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Observation of string breaking on a (2 + 1)D Rydberg quantum simulator

Nature volume 642, pages 321–326 (2025)Cite this article

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Abstract

Lattice gauge theories (LGTs) describe a broad range of phenomena in condensed matter and particle physics. A prominent example is confinement, responsible for bounding quarks inside hadrons such as protons or neutrons1. When quark–antiquark pairs are separated, the energy stored in the string of gluon fields connecting them grows linearly with their distance, until there is enough energy to create new pairs from the vacuum and break the string. Although these phenomena are ubiquitous in LGTs, simulating the resulting dynamics is a challenging task2. Here we report the observation of string breaking in synthetic quantum matter using a programmable quantum simulator based on neutral atom arrays3,4,5. We show that a (2 + 1)-dimensional LGT with dynamical matter can be efficiently implemented when the atoms are placed on a Kagome geometry6, with a local U(1) symmetry emerging from the Rydberg blockade7. Long-range Rydberg interactions naturally give rise to a linear confining potential for a pair of charges, allowing us to tune both their masses and the string tension. We experimentally probe string breaking in equilibrium by adiabatically preparing the ground state of the atom array in the presence of defects, distinguishing regions within the confined phase dominated by fluctuating strings or by broken string configurations. Finally, by harnessing local control over the atomic detuning, we quench string states and observe string-breaking dynamics exhibiting a many-body resonance phenomenon. Our work provides opportunities for exploring phenomena in high-energy physics using programmable quantum simulators.

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Fig. 1: Emergent confinement and string breaking on a (2 + 1)D Rydberg atom array.
Fig. 2: String breaking in equilibrium.
Fig. 3: String-breaking dynamics.
Fig. 4: Many-body spectroscopy of string-breaking resonances.

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Acknowledgements

We thank H. Pichler, E. Zohar, R. Samajdar and G. Semeghini for their discussions. D.G.-C. acknowledges support from the European Union’s Horizon Europe program under the Marie Skłodowska Curie Action PROGRAM (grant 101150724). The Innsbruck team was supported by the Horizon Europe research and innovation programme of the European Union under grant agreement no. 101113690 (PASQuanS2.1). The experimental work was supported by the DARPA ONISQ programme (grant no. W911NF2010021) and the DARPA-STTR award (award no. 140D0422C0035). Work at Harvard was supported by the US Department of Energy (DOE Quantum Systems Accelerator Center, grant nos. DE-AC02-05CH11231 and DE-SC0021013). The QuEra team also acknowledges the support of Amazon Braket in developing and validating the local detuning capability on Aquila by providing machine time and their discussions with P. Kómár, M. Lin and D. Becker.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Innsbruck, Innsbruck, Austria

    Daniel González-Cuadra, Torsten V. Zache & Peter Zoller

  2. Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria

    Daniel González-Cuadra, Torsten V. Zache & Peter Zoller

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

    Daniel González-Cuadra & Mikhail D. Lukin

  4. Institute of Fundamental Physics, IFF-CSIC, Madrid, Spain

    Daniel González-Cuadra

  5. QuEra Computing, Boston, MA, USA

    Majd Hamdan, Boris Braverman, Milan Kornjača, Alexander Lukin, Sergio H. Cantú, Fangli Liu, Sheng-Tao Wang, Alexander Keesling & Alexei Bylinskii

  6. Department of Physics, University of Toronto, Toronto, Ontario, Canada

    Boris Braverman

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Contributions

D.G.-C., T.V.Z. and P.Z. developed the idea of studying the (2 + 1)D LGT with confinement in Rydberg atom arrays. D.G.-C., T.V.Z., B.B., M.K., A.L., F.L., S.-T.W., A.K., M.D.L. and A.B. proposed specific experiments in this study. M.H., B.B., S.H.C., A.L. and A.B. developed the local detuning control necessary for the experiments. M.H., B.B. and A.B. performed the experiments and took the data. D.G.-C., M.H., T.V.Z. and A.B. analysed the data. D.G.-C. and T.V.Z. performed numerical simulations. M.D.L., P.Z. and A.B. guided the work and managed the resources. All authors discussed the results and contributed to writing or reviewing the paper.

Corresponding authors

Correspondence to Daniel González-Cuadra or Alexei Bylinskii.

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Competing interests

M.H., B.B., M.K., A.L., S.H.C., F.L., S.W., A.K., M.D.L. and A.B. are shareholders of QuEra Computing and M.H., M.K., A.L., S.H.C., F.L., S.W., A.K. and A.B. are also employees of QuEra Computing. Other authors do not have any competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Experimental Hamiltonian evolution protocols.

a, Quasi-adiabatic state preparation used to obtain the ground state of the Rydberg Hamiltonian (1), where the local detuning (dashed tuquoise line) remains at zero throughout the sweep. b, Quasi-adiabatic state preparation with applied local detuning δ0(t) (dashed tuquoise line), which strongly shifts the atoms off resonance, ensuring they remain in their ground states throughout the global detuning sweep. By applying the appropriate local detuning pattern (e.g. the one shown in d), one can selectively prepare either one of the string states or the broken string state. c, Quasi-adiabatic state preparation followed by a quench in local detuning δ0 (dashed tuquoise line) that tensions the initially prepared string, such that the energies of the broken and unbroken string configurations become comparable. d, For the string breaking studies with d = 2 charge separation, the local detuning pattern applied is shown in open turquoise circles over the atom geometry. This same detuning pattern can be used to initially prepare the broken string state via the protocol described in b.

