Transition probabilities for a Rydberg atom in the field of a gravitational wave

TL;DR

This paper explores the theoretical potential of using highly excited Rydberg atoms to detect gravitational waves on Earth by calculating transition probabilities and absorption cross sections, highlighting fundamental constants involved.

Contribution

It introduces a theoretical framework for gravitational wave detection using Rydberg atoms with high principal quantum numbers, emphasizing the role of fundamental constants.

Findings

Transition probabilities increase with quantum number and interaction strength.

Absorption cross section depends only on fundamental constants, not particle properties.

Estimated transition rates suggest potential detectability with realistic gravitational sources.

Abstract

The possibility of an atomic detection of gravitational waves on earth is considered. The combination of extremely high lifetimes and resulting small radiative transition probabilities with rapidly growing interaction strength for Rydberg atoms having principal quantum numbers in a region $10^4\ldots 10^5$ might result in transition probabilities which are high enough to open up such a possibility. Transition probabilities and absorption cross sections are calculated as a function of the relevant quantum numbers of a highly excited electron. The orders of magnitude for the transition rate are evaluated for a realistic source of gravitational radiation. It is shown that no specific particle property enters the expression for the absorption cross section for gravitational waves. The only fundamental constant contained in this cross section is, apart from the fine structure constant $\alpha$, the Planck length $L^*=(\hbar G /c^3)^{1/2}$.