Not yet reviewed by Pith; the record is open.

The gravitational field of compact objects, such as primordial black holes, can create multiple images of background sources. For transients such as fast radio bursts (FRBs), these multiple images can be resolved in the time domain. Under certain circumstances, these images not only have similar burst morphologies but are also phase-coherent at the electric field level. With a novel dechannelization algorithm and a matched filtering technique, we search for repeated copies of the same electric field waveform in observations of FRBs detected by the FRB backend of the Canadian Hydrogen Mapping Intensity Experiment (CHIME). An interference fringe from a coherent gravitational lensing signal will appear in the time-lag domain as a statistically-significant peak in the time-lag autocorrelation function. We calibrate our statistical significance using telescope data containing no FRB signal. Our dataset consists of $\sim$100-ms long recordings of voltage data from 172 FRB events, dechannelized to 1.25-ns time resolution. This coherent search algorithm allows us to search for gravitational lensing signatures from compact objects in the mass range of $10^{-4}-10^{4} ~\mathrm{M_{\odot}}$. After ruling out an anomalous candidate due to diffractive scintillation, we find no significant detections of gravitational lensing in the 172 FRB events that have been analyzed. In a companion work [Leung, Kader+2022], we interpret the constraints on dark matter from this search.