  We suggest a novel experimental method to search for axion dark matter with
an optical ring cavity. Our cavity measures the difference of the resonant
frequencies between two circular-polarizations of the laser beam. Its technical
design adopts double-pass configuration to realize a null experiment and reject
environmental common-mode noises. We reveal that it can probe the axion-photon
coupling constant with a broad range of axion mass $10^{-17} \text{eV} \lesssim
m \lesssim 10^{-10} \text{eV}$, up to several orders of magnitude beyond the
current limits. We expect that this cavity experiment establishes a new window
to develop the axion research.
