Beating the Heisenberg limit in a single atom for dark matter search

Quantum metrology for frequency measurement has been used to surpass the Heisenberg scaling of the measurement uncertainty with observation time. In a single ion experiment, we show that the uncertainty in the frequency measurement scales as $1/T^2$ for over 100 $\mu$s time scale limited by the de-phasing time of the probe state. The proof-of-principle experiment also sets a limit on the coupling strength of axion like dark matter particle wind to interact with an electron spin. Even though the limit is a weak limit, we provide feasible experiment by which the limit can be strengthened to complement the other dark matter search experiments. The scheme is based on the proposal by Pang et al. [Pang2017] implemented on a laser cooled single ion probe which has been subjected to an external time dependent field coupling.