Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms

By M. Aidelsburger, M. Lohse, C. Schweizer, M. Atala, J. Barreiro, Sylvain Nascimbene, N. Cooper, I. Bloch, Nathan Goldman. Nature Physics, 2014

833 citations recorded by the source corpus.

Chern numbers characterize the quantum Hall effect conductance—non-zero values are associated with topological phases. Previously only spotted in electronic systems, they have now been measured in ultracold atoms subject to artificial gauge fields. Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic metals1. A striking manifestation of this transverse transport was then revealed in the quantum Hall effect2 where the plateaux depicted by the Hall conductivity were attributed to a topological invariant characterizing the Bloch bands: the Chern number3. Until now, topological transport associated with non-zero Chern numbers has only been observed in electronic systems2,4,5. Here we use the transverse deflection of an atomic cloud in response to an optical gradient to measure the Chern number of artificially generated Hofstadter bands6. These topological bands are very flat and thus constitute good candidates for the realization of fractional Chern insulators7. Combining these deflection measurements with the determination of the band populations, we obtain an experimental value for the Chern number of the lowest band νexp = 0.99(5). This first Chern-number measurement in a non-electronic system is facilitated by an all-optical artificial gauge field scheme, generating uniform flux in optical superlattices.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/2ebca9b75a905f1d8b662d88e9cc917940cd37ec

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Citations in the corpus

Artificial gauge fields in materials and engineered systems (2017, positive): “This led to the observation of chiral Meissner-like currents in bosonic flux ladders [171], but also to the first cold-atom measurement of the topologically-invariant Chern number [67], which was achieved by loading bosonic atoms into the lowest Hofstadter band for α = 1/4; this topological transpor”
Topological Phases of Non-Hermitian Systems (2018, background): “The potential gradient can be made from an optical dipole force via an additional laser beam [16] and may be chosen to be, e.”
Topological bands for ultracold atoms (2018, positive): “14(c) by using the staggered potential inside individual four-site plaquettes and laserinduced hopping to establish tunneling along all the lattice directions, enabling the measurement of the Chern number (Aidelsburger et al., 2015); see Sec.”
Topological photonics (2018, background): “, 1982; Xiao, Chang, and Niu, 2010) and to recent experiments with ultracold atoms (Aidelsburger et al., 2015), the spatial displacement of the center of mass of the light intensity distribution then provides information on the Chern number of the band.”
Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport (2016, background): “electronic systems; rather, it is universal: it was recently demonstrated for photons [9–11], cold atoms [12,13], mechanical systems [14,15], and was also predicted for”
Symmetry and Topology in Non-Hermitian Physics (2018, background): “[200] M.”
Topological insulator laser: Theory (2018, background): “Topological protection is now known to be a ubiquitous phenomenon, occurring in physical settings as varied as electromagneticwaves (6, 11–16), cold atoms (17, 18), and acoustic, mechanical, and elastic systems (19–22).”