Landau Levels in Strained Optical Lattices

Abstract

We propose a hexagonal optical lattice system with spatial variations in the hopping matrix elements. Just like in the valley Hall effect in strained Graphene, for atoms near the Dirac points the variations in the hopping matrix elements can be described by a pseudo-magnetic field and result in the formation of Landau levels. We show that the pseudo-magnetic field leads to measurable experimental signatures in momentum resolved Bragg spectroscopy, Bloch oscillations, cyclotron motion, and quantization of in-situ densities. Our proposal can be realized by a slight modification of existing experiments. In contrast to previous methods, pseudo-magnetic fields are realized in a completely static system avoiding common heating effects and therefore opening the door to studying interaction effects in Landau levels with cold atoms.

5 pages, 3 figures

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• Geometric characterization of anomalous Landau levels of isolated flat bands
• Pseudo-Landau levels of Bogoliubov quasiparticles in strained nodal superconductors
• Strain and pseudo-magnetic fields in optical lattices from density-assisted tunneling
• Two-dimensional optical quasicrystal potentials for ultracold atom experiments
• RKKY Interactions in Graphene Landau Levels
• Unification of valley and anomalous Hall effects in a strained lattice
• Magnetic Phases in Periodically Rippled Graphene
• Topological phonons in arrays of ultracold dipolar particles
• Emulating topological currents arising from a dipolar parity anomaly in two-dimensional optical lattices
• Fractional quantum Hall states of dipolar fermions in a strained optical lattice
• Quantized valley Hall response from local bulk density variations
• Nodal semimetals in $d\ge 3$ to sharp pseudo-Landau levels by dimensional reduction