^{1}

^{,*}

^{2}

^{,†}

^{3,4}

^{,‡}

^{5,6}

^{,§}

^{3}.

Axionlike particles (ALPs) with couplings to electromagnetism have long been postulated as extensions to the standard model. String theory predicts an “axiverse” of many light axions, some of which may make up the dark matter in the Universe and/or solve the strong

Axions are well motivated new particles that have been proposed as a solution to the strong

There are several general approaches for finding ALPs, roughly analogous to the multipronged approach of direct detection, indirect detection, and collider production for WIMP DM. If the ALP makes up the DM of the Universe, it may be detected in the laboratory by converting ALPs to electromagnetic energy (see Refs.

In this Letter, we propose a new experiment along the lines of an LSW experiment that utilizes light-by-light scattering mediated by

Famously, loop contributions from virtual electrons will also induce such nonlinearities in pure quantum electrodynamics (QED), which are parametrized by the Euler-Heisenberg (EH) Lagrangian

Comparing Eqs.

Schematic of our proposed experiment, adapted from Ref.

While it was demonstrated in Ref.

Unless otherwise specified, we now restrict to the case of a single ALP,

Suppose the cavity is pumped at resonant frequencies

The ALP-dependent terms on the right-hand side of Eqs.

To estimate the size of the signal, we normalize the pump modes such that

In the limit

In the limit

As an example, consider a right cylindrical cavity with

To measure the signal, we imagine a filtering geometry as suggested in Ref.

Our expected sensitivity to

For a fixed choice of modes and cavity size (hence fixed

At 1.5 K, the thermal noise in the signal mode is

We first consider the case where the injected pump bandwidth is comparable to the cavity bandwidth,

One could also pump the cavity with a bandwidth narrower than the cavity itself, for example, by locking the pump tones to an atomic clock. Taking

Projected sensitivities of our proposal (approximations for

For phase 2, we assume the cylindrical cavity geometry from phase 1, but with

Naively, the sensitivity of this proposal to probe ALPs becomes limited when

Revisiting the axiverse scenario, suppose that

A. H., Y. K., and Y. S. thank Ben Safdi and the University of Michigan Slack channel for facilitating discussion in the early stages of this work. Y. K. thanks Prateek Agrawal, M. C. David Marsh, and the participants of the workshop “Axions in Stockholm—Reloaded” for discussions about the axiverse, and James Halverson and Cody Long for discussions about axions in string compactifications. We thank Daniel Bowring, Fritz Caspers, Aaron Chou, Anna Grassellino, Roni Harnik, Kent Irwin, Akira Miyazaki, Jonathan Ouellet, Sam Posen, Alexander Romanenko, and Slava Yakovlev for enlightening discussions regarding cavity design and photon readout. We thank Junwu Huang, Gilad Perez and Jesse Thaler for helpful comments, and Lindley Winslow for support in the early stages of this project. A. H. is supported in part by the NSF under Grant No. PHY-1620074 and by the Maryland Center for Fundamental Physics (MCFP). The work of Z. B. is supported by the National Science Foundation under Grant No. NSF PHY-1806440. This work was supported in part by the Kavli Institute for Cosmological Physics at the University of Chicago through an endowment from the Kavli Foundation and its founder Fred Kavli.