**April 2019.** The ICFO team has used quantum non-demolition (QND) measurement to generate long-lived, long-range entanglement in a dense, hot, strongly-interacting atomic system [1]. This implements a central element of proposals for detection [2-4] and production [5] of complex anti-ferromagnetic phases. The resulting entangled state is exceptionally resistant to thermal decoherence, and shares several traits with a quantum spin-liquid [6].

The quantum synthesis approach to quantum simulation uses non-destructive optical measurement of collective atomic variables to produce entanglement. Such measurements operate on the very fast time-scale of light-matter interactions, which makes them much less sensitive to thermally-induced decoherence. The ICFO team applied non-destructive Faraday rotation measurement to a vapor at 450 K, with a density of 3.6 x 10^{14} atoms/cm^{3}. At these densities spin-exchange collisions induce local spin thermalization on a time-scale of ~25 μs. The QND measurement projects the spin of the entire probed ensemble into a macroscopic singlet state [7]. Bayesian estimation, in the form of a Kalman fitler [8], is used to infer the statistical characteristics of this state, and spin-squeezing inequalities [9, 10] are used to quantify the resulting entanglement.

The generated state is remarkable in several ways. Most immediately, the sheer number of entanglements is unprecedented: at least 1.5 x 10^{13} of the 5.3 x 10^{13} participating entangled atoms became entangled in singlet states. Second, the entanglement persists for tens of spin thermalization times. Third, the entanglement bond length distribution was measured using techniques from magnetic resonance imaging: application of varying gradients to vary the conversion rate of singlets into triplets. The results show the entanglement bonds to extend over millimeter distances, thousands of times the nearest-neighbor distance, confirming the capacity of QND measurement to generate nonlocal entanglement. Moreover, the persistence beyond the thermalization time implies that the entanglement bonds are distributed among many different atoms. All of these features are reminiscent of the spin-liquid state proposed in the context of high-temperature superconductivity [6]

[1] J. Kong, R. Jiménez-Martínez, C. Troullinou, V. G. Lucivero, and M. W. Mitchell, “Measurement-induced nonlocal entanglement in a hot, strongly-interacting atomic system,” ArXiv e-prints (2018). https://arxiv.org/abs/1804.07818

[2] K. Eckert, O. Romero-Isart, M. Rodriguez, M. Lewenstein, E. S. Polzik, and A. Sanpera, “Quantum non-demolition detection of strongly correlated systems,” Nature Physics **4**, 50 (2007). http://dx.doi.org/10.1038/nphys776

[3] K. Eckert, L. Zawitkowski, A. Sanpera, M. Lewenstein, and E. S. Polzik, “Quantum polarization spectroscopy of ultracold spinor gases,” Phys Rev Lett **98**, 100404 (2007). https://link.aps.org/doi/10.1103/PhysRevLett.98.100404

[4] T. Roscilde, M. Rodríguez, K. Eckert, O. Romero-Isart, M. Lewenstein, E. Polzik, and A. Sanpera, “Quantum polarization spectroscopy of correlations in attractive fermionic gases,” New Journal of Physics **11**, 055041 (2009). http://dx.doi.org/10.1088/1367-2630/11/5/055041

[5] P. Hauke, R. J. Sewell, M. W. Mitchell, and M. Lewenstein, “Quantum control of spin correlations in ultracold lattice gases,” Phys. Rev. A **87**, 021601 (2013). http://link.aps.org/doi/10.1103/PhysRevA.87.021601

[6] P. W. Anderson, “The Resonating Valence Bond State in La_{2}CuO_{4} and Superconductivity,” Science **235**, 1196-1198 (1987). http://www.sciencemag.org/content/235/4793/1196.abstract

[7] N. Behbood, F. Martin Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. J. Sewell, and M. W. Mitchell, “Generation of Macroscopic Singlet States in a Cold Atomic Ensemble,” Phys. Rev. Lett. **113**, 093601 (2014). http://link.aps.org/doi/10.1103/PhysRevLett.113.093601

[8] R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, “Signal Tracking Beyond the Time Resolution of an Atomic Sensor by Kalman Filtering,” Phys. Rev. Lett. **120**, 040503 (2018). https://link.aps.org/doi/10.1103/PhysRevLett.120.040503

[9] O. Gühne, and G. Tóth, “Entanglement detection,” Physics Reports **474**, 1 – 75 (2009). http://www.sciencedirect.com/science/article/pii/S0370157309000623

[10] G. Vitagliano, I. Apellaniz, I. L. Egusquiza, and G. Tóth, “Spin squeezing and entanglement for an arbitrary spin,” Phys. Rev. A **89**, 032307 (2014). http://link.aps.org/doi/10.1103/PhysRevA.89.032307