Scalable spin squeezing in a dipolar Rydberg atom array

Nature (2023)Cite this article

Metrics details

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.

This is a preview of subscription content, access via your institution

Access Nature and 54 other Nature Portfolio journals

Get Nature+, our best-value online-access subscription

$29.99 / 30 days

cancel any time

Subscribe to this journal

Receive 51 print issues and online access

$199.00 per year

only $3.90 per issue

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

The data are available from the corresponding author on reasonable request.

Giovannetti, V., Lloyd, S. & Maccone, L. Advances in quantum metrology. Nat. Photon. 5, 222–229 (2011).

Article ADS CAS Google Scholar

Pezzè, L., Smerzi, A., Oberthaler, M. K., Schmied, R. & Treutlein, P. Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 (2018).

Article ADS MathSciNet Google Scholar

Wineland, D. J., Bollinger, J. J., Itano, W. M., Moore, F. L. & Heinzen, D. J. Spin squeezing and reduced quantum noise in spectroscopy. Phys. Rev. A 46, R6797–R6800 (1992).

Article ADS CAS PubMed Google Scholar

Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138–5143 (1993).

Article ADS CAS PubMed Google Scholar

Ma, J., Wang, X., Sun, C. & Nori, F. Quantum spin squeezing. Phys. Rep. 509, 89–165 (2011).

Article ADS MathSciNet CAS Google Scholar

Perlin, M. A., Qu, C. & Rey, A. M. Spin squeezing with short-range spin-exchange interactions. Phys. Rev. Lett. 125, 223401 (2020).

Article ADS CAS PubMed Google Scholar

Comparin, T., Mezzacapo, F. & Roscilde, T. Robust spin squeezing from the tower of states of U(1)-symmetric spin Hamiltonians. Phys. Rev. A 105, 022625 (2022).

Article ADS MathSciNet CAS Google Scholar

Comparin, T., Mezzacapo, F., Robert-de Saint-Vincent, M. & Roscilde, T. Scalable spin squeezing from spontaneous breaking of a continuous symmetry. Phys. Rev. Lett. 129, 113201 (2022).

Article ADS CAS PubMed Google Scholar

Comparin, T., Mezzacapo, F. & Roscilde, T. Multipartite entangled states in dipolar quantum simulators. Phys. Rev. Lett. 129, 150503 (2022).

Article ADS CAS PubMed Google Scholar

Block, M. et al. A universal theory of spin squeezing. Preprint at https://arxiv.org/abs/2301.09636 (2023).

Tse, M. et al. Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy. Phys. Rev. Lett. 123, 231107 (2019).

Article ADS CAS PubMed Google Scholar

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

Article ADS CAS PubMed MATH Google Scholar

Pedrozo-Peñafiel, E. et al. Entanglement on an optical atomic-clock transition. Nature 588, 414–418 (2020).

Article ADS PubMed Google Scholar

Robinson, J. M. et al. Direct comparison of two spin squeezed optical clocks below the quantum projection noise limit. Preprint at https://arxiv.org/abs/2211.08621 (2022).

Foss-Feig, M., Gong, Z.-X., Gorshkov, A. V. & Clark, C. W. Entanglement and spin-squeezing without infinite-range interactions. Preprint at https://arxiv.org/abs/1612.07805 (2016).

Gil, L. I. R., Mukherjee, R., Bridge, E. M., Jones, M. P. A. & Pohl, T. Spin squeezing in a Rydberg lattice clock. Phys. Rev. Lett. 112, 103601 (2014).

Article ADS CAS PubMed Google Scholar

Young, J. T., Muleady, S. R., Perlin, M. A., Kaufman, A. M. & Rey, A. M. Enhancing spin squeezing using soft-core interactions. Phys. Rev. Res. 5, L012033 (2023).

Article CAS Google Scholar

Roscilde, T., Comparin, T. & Mezzacapo, F. Entangling dynamics from effective rotor/spin-wave separation in U(1)-symmetric quantum spin models. Preprint at https://arxiv.org/abs/2302.09271 (2023).

Yan, B. et al. Observation of dipolar spin-exchange interactions with lattice-confined polar molecules. Nature 501, 521–525 (2013).

