The motion of trapped atoms plays an essential role in quantum mechanical sensing, simulations and computing. Small disturbances of atomic vibrations are still challenging to be sensitively detected. It requires a reliable coupling between individual phonons and internal electronic levels that light can readout. As available information in a few electronic levels about the phonons is limited, the coupling needs to be sequentially repeated to further harvest the remaining information. We analyze such phonon measurements on the simplest example of the force and heating sensing using motional Fock states. We prove that two sequential measurements are sufficient to reach sensitivity to force and heating for realistic Fock states and saturate the quantum Fisher information for a small amount of force or heating. It is achieved by the conventionally available Jaynes–Cummings coupling. The achieved sensitivities are found to be better than those obtained from classical states. Further enhancements are expectable when the higher Fock state generation is improved. The result opens additional applications of sequential phonon measurements of atomic motion. This measurement scheme can also be directly applied to other bosonic systems including cavity QED and circuit QED.

被困原子的运动在量子力学传感、模拟和计算中起着至关重要的作用。原子振动的小扰动仍然难以灵敏地检测。它需要单个声子和光可以读出的内部电子水平之间的可靠耦合。由于有关声子的几个电子级别的可用信息有限，因此需要按顺序重复耦合以进一步收集剩余信息。我们在使用运动 Fock 状态的力和热感测的最简单示例上分析了此类声子测量。我们证明了两个连续的测量足以达到对真实 Fock 状态的力和加热的敏感性，并在少量的力或加热下使量子 Fisher 信息饱和。它是通过常规可用的 Jaynes-Cummings 耦合实现的。发现获得的灵敏度优于从经典状态获得的灵敏度。当更高的 Fock 状态生成得到改进时，可以预期进一步的增强。该结果开启了原子运动顺序声子测量的其他应用。这种测量方案也可以直接应用于其他玻色子系统，包括腔 QED 和电路 QED。