A common perception is that laboratory tests of fundamental physics necessarily require large particle colliders. However, thanks to the development of ultra high-intensity optical lasers and 4th generation light sources, new approaches are now possible that exploit the simultaneous interactions of multiple photons with matter and vacua via quantum field fluctuations. In this proposal, we will employ these high-field non-perturbative quantum optics processes to search for new fundamental particles. Since accelerator-based searches have not yet found new physics at high energies, ultra high-intensity optical lasers and 4th generation light sources offer a novel complementary approach for searches at optical and X-ray energies. This proposal addresses an important question in fundamental physics by developing a laboratory search for new particles beyond the Standard Model called axions. Our work will be able to probe axion masses bigger than a few eV up to a keV - a region that is currently inaccessible to laboratory searches. In the eV-keV mass range. the searches proposed here are the only model-independent ones, meaning that the experiments have full control over both the production and reconversion of axions within the same apparatus - without the need to assume that axions are produced by astrophysical objects (such as the Sun) or constitute a large fraction of the dark matter.