Ultralight bosons can potentially accumulate around these supermassive black holes and form a gravitational atom-like bound state. A new way to look for the gravitational atom made of axion is through birefringence effect from the axion-photon coupling.The presence of coherently oscillating axion leads to a frequency independent oscillation to the electric vector position angle (EVPA) of the linearly polarized radiation. For a nearly face-on M87^\star*, this oscillation in the EVPA appears as a propagating wave along the photon ring. We leverage the azimuthal distribution of EVPA measured by the EHT to study the axion-photon coupling. We propose a novel differential analysis procedure to reduce the astrophysical background, and derive stringent constraints on the existence of axions in the previously unexplored mass window. One can also dissect the profile of the gravitational atom by correlating the spatial and temporal variation of the EVPAs.