  Pulsar timing arrays (PTAs) consisting of widely distributed and well-timed
millisecond pulsars can serve as a galactic interferometer to measure
gravitational waves. With the same data acquired for PTAs, we propose to
develop pulsar polarization arrays (PPAs), to explore astrophysics and
fundamental physics. As in the case of PTAs, PPAs are best suited to reveal
temporal and spatial correlations at large scales that are hard to mimic by
local noise. To demonstrate the physical potential of PPAs, we consider
detection of ultralight axion-like dark matter (ALDM), through cosmic
birefringence induced by its Chern-Simon coupling. Because of its tiny mass,
the ultralight ALDM can be generated as a Bose-Einstein condensate,
characterized by a strong wavy nature. Incorporating both temporal and spatial
correlations of the signal, we show that PPAs have a potential to probe the
Chern-Simon coupling up to $\sim 10^{-14}-10^{-17}$GeV$^{-1}$, with a mass
range $\sim 10^{-27} - 10^{-21}$eV.
