Probing Planck Scale Spacetime By Cavity Opto-Atomic $^{87}$Rb Interferometry

TL;DR

This paper proposes a novel atomic interferometry experiment using $^{87}$Rb in a high finesse optical cavity to test quantum gravity effects, specifically the generalized uncertainty principle, at low energies.

Contribution

It introduces a new cavity opto-atomic interferometry setup with micro-electro-opto-mechanical systems to probe Planck scale quantum spacetime features.

Findings

Set upper bounds on GUP parameters using $^{87}$Rb atomic interferometry.

Achieved tight constraints on the dimensionless GUP parameter, close to unity.

Demonstrated feasibility of low-energy quantum gravity phenomenology experiments.

Abstract

The project of \emph{"quantum spacetime phenomenology"} focuses on searching pragmatically for the Planck scale quantum features of spacetime. Among these features is the existence of a characteristic length scale addressed commonly by effective approaches to quantum gravity (QG). This characteristic length scale could be realized, for instance and simply, by generalizing the standard Heisenberg uncertainty principle (HUP) to a \emph{"generalized uncertainty principle"} (GUP). While usually it is expected that phenomena belonging to the realm of QG are essentially probable solely at the so-called Planck energy, here we show how a GUP proposal containing the most general modification of coordinate representation of the momentum operator could be probed by a \emph{"cold atomic ensemble recoil experiment"} (CARE) as a low energy quantum system. This proposed atomic interferometer setup has advantages over the conventional architectures owing to the enclosure in a high finesse optical cavity which is supported by a new class of low power consumption integrated devices known as \emph{"micro-electro-opto-mechanical systems"} (MEOMS). The proposed system comprises of a micro mechanical oscillator instead of spherical confocal mirrors as one of the components of high finesse optical cavity. In the framework of a bottom-up QG phenomenological viewpoint and by taking into account the measurement accuracy realized for the fine structure constant (FSC) from the Rubidium ($^{87}$Rb) CARE, we set some constraints as upper bounds on the characteristic parameters of the underlying GUP. In the case of superposition of the possible GUP modification terms, we managed to set a tight constraint as $0.999978<\lambda_0<1.00002$ for the dimensionless characteristic parameter.