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Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon

An Erratum to this article was published on 14 May 2015


Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized1,2,3,4,5,6,7,8,9,10, but these states display Gaussian spin distribution functions with a non-negative Wigner quasiprobability distribution function. Non-Gaussian entangled states have been produced in small ensembles of ions11,12, and very recently in large atomic ensembles13,14,15. Here we generate entanglement in a large atomic ensemble via an interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function—an important hallmark of non-classicality—and verify an entanglement depth (the minimum number of mutually entangled atoms) of 2,910 ± 190 out of 3,100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. Although the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing. More generally, our results demonstrate the power of heralded methods for entanglement generation, and illustrate how the information contained in a single photon can drastically alter the quantum state of a large system.

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Figure 1: Scheme for heralded entanglement generation in a large atomic ensemble by single-photon detection.
Figure 2: Collective-spin distribution of atomic state heralded by one photon.
Figure 3: Reconstruction of the heralded many-atom entangled state.


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We thank M. H. Schleier-Smith, E. S. Polzik and S. L. Christensen for discussions. This work was supported by the NSF, DARPA (QUASAR), and a MURI grant through AFOSR. S.Ć. acknowledges support from the Ministry of Education, Science and Technological Development of the Republic of Serbia, through grant numbers III45016 and OI171038.

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Authors and Affiliations



The experiment and analysis were carried out by R.M., H.Z., J.H. and S.Ć.; V.V. supervised the work; all authors discussed the results and contributed to the manuscript.

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Correspondence to Vladan Vuletić.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 The measured atomic state spin variance, , as a function of the heralding light photon number and corresponding probability pq of detecting one photon.

The solid red line is the prediction for broadened by the photon shot noise of the heralding light. The dashed black line shows the CSS variance for 2,030 F = 1 effective atoms used in this measurement. Error bars, 1 s.d.

Extended Data Figure 2 Dependence of the reconstructed distribution of collective spin Sz on the measurement photon number.

This dependence is illustrated by reconstructed spin distributions for photon numbers 0.5 × 104 (a), 1.1 × 104 (b), 1.7 × 104 (c), 2.7 × 104 (d) and 3.6 × 104 (e). Blue lines correspond to the CSS and red lines correspond to the heralded states. The shaded area indicates an uncertainty of 1 s.d.

Extended Data Table 1 Resonator parameters

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McConnell, R., Zhang, H., Hu, J. et al. Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon. Nature 519, 439–442 (2015).

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