We propose a novel experiment to search for axion dark matter that differentiates the phase velocities of the left- and right-handed polarized photons. Our optical cavity measures the difference of the resonant frequencies between two circular polarizations of the laser beam. The design of our cavity adopts a double-pass configuration to realize a null experiment and give a high common mode rejection of environmental disturbances. We estimate the potential sensitivity to the axion-photon coupling constant gaγ for the axion mass m10-10 eV. In a low mass range m10-15 eV, we can achieve gaγ3×10-16 GeV-1, which is beyond the current bound by several orders of magnitude.
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