Article ADS CAS PubMed Google Scholar

Bao, Y. et al. Dipolar spin-exchange and entanglement between molecules in an optical tweezer array. Preprint at https://arxiv.org/abs/2211.09780 (2022).

Holland, C. M., Lu, Y. & Cheuk, L. W. On-demand entanglement of molecules in a reconfigurable optical tweezer array. Peprint at https://arxiv.org/abs/2210.06309 (2022).

Christakis, L. et al. Probing site-resolved correlations in a spin system of ultracold molecules. Nature 614, 64–69 (2023).

Article ADS CAS PubMed Google Scholar

Wolfowicz, G. et al. Quantum guidelines for solid-state spin defects. Nat. Rev. Mater. 6, 906–925 (2021).

Article ADS CAS Google Scholar

de Léséleuc, S., Barredo, D., Lienhard, V., Browaeys, A. & Lahaye, T. Optical control of the resonant dipole-dipole interaction between Rydberg atoms. Phys. Rev. Lett. 119, 053202 (2017).

Article ADS PubMed Google Scholar

Chen, C. et al. Continuous symmetry breaking in a two-dimensional Rydberg array. Nature 616, 691–695 (2023).

Article ADS CAS PubMed Google Scholar

Geier, S. et al. Floquet Hamiltonian engineering of an isolated many-body spin system. Science 374, 1149–1152 (2021).

Article ADS CAS PubMed Google Scholar

Scholl, P. et al. Microwave engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms. PRX Quantum 3, 020303 (2022).

Article ADS Google Scholar

Scholl, P. et al. Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms. Nature 595, 233–238 (2021).

Article ADS CAS PubMed Google Scholar

Browaeys, A. & Lahaye, T. Many-body physics with individually controlled Rydberg atoms. Nat. Phys. 16, 132–142 (2020).

Article CAS Google Scholar

Wineland, D. J., Bollinger, J. J., Itano, W. M. & Heinzen, D. J. Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A 50, 67–88 (1994).

Article ADS CAS PubMed Google Scholar

Sørensen, A., Duan, L.-M., Cirac, J. I. & Zoller, P. Many-particle entanglement with Bose–Einstein condensates. Nature 409, 63–66 (2001).

Article ADS PubMed Google Scholar

Sørensen, A. S. & Mølmer, K. Entanglement and extreme spin squeezing. Phys. Rev. Lett. 86, 4431–4434 (2001).

Article ADS PubMed Google Scholar

Estéve, J., Gross, C., Weller, A., Giovanazzi, S. & Oberthaler, M. K. Squeezing and entanglement in a Bose-Einstein condensate. Nature 455, 1216–1219 (2008).

Article ADS PubMed Google Scholar

Riedel, M. F. et al. Atom-chip-based generation of entanglement for quantum metrology. Nature 464, 1170–1173 (2010).

Article ADS CAS PubMed Google Scholar

Roscilde, T., Mezzacapo, F. & Comparin, T. Spin squeezing from bilinear spin-spin interactions: two simple theorems. Phys. Rev. A 104, L040601 (2021).

Article ADS MathSciNet CAS Google Scholar

Anderson, P. W. An approximate quantum theory of the antiferromagnetic ground state. Phys. Rev. 86, 694–701 (1952).

Article ADS CAS MATH Google Scholar

Anderson, P. W. Basic Notions Of Condensed Matter Physics 1st edn (Westview Press/Addison-Wesley, 1997).

Roscilde, T., Comparin, T. & Mezzacapo, F. Rotor/spin-wave theory for quantum spin models with U(1) symmetry. Preprint at https://arxiv.org/abs/2303.00380 (2023).

Pezzé, L. & Smerzi, A. Entanglement, nonlinear dynamics, and the Heisenberg limit. Phys. Rev. Lett. 102, 100401 (2009).

Article ADS MathSciNet PubMed Google Scholar

Muessel, W. et al. Twist-and-turn spin squeezing in Bose-Einstein condensates. Phys. Rev. A 92, 023603 (2015).

Article ADS Google Scholar

Sorelli, G., Gessner, M., Smerzi, A. & Pezzè, L. Fast and optimal generation of entanglement in bosonic Josephson junctions. Phys. Rev. A 99, 022329 (2019).

