Interaction-based quantum metrology showing scaling beyond the Heisenberg limit
Interaction-based quantum metrology showing scaling beyond the Heisenberg limit
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DOI：
10.1038/nature09778
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发表时间：
2011-03-24
期刊：
影响因子：
64.8
通讯作者：
Mitchell, M. W.
中科院分区：
文献类型：
--
作者：
Napolitano, M.;Koschorreck, M.;Mitchell, M. W.
量子计量学旨在利用纠缠和其他量子资源来提高精度测量(1)。使用N个独立粒子测量参数X的干涉仪最多只能达到标准量子灵敏度极限，增量X与N-1/2成正比。然而，使用N个纠缠粒子和奇异态(2)，这样的干涉仪(3)原则上可以达到海森堡极限，增量X与N-1成正比。最近的理论工作(4-6)认为，粒子之间的相互作用可能是量子计量学的宝贵资源，使标度超过海森堡极限。具体地说，k粒子相互作用在适当的纠缠态下将产生与N-k成正比的灵敏度增量X，即使没有纠缠也会产生与N-(k-1/2)成正比的灵敏度。在这里，我们演示了在一个原子系综(12)的磁化强度(10，11)的非线性非破坏性测量(8，9)中，X与N-3/2成正比的“超海森堡”标度。我们使用快速光学非线性来产生成对的光子-光子相互作用(13)(对应于k=2)，同时保持量子噪声限制性能(7，14)。我们在N中观察到两个数量级的超海森堡标度，受到高阶非线性效应的限制，这与理论(13)很好地一致。对于有限持续时间的测量，超海森堡标度允许非线性测量在灵敏度上超过具有相同光子数的可比线性测量。然而，在其他情况下，高阶非线性阻止了这种交叉的发生，反映了非线性系统中标度和灵敏度之间的微妙关系。我们的工作表明，粒子间的相互作用可以提高量子受限测量的灵敏度，并在实验上展示了一种新的量子计量学资源。
Quantum metrology aims to use entanglement and other quantum resources to improve precision measurement(1). An interferometer using N independent particles to measure a parameter X can achieve at best the standard quantum limit of sensitivity, delta X proportional to N-1/2. However, using N entangled particles and exotic states(2), such an interferometer(3) can in principle achieve the Heisenberg limit, delta X proportional to N-1. Recent theoretical work(4-6) has argued that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity delta X proportional to N-k with appropriate entangled states and delta X proportional to N-(k-1/2) even without entanglement(7). Here we demonstrate 'super-Heisenberg' scaling of delta X proportional to N-3/2 in a nonlinear, non-destructive(8,9) measurement of the magnetization(10,11) of an atomic ensemble(12). We use fast optical nonlinearities to generate a pairwise photon-photon interaction(13) (corresponding to k = 2) while preserving quantum-noise-limited performance(7,14). We observe super-Heisenberg scaling over two orders of magnitude in N, limited at large numbers by higher order nonlinear effects, in good agreement with theory(13). For a measurement of limited duration, super-Heisenberg scaling allows the nonlinear measurement to overtake in sensitivity a comparable linear measurement with the same number of photons. In other situations, however, higher-order nonlinearities prevent this crossover from occurring, reflecting the subtle relationship between scaling and sensitivity in nonlinear systems. Our work shows that interparticle interactions can improve sensitivity in a quantum-limited measurement, and experimentally demonstrates a new resource for quantum metrology.