Line search by quantum logic spectroscopy enhanced with squeezing and statistical tests

In quantum logic spectroscopy, internal transitions of trapped ions and molecules can be probed by detecting the motional displacement caused by an applied light field of variable frequency. This provides a solution to ``needle in a haystack'' problems, such as the search for narrow clock transitions in highly charged ions, recently discussed by S. Chen et al. (Phys. Rev. Applied 22, 054059). The main bottleneck is the search speed over a frequency bandwitdh, which can be increased by enhancing the sensitivity of displacement detection. In this work, we explore two complementary improvements: the use of squeezed motional states and optimal statistical postprocessing of data using a hypothesis testing framework. We demonstrate that each method independently provides a substantial boost to scan speed. Their combination effectively mitigates state preparation and measurement errors, improving the scan speed by an order of magnitude and fully leveraging the quantum enhancement offered by squeezing.