According to the Heisenberg uncertainty principle, the energy or frequency uncertainty of a measurement can be at the best inversely proportional to the observation time (\(T\)). The observation time in an experiment using a quantum mechanical probe is ultimately limited by the coherence time of the probe. Therefore the inverse proportionality of the statistical uncertainty of a frequency measurement to the observation time is also limited up to the coherence time of the probe, provided the systematic uncertainties are well below the statistical uncertainties. With a single laser-cooled barium ion as a quantum probe, we show that the uncertainty in the frequency measurement for a general 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. These measurements, based on controlled feedback Hamiltonian and implemented on a laser cooled single ion, allowed precise measurement of noise frequency in the kHz range. Moreover, based on the observed sensitivity of a single ion experiment presented here, we propose the use of a similar protocol with enhanced sensitivity as a tool to directly verify the existence of certain types of light mass axion-like dark matter particles where no direct measurement protocol exists.

根据海森堡不确定性原理，测量的能量或频率不确定性最好与观测时间（\（T \））成反比。在使用量子机械探针的实验中，观察时间最终受到探针相干时间的限制。因此，如果系统不确定度远低于统计不确定度，则频率测量的统计不确定度与观察时间的反比例也将受到探针相干时间的限制。用单个激光冷却的钡离子作为量子探针，我们表明，一般时变哈密顿量的频率测量不确定度为\（1 / {T} ^ {1.75 \ pm 0.03} \，而不是\（1 / T \），由与时间无关的哈密顿量的海森堡极限给出。这些测量基于受控反馈哈密顿量，并在激光冷却的单离子上进行，可以精确测量kHz范围内的噪声频率。此外，根据此处介绍的单个离子实验的观测灵敏度，我们建议使用具有增强灵敏度的类似协议作为工具来直接验证某些类型的轻质轴突样暗物质颗粒的存在，而无需直接测量协议存在。