被俘获的离子是激发离子运动的弱力和电场的灵敏探测器。在这里测量的质心运动的捕获离子晶体是相位相干的施加弱外力的报告。这些实验进行远离陷阱运动频率的二维捕获离子晶体约100个离子，并确定我们的协议的基本测量不精确度与质心模式相关的噪音。驱动的正弦位移的晶体检测通过耦合的离子晶体运动的内部自旋自由度的离子，使用振荡的自旋相关的光偶极子力。由此产生的诱导自旋进动与晶体的位移幅度成比例，并且以近投影噪声限制的分辨率测量。一个$49\,$ pm位移检测与一个单一的测量信号噪声比为1，这是一个数量级的改善，在以前的相位不相干的实验。该位移幅度比零点波动小$40$倍。利用我们的重复率，实现了$8.4\,$ pm $/\sqrt{\mathrm{Hz}}$位移灵敏度，这意味着分别对力和电场的$12\,$ yN $/\mathrm{ion}/\sqrt{\mathrm{Hz}}$和$77\,μ$ V $/$ m $/\sqrt{\mathrm{Hz}}$灵敏度。当与质心模式共振应用时，该位移灵敏度分别指示弱力和电场检测低于$10^{-3}\,$ yN/ion和$1\,$ nV/m的可能性。
英文摘要：
Trapped ions are sensitive detectors of weak forces and electric fields that excite ion motion. Here measurements of the center-of-mass motion of a trapped-ion crystal that are phase-coherent with an applied weak external force are reported. These experiments are conducted far from the trap motional frequency on a two-dimensional trapped-ion crystal of approximately 100 ions, and determine the fundamental measurement imprecision of our protocol free from noise associated with the center-of-mass mode. The driven sinusoidal displacement of the crystal is detected by coupling the ion crystal motion to the internal spin-degree of freedom of the ions using an oscillating spin-dependent optical dipole force. The resulting induced spin-precession is proportional to the displacement amplitude of the crystal, and is measured with near-projection-noise-limited resolution. A $49\,$pm displacement is detected with a single measurement signal-to-noise ratio of 1, which is an order-of-magnitude improvement over prior phase-incoherent experiments. This displacement amplitude is $40$ times smaller than the zero-point fluctuations. With our repetition rate, a $8.4\,$pm$/\sqrt{\mathrm{Hz}}$ displacement sensitivity is achieved, which implies $12\,$yN$/\mathrm{ion}/\sqrt{\mathrm{Hz}}$ and $77\,μ$V$/$m$/\sqrt{\mathrm{Hz}}$ sensitivities to forces and electric fields, respectively. This displacement sensitivity, when applied on-resonance with the center-of-mass mode, indicates the possibility of weak force and electric field detection below $10^{-3}\,$yN/ion and $1\,$nV/m, respectively.
Motional studies of one and two laser-cooled trapped ions for electric-field sensing applications
我们研究了一个和两个激光冷却捕获的$^{40}$ Ca $^+$离子的动力学通过施加不同性质的电场沿轴向的陷阱，即，驱动的运动与谐波偶极场，或与白噪声。这两种类型的驱动诱导不同的运动状态的轴向模式;相干振荡的偶极场，或增强的布朗运动由于额外的贡献，从电噪声的加热速率。在这两种情况下，一个孤立的离子和激光冷却的双离子晶体的灵敏度进行了评估和比较。这种动力学的分析和理解是重要的实现一种新的潘宁阱质谱技术的基础上，光学检测，旨在提高精度和灵敏度。
