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Domain-wall confinement and dynamics in a quantum simulator


Particles subject to confinement experience an attractive potential that increases without bound as they separate. A prominent example is colour confinement in particle physics, in which baryons and mesons are produced by quark confinement. Confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. Here we report the observation of magnetic domain-wall confinement in interacting spin chains with a trapped-ion quantum simulator. By measuring how correlations spread, we show that confinement can suppress information propagation and thermalization in such many-body systems. We quantitatively determine the excitation energy of domain-wall bound states from the non-equilibrium quench dynamics. We also study the number of domain-wall excitations created for different quench parameters, in a regime that is difficult to model with classical computers. This work demonstrates the capability of quantum simulators for investigating high-energy physics phenomena, such as quark collision and string breaking.

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Fig. 1: Effective confining potential and experiment sequence.
Fig. 2: Confinement dynamics at B/J0 ≈ 0.75, L = 11.
Fig. 3: Low-energy excited states.
Fig. 4: Number of domain walls in two dynamical regimes.

Data availability

The data presented in the figures of this Article are available from the corresponding authors upon reasonable request.

Code availability

All custom code used to support claims and analyse data presented in this Article is available from the corresponding authors upon reasonable request.


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We thank D. A. Abanin, P. Bienias, P. Calabrese, M. Dalmonte, Z. Davoudi, A. Deshpande, A. Gambassi, M. Heyl, A. Lerose, J. Preskill, A. Silva, P. Titum and R. Verdel for enlightening discussions. This work was supported by the NSF PFCQC STAQ programme, the AFOSR MURIs on Quantum Measurement/Verification, the ARO MURI on Modular Quantum Systems, the AFOSR and ARO QIS and AMO Programmes, the DARPA DRINQS programme, DOE BES award number DE-SC0019449, DOE HEP award number DE-SC0019380 and the NSF QIS programme. F.L. also acknowledges support from the Ann G. Wylie Dissertation Fellowship of the University of Maryland. Specific product citations are for the purpose of clarification only, and are not an endorsement by the authors or NIST.

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Authors and Affiliations



F.L. and G.P. suggested the research topic. W.L.T., P.B., G.P., K.S.C., A.D., L.F., H.B.K., A.K., W.M. and C.M. contributed to the experimental design, construction, data collection and analysis. F.L., R.L., S.W., K.S.C., W.L.T., P.B. and G.P. carried out numerical simulations. F.L., R.L., S.W. and A.V.G. provided theoretical support. All authors contributed to the discussion of the results and the manuscript.

Corresponding authors

Correspondence to W. L. Tan or P. Becker.

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Competing interests

C.M. is Co-Founder and Chief Scientist at IonQ, Inc.

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Peer review informationNature Physics thanks Roee Ozeri and other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Evolution of domain wall population.

Experimental data of evolution of the number of domain walls \(\left\langle {\mathcal{N}}\right\rangle\) during a quench of Hamiltonian (1) with B/J0 ≈ 10 for multiple system sizes. The shaded area indicates when \(\left\langle {\mathcal{N}}\right\rangle\) converges to a steady state and before qubit dephasing occurs.

Extended Data Fig. 2 Bit-flip error numerical study in L = 11 chain for dynamical regimes investigation.

Red dots show the L = 11 data displayed in Fig. 4a. The blue line illustrates the numerical value of \(\langle {\mathcal{N}}\rangle\) with increasing B-field, taking bit-flip error into account. We found that a bit-flip error per ion of 2.47% in the numerical calculation matches the experimental data well. The most notable effect of bit-flip errors is an increase in the number of domain walls at B/J0 = 0 (see Fig. 4a for comparison with the zero bit-flip error numerical predictions).

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Supplementary Figs. 1–6 and discussion..

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Tan, W.L., Becker, P., Liu, F. et al. Domain-wall confinement and dynamics in a quantum simulator. Nat. Phys. 17, 742–747 (2021).

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