  The Crab Nebula, also known as Tau A, is a polarized astronomical source at
millimeter wavelengths. It has been used as a stable light source for
polarization angle calibration in millimeter-wave astronomy. However, it is
known that its intensity and polarization vary as a function of time at a
variety of wavelengths. Thus, it is of interest to verify the stability of the
millimeter-wave polarization. If detected, polarization variability may be used
to better understand the dynamics of Tau A, and for understanding the validity
of Tau~A as a calibrator. One intriguing application of such observation is to
use it for the search of axion-light particles (ALPs). Ultralight ALPs couple
to photons through a Chern-Simons term, and induce a temporal oscillation in
the polarization angle of linearly polarized sources. After assessing a number
of systematic errors and testing for internal consistency, we evaluate the
variability of the polarization angle of the Crab Nebula using 2015 and 2016
observations with the 150 GHz POLARBEAR instrument. We place a median 95% upper
bound of polarization oscillation amplitude $A < 0.065^\circ$ over the
oscillation frequencies from $0.75~\mathrm{year}^{-1}$ to
$0.66~\mathrm{hour}^{-1}$. Assuming that no sources other than ALP are causing
Tau A's polarization angle variation, that the ALP constitutes all the dark
matter, and that the ALP field is a stochastic Gaussian field, this bound
translates into a median 95% upper bound of ALP-photon coupling
$g_{a\gamma\gamma} < 2.16\times10^{-12}\,\mathrm{GeV}^{-1}\times(m_a/10^{-21}
\mathrm{eV})$ in the mass range from $9.9\times10^{-23} \mathrm{eV}$ to
$7.7\times10^{-19} \mathrm{eV}$. This demonstrates that this type of analysis
using bright polarized sources is as competitive as those using the
polarization of cosmic microwave background in constraining ALPs.
