A MHz gravitational wave search for harmonic sources was conducted using a 704-hr dataset obtained from the Holometer, a pair of 40-meter power recycled Michelson interferometers. Our search was designed to look for cosmic string loops and eccentric black hole binaries in an entirely unexplored frequency range from 1 to 25 MHz. The measured cross-spectral density between both interferometers was used to perform four different searches. First, we search to identify any fundamental frequencies bins that have excess power above 5$sigma$. Second, we reduce the per-bin threshold on any individual frequency bin by employing that a fundamental frequency and its harmonics all collectively lie above a threshold. We vary the number of harmonics searched over from $n= 4$ up to $n=23$. Third, we perform an agnostic approach to identify harmonic candidates that may have a single contaminated frequency bin or follow a power-law dependence. Lastly, we expand on the agnostic approach for individual candidates and search for a potential underlying population of harmonic sources. Each method was tested on the interferometer dataset, as well as a dark noise, photon shot-noise-limited, and simulated Gaussian-noise datasets. We conclude that these four different search methods did not find any candidate frequencies that would be consistent with harmonic sources. This work presents a new way of searching for gravitational wave candidates, which allowed us to survey a previously unexplored frequency range.
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