Quantum metrology algorithms for dark matter searches with ²²⁹Th³⁺

Quantum metrology aims to apply algorithms from quantum information science to improve the sensitivity of a quantum sensor while minimizing susceptibility to noise. Among the most sensitive quantum sensors are quantum clocks, which have been shown to be ideal devices for searches for local ultralight scalar dark matter. While current atomic clocks reach unprecedented stability, nuclear clocks based on Thorium-229m isomer have been proposed which not only allow for an improvement of the clock stability, but also offer increased sensitivity to possible dark matter signals by many orders of magnitude. Here we explore different quantum metrology algorithms in the context of dark matter searches using nuclear clocks. We propose a new quantum algorithm and compare it to previously explored quantum metrology protocols. We develop numerical simulations taking into account dark matter decoherence, laser noise and quantum projection noise and report improved sensitivity of nuclear clocks to dark matter.