Photon propagation in a cold axion condensate

We discuss some striking properties of photons propagating in a cold axion condensate oscillating coherently in time with a frequency $1/m_a$. Three effects are discussed in this contribution: (a) due to the time dependence of the background, photons moving in the cold axion background have no definite energies and some momenta are not accessible to them. (b) we investigate the combined influence of a magnetic field and the cold axion background and propose a possible interferometric experiment to detect the latter. (c) if the axion condensate has a space dependence, the photon refraction index is modified in the medium, possibly leading to total reflection at the interface with the ordinary vacuum.