Abstract
The standard quantum limit bounds the precision of measurements that can be achieved by ensembles of uncorrelated particles. Fundamentally, this limit arises from the non-commuting nature of quantum mechanics, leading to the presence of fluctuations often referred to as quantum projection noise. Quantum metrology relies on the use of non-classical states of many-body systems to enhance the precision of measurements beyond the standard quantum limit1,2. To do so, one can reshape the quantum projection noise—a strategy known as squeezing3,4. In the context of many-body spin systems, one typically uses all-to-all interactions (for example, the one-axis twisting model4) between the constituents to generate the structured entanglement characteristic of spin squeezing5. Here we explore the prediction, motivated by recent theoretical work6,7,8,9,10, that short-range interactions—and in particular, the two-dimensional dipolar XY model—can also enable the realization of scalable spin squeezing. Working with a dipolar Rydberg quantum simulator of up to N = 100 atoms, we demonstrate that quench dynamics from a polarized initial state lead to spin squeezing that improves with increasing system size up to a maximum of −3.5 ± 0.3 dB (before correcting for detection errors, or roughly −5 ± 0.3 dB after correction). Finally, we present two independent refinements: first, using a multistep spin-squeezing protocol allows us to further enhance the squeezing by roughly 1 dB, and second, leveraging Floquet engineering to realize Heisenberg interactions, we demonstrate the ability to extend the lifetime of the squeezed state by freezing its dynamics.
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Acknowledgements
We acknowledge the insights of and discussions with M. P. Zaletel, B. Halperin, B. Roberts, C. Laumann, E. Davis, S. Chern, W. Wu, Z. Wang, A.-M. Rey, F. Yang and Q. Liu. This work is supported by the Agence Nationale de la Recherche (ANR, project nos. RYBOTIN and ANR-22-PETQ-0004 France 2030, project no. QuBitAF), and the European Research Council (Advanced grant no. 101018511-ATARAXIA). B.Y. acknowledges support from the AFOSR MURI programme (grant no. W911NF-20-1-0136). M. Block acknowledges support through the Department of Defense through the National Defense Science and Engineering Graduate Fellowship Program. M. Bintz acknowledges support from the Army Research Office (grant no. W911NF-21-1-0262). N.Y.Y. acknowledges support from the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator. D.B. acknowledges support from MCIN/AEI/10.13039/501100011033 (grant nos. RYC2018-025348-I, PID2020-119667GA-I00 and European Union NextGenerationEU PRTR-C17.I1). The computational results presented were performed in part using the Faculty of Arts and Sciences Research Computing (FASRC) Cannon cluster supported by the Faculty of Arts and Sciences (FAS) Division of Science Research Computing Group at Harvard University, the Savio computational cluster resource provided by the Berkeley Research Computing programme at the University of California and the Pôle Scientifique de Modélisation Numérique (PSMN) cluster at the ENS Lyon.
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G.B., G.E., C.C., J.A.B. and D.B. carried out the experiments. B.Y., M. Block, M. Bintz, T.C. and F.M. conducted the theoretical analysis and simulations. T.R., T.L., N.Y.Y. and A.B. supervised the work. All authors contributed to the data analysis, progression of the project and both the experimental and theoretical aspects. All authors contributed to the writing of the manuscript.
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Extended data figures and tables
Extended Data Fig. 2 Minimum squeezing parameter as a function of atom number N.
The circles and diamonds correspond to raw and corrected data, respectively. The solid coloured lines are power-law fits. The purple shaded region shows the simulations including 97.5 ± 1% (resp. 99 ± 1%) detection efficiency of \(\left|\uparrow \right\rangle \) (resp. \(\left|\downarrow \right\rangle \)). The dashed curves represent the results of simulations of the XY dipolar model without state preparation and measurement errors (grey) and without detection errors only (pink). The dashed black curve represents the exact results for the OAT model. The inaccessible region corresponds to values of the squeezing parameter smaller than 2/(2 + N)2.
Extended Data Fig. 3 Magnetization dynamics and its contributions.
a, Dynamics of the magnetization per spin for the dipolar XY model on a periodic square lattice. Results from tVMC calculations and RSW theory for various system sizes (N = 16, . . . , 144). We also show the rotor contribution to the magnetization, corresponding to an effective one-axis-twisting model (see text). b, Spin-wave (SW) contribution to the magnetization.
Extended Data Fig. 4 Schematic depicting the multi-step squeezing protocol.
a, Semi-classical description of a y-polarized initial state. b, c, Normal spin squeezing dynamics. d, e, Multi-step squeezing dynamics enabled by an extra rotation along the mean spin direction.
Extended Data Fig. 5 Multistep squeezing, comparison between data and simulation.
Measurements of the squeezing parameter obtained with two different procedures. The first one (purple dots) is the original sequence illustrated in Fig. 1(c). The second one (dark green dots) is the multistep sequence. The shaded regions show the simulations including 97.5 ± 1% (resp. 99 ± 1%) detection efficiency of \(\left|\uparrow \right\rangle \) (resp. \(\left|\downarrow \right\rangle \)). These data correspond to a 6 × 6 array.
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Bornet, G., Emperauger, G., Chen, C. et al. Scalable spin squeezing in a dipolar Rydberg atom array. Nature 621, 728–733 (2023). https://doi.org/10.1038/s41586-023-06414-9
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DOI: https://doi.org/10.1038/s41586-023-06414-9
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