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Measurement noise 100 times lower than the quantum-projection limit using entangled atoms


Quantum metrology uses quantum entanglement—correlations in the properties of microscopic systems—to improve the statistical precision of physical measurements1. When measuring a signal, such as the phase shift of a light beam or an atomic state, a prominent limitation to achievable precision arises from the noise associated with the counting of uncorrelated probe particles. This noise, commonly referred to as shot noise or projection noise, gives rise to the standard quantum limit (SQL) to phase resolution. However, it can be mitigated down to the fundamental Heisenberg limit by entangling the probe particles. Despite considerable experimental progress in a variety of physical systems, a question that persists is whether these methods can achieve performance levels that compare favourably with optimized conventional (non-entangled) systems. Here we demonstrate an approach that achieves unprecedented levels of metrological improvement using half a million 87Rb atoms in their ‘clock’ states. The ensemble is 20.1 ± 0.3 decibels (100-fold) spin-squeezed via an optical-cavity-based measurement. We directly resolve small microwave-induced rotations 18.5 ± 0.3 decibels (70-fold) beyond the SQL. The single-shot phase resolution of 147 microradians achieved by the apparatus is better than that achieved by the best engineered cold atom sensors despite lower atom numbers2,3. We infer entanglement of more than 680 ± 35 particles in the atomic ensemble. Applications include atomic clocks4, inertial sensors5, and fundamental physics experiments such as tests of general relativity6 or searches for electron electric dipole moment7. To this end, we demonstrate an atomic clock measurement with a quantum enhancement of 10.5 ± 0.3 decibels (11-fold), limited by the phase noise of our microwave source.

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Figure 1: Overall setup.
Figure 2: Squeezing and metrology.
Figure 3: Measured spin-noise reduction and coherence.
Figure 4: Clock implementation.


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We thank I. Teper, G. Vrijsen and J. Lee for technical contributions to the experiment. This work was support by DTRA, an NSSEFF fellowship and the ONR.

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Authors and Affiliations



O.H., N.J.E., R.K. and M.A.K. carried out the experiment, analysed the data, and prepared the manuscript.

Corresponding author

Correspondence to Mark A. Kasevich.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Inferred entanglement depths, quantifying multi-particle entanglement.

The inferred spin noise variance (y axis) and the mean-square Bloch vector lengths (x axis) are plotted for the 5 × 105 atom data set. Note that the probe power decreases from left to right. The x-axis values are conservatively chosen to be the most probable value of the measured Bloch vector length distributions (Fig. 2c). A state below an M-particle boundary (purple lines labelled with particle numbers) is guaranteed to contain at least groups of M particles whose quantum states are non-separable. The blue data set establishes a lower bound on entanglement depth taking into account the residual inhomogeneity in atom–cavity coupling. The red data set, for reference, shows what we would have obtained had we ignored the small inhomogeneity. The ellipses correspond to the 68% statistical confidence intervals on the quoted values. Jmax = N/2. The third data point in each set shows the largest metrological improvement.

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Hosten, O., Engelsen, N., Krishnakumar, R. et al. Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature 529, 505–508 (2016).

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