超高康普顿频率、宇称无关、海森堡有限灵敏度的介观薛定谔猫原子干涉仪
Ultra-high Compton Frequency, Parity Independent, Mesoscopic Schrödinger Cat Atom Interferometer with Heisenberg Limited Sensitivity
摘要：
提出了一种通过集体态探测和单轴扭转自旋压缩的临界调谐，使原子干涉仪达到海森堡极限（HL）的方案，其系数为$\sim$ $\sqrt{2}$。它产生一个薛定谔猫（SC）态，作为两个极端集体态的叠加。当这种SC干涉仪被用作陀螺仪时，干涉发生在100康普顿频率，对应于质量为$Nm$的介观单个物体，其中$N$是系综中的粒子数，$m$是每个粒子的质量。例如，对于$^{87}$ Rb原子和$N=10^{6}$，干涉将发生在$\sim$ $2 \times 10^{31}$ Hz的康普顿频率处。在这种方案下，发现信号关键地依赖于$N$的奇偶性。我们提出了两个变种的协议。在协议A下，对于一个奇偶校验，条纹以$N$的因子变窄，而对于另一个奇偶校验，信号为零。在协议B下，对于一个奇偶校验，条纹以$N$的因子变窄，而对于另一个奇偶校验，条纹以$\sqrt{N}$的因子变窄。两个协议都可以以反转两个奇偶校验的信号行为的方式进行修改。在偶数或奇数概率相等的重复测量中，两个方案版本的平均灵敏度均小于HL，小于因子为$\sim$ $\sqrt{2}$。我们表明，当SC干涉仪被配置为加速度计，有效的双光子波矢量增强了一个因素的$N$，导致相同程度的增强灵敏度。我们还表明，这样一个介观的单一对象可以用来增加一个原子钟的有效基频的一个因素$N$，与HL的灵敏度是相当的，在一个因素$\sim$ $\sqrt{2}$。
英文摘要：
We present a protocol for an atomic interferometer that reaches the Heisenberg Limit (HL), within a factor of $\sim$ $\sqrt{2}$, via collective state detection and critical tuning of one-axis twist spin squeezing. It generates a Schrödinger cat (SC) state, as a superposition of two extremal collective states. When this SC interferometer is used as a gyroscope, the interference occurs at an ultrahigh Compton frequency, corresponding to a mesoscopic single object with a mass of $Nm$, where $N$ is the number of particles in the ensemble, and $m$ is the mass of each particle. For $^{87}$Rb atoms, with $N=10^{6}$, for example, the intereference would occur at a Compton frequency of $\sim$ $2 \times 10^{31}$ Hz. Under this scheme, the signal is found to depend critically on the parity of $N$. We present two variants of the protocol. Under Protocol A, the fringes are narrowed by a factor of $N$ for one parity, while for the other parity the signal is zero. Under Protocol B, the fringes are narrowed by a factor of $N$ for one parity, and by a factor of $\sqrt{N}$ for the other parity. Both protocols can be modified in a manner that reverses the behavior of the signals for the two parities. Over repeated measurements under which the probability of being even or odd is equal, the averaged sensitivity is smaller than the HL by a factor of $\sim$ $\sqrt{2}$ for both versions of the protocol. We show that when the SC interferometer is configured as an accelerometer, the effective two-photon wave vector is enhanced by a factor of $N$, leading to the same degree of enhancement in sensitivity. We also show that such a mesoscopic single object can be used to increase the effective base frequency of an atomic clock by a factor of $N$, with a sensitivity that is equivalent to the HL, within a factor of $\sim$ $\sqrt{2}$.
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