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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Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138–5143 (1993)
Appel, J. et al. Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit. Proc. Natl Acad. Sci. USA 106, 10960–10965 (2009)
Takano, T., Tanaka, S.-I.-R., Namiki, R. & Takahashi, Y. Manipulation of nonclassical atomic spin states. Phys. Rev. Lett. 104, 013602 (2010)
Schleier-Smith, M. H., Leroux, I. D. & Vuletić, V. States of an ensemble of two-level atoms with reduced quantum uncertainty. Phys. Rev. Lett. 104, 073604 (2010)
Leroux, I. D., Schleier-Smith, M. H. & Vuletić, V. Implementation of cavity squeezing of a collective atomic spin. Phys. Rev. Lett. 104, 073602 (2010)
Gross, C., Zibold, T., Nicklas, E., Estève, J. & Oberthaler, M. K. Nonlinear atom interferometer surpasses classical precision limit. Nature 464, 1165–1169 (2010)
Riedel, M. F. et al. Atom-chip-based generation of entanglement for quantum metrology. Nature 464, 1170–1173 (2010)
Hamley, C. D., Gerving, C. S., Hoang, T. M., Bookjans, E. M. & Chapman, M. S. Spin-nematic squeezed vacuum in a quantum gas. Nature Phys. 8, 305–308 (2012)
Sewell, R. J. et al. Magnetic sensitivity beyond the projection noise limit by spin squeezing. Phys. Rev. Lett. 109, 253605 (2012)
Bohnet, J. G. et al. Reduced spin measurement back-action for a phase sensitivity ten times beyond the standard quantum limit. Nature Photon. 8, 731–736 (2014)
Leibfried, D. et al. Creation of a six-atom ‘Schrödinger cat’ state. Nature 438, 639–642 (2005)
Monz, T. et al. 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011)
Haas, F., Volz, J., Gehr, R., Reichel, J. & Estéve, J. Entangled states of more than 40 atoms in an optical fiber cavity. Science 344, 180–183 (2014)
Strobel, H. et al. Fisher information and entanglement of non-Gaussian spin states. Science 345, 424–427 (2014)
Lücke, B. et al. Detecting multiparticle entanglement of Dicke states. Phys. Rev. Lett. 112, 155304 (2014)
Leibfried, D. et al. Experimental determination of the motional quantum state of a trapped atom. Phys. Rev. Lett. 77, 4281–4285 (1996)
Lvovsky, A. I. et al. Quantum state reconstruction of the single-photon Fock state. Phys. Rev. Lett. 87, 050402 (2001)
Vlastakis, B. et al. Deterministically encoding quantum information using 100-photon Schrödinger cat states. Science 342, 607–610 (2013)
Sørensen, A. S. & Mølmer, K. Entanglement and extreme spin squeezing. Phys. Rev. Lett. 86, 4431–4434 (2001)
McConnell, R. et al. Generating entangled spin states for quantum metrology by single-photon detection. Phys. Rev. A 88, 063802 (2013)
Arecchi, F. T., Courtens, E., Gilmore, R. & Thomas, H. Atomic coherent states in quantum optics. Phys. Rev. A 6, 2211–2237 (1972)
Dowling, J. P., Agarwal, G. S. & Schleich, W. P. Wigner distribution of a general angular-momentum state: applications to a collection of two-level atoms. Phys. Rev. A 49, 4101–4109 (1994)
Agarwal, G. S., Lougovski, P. & Walther, H. Multiparticle entanglement and the Schrödinger cat state using ground-state coherences. J. Mod. Opt. 52, 1397–1404 (2005)
Duan, L. M., Lukin, M. D., Cirac, J. I. & Zoller, P. Long-distance quantum communication with atomic ensembles and linear optics. Nature 414, 413–418 (2001)
Matsukevich, D. N. et al. Deterministic single photons via conditional quantum evolution. Phys. Rev. Lett. 97, 013601 (2006)
Kuzmich, A. et al. Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles. Nature 423, 731–734 (2003)
Simon, J., Tanji, H., Thompson, J. K. & Vuletić, V. Interfacing collective atomic excitations and single photons. Phys. Rev. Lett. 98, 183601 (2007)
Choi, K. S., Goban, A., Papp, S. B., van Enk, S. J. & Kimble, H. J. Entanglement of spin waves among four quantum memories. Nature 468, 412–416 (2010)
Christensen, S. L. et al. Towards quantum state tomography of a single polariton state of an atomic ensemble. New J. Phys. 15, 015002 (2013)
Christensen, S. L. et al. Quantum interference of a single spin excitation with a macroscopic atomic ensemble. Phys. Rev. A 89, 033801 (2014)
Tanji-Suzuki, H. et al. Interaction between atomic ensembles and optical resonators: classical description. Adv. At. Mol. Opt. Phys. 60, 201–237 (2011)
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.
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.
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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). https://doi.org/10.1038/nature14293
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