Testing Einstein's weak equivalence principle with a 0.4-nanosecond giant pulse of the Crab pulsar

Einstein's weak equivalence principle (EEP) can be tested through the arrival time delay between photons with different frequencies. Assuming that the arrival time delay is solely caused by the gravitational potential of the Milky Way, we show that a "nano-shot" giant pulse with a time delay between energies corrected for all known effects, e.g. $\Delta t<0.4~\rm{ns}$, from the Crab pulsar poses a new upper limit on the deviation from EEP, i.e. $\Delta\gamma < (0.6-1.8)\times 10^{-15}$. This result provides the hitherto most stringent constraint on the EEP, improving by at least 2 to 3 orders of magnitude from the previous results based on fast radio bursts.