical solutions and identifying potential observable effects of quantum gravity in quantum optical systems.

Contribution

It analytically derives GUP corrections to the Jaynes-Cummings Model and predicts measurable signatures of quantum gravity in optical experiments.

Findings

Derived corrected Rabi frequency under GUP

Predicted photon-added coherent states due to dispersive interaction

Identified changes in the Wigner function as quantum gravity signatures

Abstract

The Generalized Uncertainty Principle (GUP) is a modification of Heisenberg's Uncertainty Principle predicted by several theories of quantum gravity. In this work, we compute GUP corrections to the well-known Jaynes-Cummings Model (JCM) with the aim of eventually observing quantum gravity effects in quantum optical systems. To this end, we first analytically solve the GUP-corrected JCM and obtain the corrected Rabi frequency in the quadratic GUP model. Following this, we calculate the effects of a dispersive interaction with light in a coherent state and show that this gives rise to photon-added coherent states that were first studied by Agarwal and Tara in 1991. The latter causes a change in the value of the Wigner function, which if detected in the laboratory, would in effect be a signature of quantum gravity.