Quantum simulation of antiferromagnetic spin chains in an optical lattice

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Abstract

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications for systems ranging from high-temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers, owing to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we use a degenerate Bose gas of rubidium atoms confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary a magnetic field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase, the interaction between the spins is overwhelmed by the applied field, which aligns the spins. In the antiferromagnetic phase, the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, thereby improving our understanding of real magnetic materials.

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Figure 1: Spin model and its phase diagram.
Figure 2: Tilted Hubbard model and mapping to spin model.
Figure 3: Probing the paramagnet to antiferromagnet phase transition.
Figure 4: Effect of harmonic confinement.
Figure 5: Site-resolved transition in near-homogeneous Ising model.
Figure 6: Dynamics of antiferromagnetic domain formation.

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Acknowledgements

We thank E. Demler, W. Ketterle, T. Kitagawa, M.D. Lukin, S. Pielawa and S. Sachdev for discussions. This work was supported by the Army Research Office DARPA OLE programme, an AFOSR MURI programme, and by grants from the NSF.

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All authors contributed to the construction of the experiment, the collection and analysis of the data, and the writing of the manuscript.

Correspondence to Markus Greiner.

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The authors declare no competing financial interests.

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Simon, J., Bakr, W., Ma, R. et al. Quantum simulation of antiferromagnetic spin chains in an optical lattice. Nature 472, 307–312 (2011) doi:10.1038/nature09994

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