Article ADS CAS Google Scholar

Waugh, J. S., Huber, L. M. & Haeberlen, U. Approach to high-resolution NMR in solids. Phys. Rev. Lett. 20, 180–182 (1968).

Article ADS CAS Google Scholar

Eckner, W. J. et al. Realizing spin squeezing with Rydberg interactions in a programmable optical clock. Preprint at https://arxiv.org/abs/2303.08078 (2023).

Hines, J. A. et al. Spin squeezing by Rydberg dressing in an array of atomic ensembles. Preprint at https://arxiv.org/abs/2303.08805 (2023).

Franke, J. et al. Quantum-enhanced sensing on an optical transition via emergent collective quantum correlations. Preprint at https://arxiv.org/abs/2303.10688 (2023).

Norcia, M. A., Young, A. W. & Kaufman, A. M. Microscopic control and detection of ultracold strontium in optical-tweezer arrays. Phys. Rev. X 8, 041054 (2018).

Google Scholar

Cooper, A. et al. Alkaline-earth atoms in optical tweezers. Phys. Rev. X 8, 041055 (2018).

CAS Google Scholar

Saskin, S., Wilson, J. T., Grinkemeyer, B. & Thompson, J D. Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array. Phys. Rev. Lett. 122, 143002 (2019).

Article ADS CAS PubMed Google Scholar

Madjarov, I. S. et al. An atomic-array optical clock with single-atom readout. Phys. Rev. X 9, 041052 (2019).

CAS Google Scholar

Young, A. W. et al. Half-minute-scale atomic coherence and high relative stability in a tweezer clock. Nature 588, 408–413 (2020).

Article ADS CAS PubMed Google Scholar

Barredo, D., de Léséleuc, S., Lienhard, V., Lahaye, T. & Browaeys, A. An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays. Science 354, 1021–1023 (2016).

Article ADS CAS PubMed Google Scholar

Kahanamoku-Meyer, G. D. & Wei, J. Gregdmeyer/dynamite: v.0.3.0. Zenodo https://doi.org/10.5281/zenodo.7622981 (2023).

Hauschild, J. & Pollmann, F. Efficient numerical simulations with tensor networks: tensor network Python (TeNPy). SciPost Phys. Lect. Notes https://scipost.org/10.21468/SciPostPhysLectNotes.5 (2018).

Download references

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.

These authors contributed equally: Guillaume Bornet, Gabriel Emperauger, Cheng Chen, Bingtian Ye, Maxwell Block

Charles Fabry Laboratory University of Paris-Saclay, Institute of Optics Graduate School, CNRS, Palaiseau Cedex, France

Guillaume Bornet, Gabriel Emperauger, Cheng Chen, Jamie A. Boyd, Daniel Barredo, Thierry Lahaye & Antoine Browaeys

Department of Physics, Harvard University, Cambridge, MA, USA

Bingtian Ye, Maxwell Block, Marcus Bintz & Norman Y. Yao

Nanomaterials and Nanotechnology Research Center (CINN-CSIC), University of Oviedo (UO), El Entrego, Spain

Daniel Barredo

Laboratory of Physics, University of Lyon, Ens de Lyon, CNRS, Lyon, France

Tommaso Comparin, Fabio Mezzacapo & Tommaso Roscilde

Department of Physics, University of California, Berkeley, CA, USA

Norman Y. Yao

Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

Norman Y. Yao

You can also search for this author in PubMed Google Scholar

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.

Correspondence to Cheng Chen.

A.B. and T.L. are cofounders and shareholders of PASQAL. The remaining authors declare no competing interests.

Nature thanks Joonhee Choi, Luming Duan and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

a, Schematics of the atomic levels relevant for the experiment. b, Sequence of optical and microwave pulses (not to scale) used for all the experiments reported in Figs. 1, 2 and 3 of the main text.

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.

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.

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.

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.

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

Bornet, G., Emperauger, G., Chen, C. et al. Scalable spin squeezing in a dipolar Rydberg atom array. Nature (2023). https://doi.org/10.1038/s41586-023-06414-9

Download citation

Received: 14 March 2023

Accepted: 07 July 2023

Published: 30 August 2023

DOI: https://doi.org/10.1038/s41586-023-06414-9

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.