Characterising the epoch of reionisation using the cross-correlation of the kSZ effect and CMB lensing

We investigate the cross-correlation of the kinematic Sunyaev-Zeldovich (kSZ) effect with lensing of the cosmic microwave background (CMB) as a probe of the epoch of reionisation. During reionisation, bubbles of ionised electrons form around overdensities, generating temperature perturbations in the CMB via the kSZ effect, which correlate with the projected matter density field probed by CMB lensing. We demonstrate using AMBER simulations that this effect can be probed via cross-correlating the squared kSZ field with the CMB lensing potential, and that the signal is sensitive to the duration and midpoint of reionisation. We forecast that for a Simons Observatory-like experiment with 5 mu K-arcmin white noise, covering 40% of the sky, the signal could be marginally detected at S/N = 2 to 3. Meanwhile, a futuristic experiment like CMB-HD could provide a measurement of S/N about 50, yielding informative constraints on reionisation scenarios. We investigate potential challenges in measuring the signal and explore mitigation for each: contamination from extragalactic foregrounds at low redshift, contamination of the kSZ-squared estimator by lensing, and other estimator biases.