  The primary scientific target of the CMB polarization experiments that are
currently being built and proposed is the detection of primordial tensor
perturbations. As a byproduct, these instruments will significantly improve
constraints on cosmic birefringence, or the rotation of the CMB polarization
plane. If convincingly detected, cosmic birefringence would be a dramatic
manifestation of physics beyond the standard models of particle physics and
cosmology. We forecast the bounds on the cosmic polarization rotation (CPR)
from the upcoming ground-based Simons Observatory (SO) and the space-based
LiteBIRD experiments, as well as a "fourth generation" ground-based CMB
experiment like CMB-S4 and the mid-cost space mission PICO. We examine the
detectability of both a stochastic anisotropic rotation field and an isotropic
rotation by a constant angle. CPR induces new correlations of CMB observables,
including spectra of parity-odd type in the case of isotropic CPR, and
mode-coupling correlations in the anisotropic rotation case. We find that
LiteBIRD and SO will reduce the 1$\sigma$ bound on the isotropic CPR from the
current value of 30 arcmin to 1.5 and 0.6 arcmin, respectively, while
CMB-S4-like and PICO will reduce it to $\sim 0.1$ arcmin. The bounds on the
amplitude of a scale-invariant CPR spectrum will be reduced by 1, 2 and 3
orders of magnitude by LiteBIRD, SO and CMB-S4-like/PICO, respectively. We
discuss implications of the forecasted CPR bounds for pseudoscalar fields,
primordial magnetic fields (PMF), and violations of Lorentz invariance. We find
that CMB-S4-like and PICO can reduce the 1$\sigma$ bound on the amplitude of
the scale-invariant PMF from 1 nG to 0.1 nG, while also probing the magnetic
field of the Milky Way. They will also significantly improve bounds on the
axion-photon coupling, placing stringent constraints on the string theory
axions.
