Fluctuations of atomic energy levels due to axion dark matter

TL;DR

This paper explores how axion dark matter causes atomic energy level fluctuations, proposing methods to detect these effects with atomic and nuclear clocks, and setting new limits on axion properties.

Contribution

It introduces a novel approach to search for axion dark matter using atomic clock frequency fluctuations and reinterprets existing experimental data to set new axion coupling limits.

Findings

New limits on axion coupling constant $f_a$ for specific mass range

Demonstrates potential of atomic and nuclear clocks to detect axion-induced energy shifts

Proposes a method to determine axion mass if dark matter signal is observed

Abstract

The amplitude of the pseudoscalar (axion) or scalar field fluctuates on a time scale of order of million field oscillation periods which is a typical coherence time in the virialized axion galactic dark matter halo model. This causes fluctuations of frequencies of atomic clocks on the same time scale. We show that this effect may be employed to search for the axion and scalar field dark matter with atomic and nuclear clocks. We re-purpose the results of the atomic clocks experiments comparing the variations of frequencies of hyperfine transitions in Rb and Cs atoms as well as in hydrogen atom vs cavity frequency fluctuations, and extract new limits on the axion coupling constant $f_a$ for masses in the range $2.4\times 10^{-17}\text{ eV}\lesssim m \lesssim 10^{-13}\text{ eV}$. We also show that similar energy shifts arise in the second-order perturbation theory with linear in the pseudoscalar field interaction. These shifts may be potentially measured with nuclear clocks based on the low-energy transition in $^{229}$Th nucleus. We propose a procedure which could, in principle, help determine the axion mass if the axion dark matter signal is present in experimental data sets.