  Very light pseudoscalar fields, often referred to as axions, are compelling
dark matter candidates and can potentially be detected through their coupling
to the electromagnetic field. Recently a novel detection technique using the
cosmic microwave background (CMB) was proposed, which relies on the fact that
the axion field oscillates at a frequency equal to its mass in appropriate
units, leading to a time-dependent birefringence. For appropriate oscillation
periods this allows the axion field at the telescope to be detected via the
induced sinusoidal oscillation of the CMB linear polarization. We search for
this effect in two years of POLARBEAR data. We do not detect a signal, and
place a median $95 \%$ upper limit of $0.65 ^\circ$ on the sinusoid amplitude
for oscillation frequencies between $0.02\,\text{days}^{-1}$ and
$0.45\,\text{days}^{-1}$, which corresponds to axion masses between $9.6 \times
10^{-22} \, \text{eV}$ and $2.2\times 10^{-20} \,\text{eV}$. Under the
assumptions that 1) the axion constitutes all the dark matter and 2) the axion
field amplitude is a Rayleigh-distributed stochastic variable, this translates
to a limit on the axion-photon coupling $g_{\phi \gamma} < 2.4 \times 10^{-11}
\,\text{GeV}^{-1} \times ({m_\phi}/{10^{-21} \, \text{eV}})$.
