Constraints on Axion-like Particles from the gamma-ray observation of the Galactic Center

High energy photons originating from the Galactic Center (GC) region have the potential to undergo significant photon-axion-like particle (ALP) oscillation effects, primarily induced by the presence of intense magnetic fields in this region. Observations conducted by imaging atmospheric Cherenkov telescopes have detected very high energy gamma-rays originating from a point source known as HESS J1745-290, situated in close proximity to the GC. This source is conjectured to be associated with the supermassive black hole Sagittarius A$^*$. The GC region contains diverse structures, including molecular clouds and non-thermal filaments, which collectively contribute to the intricate magnetic field configurations in this region. By utilizing a magnetic field model specific in the GC region, we explore the phenomenon of photon-ALP oscillations in the gamma-ray spectrum of HESS J1745-290. Our analysis does not reveal any discernible signature of photon-ALP oscillations, yielding significant constraints that serve as a complement to gamma-ray observations of extragalactic sources across a broad parameter region. The uncertainties arising from the outer Galactic magnetic field models have minor impacts on our results, except for ALP masses around 10$^{-7}$ eV, as the dominant influence originates from the intense magnetic field strength in the inner GC region.