Multi-component quantum gases in spin-dependent hexagonal lattices


In solid-state materials, the static and dynamic properties as well as the magnetic and electronic characteristics are crucially influenced by the crystal symmetry. Hexagonal structures play a particularly important role and lead to novel physics, such as that of carbon nanotubes or graphene. Here we report on the realization of ultracold atoms in a spin-dependent optical lattice with hexagonal symmetry. We show how the combined effects of the lattice and interactions between atoms lead to a forced antiferromagnetic Néel order when two spin-components localize at different lattice sites. We also demonstrate that the coexistence of two components—one Mott-insulating and the other one superfluid—leads to an interaction-induced modulation of the superfluid density, which is observed spectroscopically. Our studies reveal the vast impact of the interaction-induced modulation on the superfluid-to-Mott-insulator transition. The observations are consistent with theoretical predictions using Gutzwiller mean-field theory.

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Figure 1: Spin-dependent hexagonal lattice.
Figure 2: Microwave spectroscopy measurements.
Figure 3: Superfluid order parameter at σ+ and σ lattice sites.
Figure 4: Superfluid-to-Mott-insulator transition for pure and mixed atomic spin-states.
Figure 5: Phase diagram of the multi-component Bose–Hubbard model.


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We thank D-S. Lühmann and A. Eckardt for stimulating discussions. The work has been performed within the Excellence Cluster Frontiers in Quantum Photon Science, which is supported by the Joachim Herz Stiftung. Moreover, we thank the Deutsche Forschungsgemeinschaft DFG for financial support within the Forschergruppe FOR801 and the GRK 1355. Support by the Spanish MICINN (FIS2008-00784 and Consolider QOIT), the Alexander von Humboldt foundation, Caixa Manresa, ERC grant QUAGATUA, EU STREP NAMEQUAM, and by the EU Integrated Project AQUTE are gratefully acknowledged. M.L. acknowledges support by the Hamburger Preis für Theoretische Physik.

Author information

The experimental work and data analysis were done by P.S-P., J.S., A.B., W.P., G.M., C.B., P.W. and K.S. Theoretical calculations using the Gutzwiller mean-field theory were done by P.H. and M.L. All authors contributed to the written text.

Correspondence to K. Sengstock.

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Soltan-Panahi, P., Struck, J., Hauke, P. et al. Multi-component quantum gases in spin-dependent hexagonal lattices. Nature Phys 7, 434–440 (2011).

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