Limits on Optical Counterparts to the Repeating Fast Radio Burst 20180916B from High-speed Imaging with Gemini-North/'Alopeke

We report on contemporaneous optical observations at approximate to 10 ms timescales from the fast radio burst (FRB) 20180916B of two repeat bursts (FRB 20201023 and FRB 20220908) taken with the 'Alopeke camera on the Gemini-North telescope. These repeats have radio fluences of 2.8 and 3.5 Jy ms, respectively, approximately in the lower 50th percentile for fluence from this repeating burst. The 'Alopeke data reveal no significant optical detections at the FRB position and we place 3 sigma upper limits to the optical fluences of <8.3 x 10(-3) and <7.7 x 10(-3) Jy ms after correcting for line-of-sight extinction. Together, these yield the most sensitive limits to the optical-to-radio fluence ratio of an FRB on these timescales with eta(nu) < 3 x 10(-3) by roughly an order of magnitude. These measurements rule out progenitor models where FRB 20180916B has a similar fluence ratio to optical pulsars, such as the Crab pulsar, or where optical emission is produced as inverse-Compton radiation in a pulsar magnetosphere or young supernova remnant. Our ongoing program with 'Alopeke on Gemini-North will continue to monitor repeating FRBs, including FRB 20180916B, to search for optical counterparts on millisecond timescales.