Extended Data Fig. 2 Experimentally prepared (2+1)D strings.

a–f, Classical string states (1) – (6) prepared in the Rydberg atom array using the quasi-adiabatic state preparation protocol assisted by local detuning patterns. The real-space average Rydberg occupation results are represented on the left, while the extracted corresponding LGT observables are represented on the right.

Extended Data Fig. 3 Decoherence due to thermal motion.

a, Thermal spread in the Rydberg-Rydberg interaction energy vs Rb/a for the different-order neighbours in the Kagome lattice (dark blue line: ∥x1 − x2∥ = a, turquoise line: ∥x1 − x2∥ = 31/2a, orange line: ∥x1 − x2∥ = 2a), showing the dominant effect from any blockade-violating states (dark blue line). b, Mean-field energy spreads of ideal string states (turquoise lines) and broken string states (orange lines) versus charge separation in the 1D geometries studied in Figs. 3 and 4. Solid lines show Rb/a = 1.2 where the dynamics data was taken, and dashed lines show Rb/a = 1.6, deep in the confined phase. The corresponding Rb/a values are marked as black dashed lines in a.

Extended Data Fig. 4 Single-atom coherence.

a, To measure the coherence of non-interacting atoms over the region used to arrange the atom array, a 5 × 4 rectangular grid of atoms is arranged instead, spaced by 21 μm. Open turquoise circles indicate atoms that have local detuning applied to them—all of them in these measurements. The grey arrow points to the atom for which \({T}_{2}^{Rabi}\) and \({T}_{2}^{Ramsey}\) results are shown in panel d. b, Single-atom coherence under drive is characterized by measuring resonant Rabi oscillations in the presence of local detuning (turquoise dashed line), with global detuning (dark blue line) chosen to be of equal magnitude in order to maintain resonance. The pulse duration τ is scanned to obtain Rabi oscillations in the Rydberg population, the decaying envelope of which is fit to an exponential to obtain \({T}_{2}^{Rabi}\) for each atom. c, Non-driven single-atom coherence is characterizeed by measuring a Ramsey fringe with local detuning (turqoise dashed line) applied during the dark time, and a large offset in the global detuning (dark blue line) applied to produce a high-frequency Ramsey fringe versus a scanned dark time τ. The envelope of the fringe is fit to an exponential in order to extract \({T}_{2}^{Ramsey}\) for each atom. The Rabi frequency amplitude (orange line) shows the resonant π/2 pulses before and after. d, Fitted values of \({T}_{2}^{Rabi}\) (dark blue) and \({T}_{2}^{Ramsey}\) (orange) versus the magnitude of the local detuning applied, for the atom highlighted with the grey arrow. The models that are fit to the data are descibed in the text.

Extended Data Fig. 5 String probabilities and blockade violations.

a–c, Time-evolved probabilities for string configurations after a quench to different values of the local detuning δ0/Ω. For each of them, we also show the probabilities for the intermediate states i and j depicted in Fig. 3a, as well as the three atomic configurations that violate the blockade constraint within the string (pv1, pv2 and pv3).

Extended Data Fig. 6 Broadening of string breaking resonances due to blockade violations in the final state.

a, Broken string probability peaks under aggressive spatial filtering for bitstring detection (left axis, orange data, fitted Gaussian width Δδ0/Ω = 0.88(5)), and under conservative spatial filtering (right axis, dark blue data, fitted Gaussian width Δδ0/Ω = 0.53(2)). b, For bitstring detection toward the final broken string state, the aggressive spatial filter includes all atoms in the orange box and the conservative spatial filter includes all atoms in the dark blue box. The expected configuration of Rydberg excitations in the broken string product state is shown by filled red circles. Error bars on experimental data correspond to a 68% confidence interval.

Extended Data Fig. 7 String breaking phase diagram for (1+1)D strings.

a,b, Real-space configuration for states with two states charges separated a distance d = 4, prepared with the global adiabatic protocol ending at Rb = 1.6, δ/Ω = 4.56 and Rb = 1.7, δ/Ω = 3.22, respectively, and consistent with an unbroken and broken strings. c,d, Unbroken (ps) and broken (pb) string probabilities, respectively, as a function of Rb and δ/Ω, obtained experimentally with the global quasi-adiabatic protocol. e,f, Corresponding theory phase diagram obtained from the ground state of the Rydberg Hamiltonian.

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González-Cuadra, D., Hamdan, M., Zache, T.V. et al. Observation of string breaking on a (2 + 1)D Rydberg quantum simulator. Nature 642, 321–326 (2025). https://doi.org/10.1038/s41586-025-09051-6

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