We describe quantum limits to field sensing that relate noise, geometry and measurement duration to fundamental constants, with no reference to particle number. We cast the Tesche and Clarke (TC) bound on dc-SQUID sensitivity as such a limit, and find analogous limits for volumetric spin-precession magnetometers. We describe how randomly-arrayed spins, coupled to an external magnetic field of interest and to each other by the magnetic dipole-dipole interaction, execute a spin dynamics that depolarizes the spin ensemble even in the absence of coupling to an external reservoir. We show the resulting spin dynamics are scale invariant, with a depolarization rate proportional to spin number density and thus a number-independent quantum limit on the energy resolution per bandwidth $E_R$. Numerically, we find $E_R \ge \alpha \hbar$, $\alpha \sim 1$, in agreement with the TC limit, for paradigmatic spin-based measurements of static and oscillating magnetic fields.

中文翻译：

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尺度不变的自旋动力学和场传感的量子极限

我们描述了场感测的量子限制，这些限制将噪声、几何形状和测量持续时间与基本常数相关联，而不涉及粒子数。我们将 dc-SQUID 灵敏度的 Tesche 和 Clarke (TC) 界限作为这样的限制，并找到了体积自旋进动磁力计的类似限制。我们描述了随机排列的自旋如何与感兴趣的外部磁场耦合并通过磁偶极子 - 偶极子相互作用相互耦合，从而执行自旋动力学，即使在没有耦合到外部储层的情况下，也会使自旋系综去极化。我们展示了由此产生的自旋动力学是尺度不变的，去极化率与自旋数密度成正比，因此每个带宽的能量分辨率存在与数量无关的量子限制 $E_R$。在数值上，我们发现 $E_R \ge \alpha \hbar$, $\alpha \sim 1$,