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According to the Heisenberg uncertainty principle, the energy or frequencyuncertainty of a measurement can be at the best inversely proportional to theobservation time ($T$). The observation time in an experiment using a quantummechanical probe is ultimately limited by the coherence time of the probe.Therefore the inverse proportionality of the statistical uncertainty of afrequency measurement to the observation time is also limited up to thecoherence time of the probe, provided the systematic uncertainties are wellbelow the statistical uncertainties. With a single laser-cooled barium ion as aquantum probe, we show that the uncertainty in the frequency measurement for ageneral time-dependent Hamiltonian scales as $1/T^{1.75\pm 0.03}$ as opposed to$1/T$, given by the Heisenberg limit for time-independent Hamiltonian. Thesemeasurements, based on controlled feedback Hamiltonian and implemented on alaser cooled single ion, allowed precise measurement of noise frequency in thekHz range. Moreover, based on the observed sensitivity of a single ionexperiment presented here, we propose the use of a similar protocol withenhanced sensitivity as a tool to directly verify the existence of certaintypes of light mass axion-like dark matter particles where no directmeasurement protocol exists.

A single atom noise probe operating beyond the Heisenberg limit