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Quasiparticle engineering and entanglement propagation in a quantum many-body system

Abstract

The key to explaining and controlling a range of quantum phenomena is to study how information propagates around many-body systems. Quantum dynamics can be described by particle-like carriers of information that emerge in the collective behaviour of the underlying system, the so-called quasiparticles1. These elementary excitations are predicted to distribute quantum information in a fashion determined by the system’s interactions2. Here we report quasiparticle dynamics observed in a quantum many-body system of trapped atomic ions3,4. First, we observe the entanglement distributed by quasiparticles as they trace out light-cone-like wavefronts5,6,7,8,9,10,11. Second, using the ability to tune the interaction range in our system, we observe information propagation in an experimental regime where the effective-light-cone picture does not apply7,12. Our results will enable experimental studies of a range of quantum phenomena, including transport13,14, thermalization15, localization16 and entanglement growth17, and represent a first step towards a new quantum-optic regime of engineered quasiparticles with tunable nonlinear interactions.

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Figure 1: Quantum dynamics in a one-dimensional spin chain following a local quench.
Figure 2: Measured quantum dynamics in a seven-ion system following local and global quenches.
Figure 3: Entanglement distribution following a local quench.
Figure 4: Measured quantum dynamics for increasing spin–spin interaction ranges.

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Acknowledgements

We acknowledge discussions with L. Tagliacozzo, M. Heyl, A. Gorshkov and S. Bose. This work was supported by the Austrian Science Fund (FWF) under grant number P25354-N20, and by the European Commission via the integrated project SIQS and by the Institut für Quanteninformation. We also acknowledge support from the European Research Council through the CRYTERION Project (number 227959).

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Contributions

P.H., B.P.L. and C.F.R. developed the research, based on theoretical ideas conceived with P.Z.; P.J., B.P.L., C. H. and C.F.R. performed the experiments; B.P.L., P.J., C.F.R. and P.H. analysed the data and carried out numerical simulations. P.J., C.H., B.P.L., R.B. and C.F.R. contributed to the experiment; B.P.L., C.F.R., P.H., P.Z. and R.B. wrote the manuscript; all authors contributed to discussions of the results and of the manuscript.

Corresponding author

Correspondence to C. F. Roos.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Quantum dynamics following local quenches in a seven-ion (seven-spin) system.

ac, Time evolution of the spatially resolved magnetization (colour coded as in Fig. 2) for three different local quenches. In each panel measured data (left-hand side) is shown next to theoretical calculations for the ideal case (right-hand side). a and d, Quench at the centre spin, α ≈ 1.36; b and e, quench at the leftmost spin, α ≈ 1.36; c and f, quench at both ends of the chain, α ≈ 1.75. Theoretical calculations employ measured laser–ion coupling strengths and distribution across the ion chain.

Extended Data Figure 2 Quantum dynamics following a global quench in a seven-ion (seven-spin) system.

a, Measured correlation matrices with elements (colour coded) at t = 0 ms, 5 ms, and 10 ms (α ≈ 1.75). b, Measured average magnetic spin–spin correlations (colour coded) as a function of time and distance n where the average was taken over all spin pairs (i, j) with |i − j| = n. c, Calculated spin–spin correlations (colour code: note the different colour scale) as a function of time and distance.

Extended Data Figure 3 Entanglement distributed by quasiparticles.

Following a quench of the central spin with short-range interactions (α ≈ 1.75), a distinct wavefront emerges. Each panel shows data (left-hand side) and theory (right-hand side) a, Measured single-spin magnetization (colour coded as in Fig. 2). b, Single-spin von Neumann entropy −Tr(ρlog(ρ)) normalized to one, derived from measured density matrices. Zero would correspond to a fully pure quantum state (black) and one (white) to a fully mixed state. The increase in entropy of any individual spin during the dynamics reflects the generation of entanglement with other spins. c, Real part of the tomographically reconstructed full density matrix of spins 3 and 5 at a time 9 ms after the quench. Imaginary parts are less than 0.03. The fidelity between the full experimentally reconstructed ρ and ideal state |ψ〉 is F = 0.975 ± 0.005, using .

Extended Data Figure 4 Quantum dynamics following a local quench in a 15-ion (15-spin) system.

a–c, Experimentally measured time evolution of (as in Fig. 4a–c). d–f, Theoretical calculations based on a measured spin–spin interaction matrix (such as presented in Fig. 1b). h–i, Theoretical calculations using , with and α extracted from a fit to the measured dispersion relation. All theory calculations are done in the single-excitation subspace. j–l, Magnetization of symmetric pairs around the centre ion as a function of time: blue, ions 7 and 9; cyan, ions 6 and 10; purple, ions 5 and 11); red, ions 4 and 12; black, ions 3 and 13. The dashed lines are Gaussian fits to the measured arrival time of the first quasiparticle maximum (from ac). m–o, Excluding the outermost ion to reduce finite-size effects, the fitted measured arrival maxima (circles) trace approximately a straight line when plotted against distance from quench site. A linear fit (solid line) yields an estimate for the propagation speed of the first quasiparticle maximum.

Extended Data Figure 5 Example of a spin–spin interaction matrix Jij.

The plot compares theory and experiment. Each element of the Jij matrix is measured directly (see Methods) in a system of N = 7 spins (solid coloured bars). Overlaid transparent bars with blue edges correspond to the results of a simulation which takes the following experimental parameters into account: the trapping frequencies; frequency of the bichromatic laser beams (see Methods); and measured individual laser–ion Rabi frequencies. The experimental data shown here are the same as in Fig. 1c. The elements J16, J27 and J17 were not measured. Small black vertical lines show one standard deviation in the experimentally measured elements.

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Jurcevic, P., Lanyon, B., Hauke, P. et al. Quasiparticle engineering and entanglement propagation in a quantum many-body system. Nature 511, 202–205 (2014). https://doi.org/10.1038/nature13461

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