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Microscopy of the interacting Harper–Hofstadter model in the two-body limit


The interplay between magnetic fields and interacting particles can lead to exotic phases of matter that exhibit topological order and high degrees of spatial entanglement1. Although these phases were discovered in a solid-state setting2,3, recent innovations in systems of ultracold neutral atoms—uncharged atoms that do not naturally experience a Lorentz force—allow the synthesis of artificial magnetic, or gauge, fields4,5,6,7,8,9,10. This experimental platform holds promise for exploring exotic physics in fractional quantum Hall systems, owing to the microscopic control and precision that is achievable in cold-atom systems11,12. However, so far these experiments have mostly explored the regime of weak interactions, which precludes access to correlated many-body states4,13,14,15,16,17. Here, through microscopic atomic control and detection, we demonstrate the controlled incorporation of strong interactions into a two-body system with a chiral band structure. We observe and explain the way in which interparticle interactions induce chirality in the propagation dynamics of particles in a ladder-like, real-space lattice governed by the interacting Harper–Hofstadter model, which describes lattice-confined, coherently mobile particles in the presence of a magnetic field18. We use a bottom-up strategy to prepare interacting chiral quantum states, thus circumventing the challenges of a top-down approach that begins with a many-body system, the size of which can hinder the preparation of controlled states. Our experimental platform combines all of the necessary components for investigating highly entangled topological states, and our observations provide a benchmark for future experiments in the fractional quantum Hall regime.

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Figure 1: Strongly interacting atoms in a gauge field.
Figure 2: Schematic of the experiments.
Figure 3: Single-particle chiral dynamics and band structure.
Figure 4: Interacting chiral trajectories.
Figure 5: Physical mechanism for chirality with interactions.


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We acknowledge conversations with M. Aidelsburger, I. Cirac, E. Demler, M. Endres, M. Foss-Feig, N. Gemelke, D. Greif, W. Ketterle, R. Ma, H. C. Po, J. Simon and A. Vishwanath. We are supported by grants from the National Science Foundation, the Gordon and Betty Moore Foundation’s EPiQS Initiative, an Air Force Office of Scientific Research MURI programme, an Army Research Office MURI programme and the NSF Graduate Research Fellowship Program (M.R.).

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M.E.T., A.L., M.R., R.S., P.M.P. and A.M.K. contributed to constructing the experiment, collecting and analysing the data, and writing the manuscript. F.G. and T.M. contributed to analysing the data and writing the manuscript. D.B. developed the short-time analytic result. M.G. supervised the work.

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Correspondence to Markus Greiner.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks L. LeBlanc and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Tai, M., Lukin, A., Rispoli, M. et al. Microscopy of the interacting Harper–Hofstadter model in the two-body limit. Nature 546, 519–523 (2017).

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