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 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.