Detecting rotation from lensing in the CMB

An excellent estimate of the lensing signal is expected from the availability of deep and high-resolution polarization data in the near future. This is most important to allow for efficient delensing, needed to detect the primordial B-mode power and with it the famous tensor-to-scalar ratio. Here we discuss in a joint manner estimators of the rotation of polarization, of the second order lensing field rotation, and standard gradient lensing reconstruction. All are most efficient when able to probe the EB power created locally, have comparable reconstruction noise in this regime, and can benefit substantially from delensing. We discuss several ongoing and planned CMB experiments. We determine their noise for lensing field rotation and polarization rotation and discuss their prospects for measuring these effects. There is an on-going controversy on whether the lensing field rotation also rotates the polarization -- if so this will be observed at high significance soon with already on going observations of the South Pole Telescope, SPT-3G, in cross-correlation with tracers of large scale structure, as we show in this paper.