  A nonlinear interaction between photons is observed in a process that
involves charge sources. To observe this process in a vacuum, there are a
growing number of theoretical and experimental studies. This process may
contain exotic contribution from new physics beyond the Standard Model of
particle physics, and is probed by experiments using a high-power laser or a
high-field magnet, and more recently using an X-ray Free-Electron Laser (XFEL).
Here, we review the present status of our experiments testing various vacuum
processes. We describe four experiments with a focus on those using an XFEL:
(i) photon-photon scattering in the x-ray region, (ii) laser-induced
birefringence and diffraction of x rays, (iii) vacuum birefringence induced by
a high-field magnet, and (iv) a dedicated search for axion-like particles using
the magnet and x rays.
