Enhancing the sensitivity to ultralight bosonic dark matter using signal correlations

In recent years, numerous experiments have been proposed and conducted to search for ultralight bosonic dark matter (ULBDM). Signals from ULBDM in such experiments are characterized by extremely narrow spectral widths. A near-optimal detection strategy is to divide the data based on the signal coherence time and sum the power across these segments. However, the signal coherence time can extend beyond a day, making it challenging to construct contiguous segments of such a duration due to detector instabilities. In this work, we present a novel detection statistic that can coherently extract ULBDM signals from segments of arbitrary durations. Our detection statistic, which we refer to as coherent SNR, is a weighed sum of data correlations, whose weights are determined by the expected signal correlations. We demonstrate that coherent SNR achieves sensitivity independent of segment duration and surpasses the performance of the conventional incoherent-sum approach, through analytical arguments and numerical experiments.