论文标题
超越海森堡不确定性关系
Retrodiction beyond the Heisenberg uncertainty relation
论文作者
论文摘要
在量子力学中，海森伯格的不确定性关系对人们可以预测粒子上位置和动量测量结果的精确度提出了最终的限制。海森伯格明确指出了预测“假设未来测量”的关系，并且没有描述与测量时间更早和更晚的知识可用的情况。我们研究了在这种情况下使用的原子合奏，其中包含$ 10^{11} $ $^{87} \ text {rb} $原子，在存在磁场的情况下几乎处于基础状态。然后，原子的集体旋转可观察物可以通过规范的位置和动量可观察物，$ \ hat {x} _a $和$ \ hat {p} _a $满足$ [\ hat {x} _a，\ hat hat {p} {p} _a _a] = i \ hbar $。 $ \ hat {p} _a $的量子非拆卸测量值$ \ hat {x} _a $ aft time $ t $允许在时间$ t $的两个可观察结果的精确估计。将精确值分配给多个可观测值并在物理过程中观察它们的变化的能力可能对量子状态估计和传感有影响。
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for the prediction of "hypothetical future measurements", and it does not describe the situation where knowledge is available about the system both earlier and later than the time of the measurement. We study what happens under such circumstances with an atomic ensemble containing $10^{11}$ $^{87}\text{Rb}$ atoms, initiated nearly in the ground state in presence of a magnetic field. The collective spin observables of the atoms are then well described by canonical position and momentum observables, $\hat{x}_A$ and $\hat{p}_A$ that satisfy $[\hat{x}_A,\hat{p}_A]=i\hbar$. Quantum non-demolition measurements of $\hat{p}_A$ before and of $\hat{x}_A$ after time $t$ allow precise estimates of both observables at time $t$. The capability of assigning precise values to multiple observables and to observe their variation during physical processes may have implications in quantum state estimation and sensing.
