Fast radio bursts (FRBs) probe the electron density of the universe along the path of propagation, making high redshift FRB sensitive to the helium reionization epoch. We analyze the signal to noise with which a detection of the amplitude of reionization can be made, and its redshift, for various cases of future FRB survey samples, assessing survey characteristics including total number, redshift distribution, peak redshift, redshift depth, and number above the reionization redshift, as well as dependence on reionization redshift. We take into account scatter in the dispersion measure due to an inhomogeneous intergalactic medium (IGM) and uncertainty in the FRB host and environment dispersion measure, as well as cosmology. For a future survey with 7000 FRBs extending out to $z=5$, and a sudden reionization, the detection of helium reionization can approach the $5\sigma$ level and the reionization redshift be determined to $\sigma (z_r)\approx 0.24$ in an optimistic scenario, or $2\sigma$ and $\sigma (z_r)\approx 0.34$ taking into account further uncertainties on IGM fraction evolution and redshift uncertainties.

• Received 7 February 2020
• Accepted 21 April 2020
• Corrected 9 December 2020

DOI:https://doi.org/10.1103/PhysRevD.101.103019