Enormous magnetic fields with bosons in hybrid lattices

The integer quantum Hall effect (IQHE) is often described in terms of skipping orbits: 2-D electrons begin nascent cyclotron orbits, only to be interrupted by the material’s boundary, and instead reflect from the edge, beginning a partial orbit anew.  These classical skipping trajectories follow the systems boundary, and in the quantum limit connect to the quantum Hall system’s conducting edge channels.  Even though decades of measurements have confirmed this overall picture, the intrinsic difficulty of imaging electrons has precluded all attempts to image these orbits.

We have directly realized a cold-atom lattice in the extreme quantum limit, where each lattice plaquette contains about 4/3 of the quantum of flux: unthinkable in crystalline materials (where it would take 10_­⁴ T fields), but achievable using engineered tunneling phases in an optical lattice.  To achieve such fields, we use a hybrid lattice geometry, where one dimension of the lattice is a normal optical lattice and the other dimension is the internal hyperfine states of the atoms; this gives us perfect single-site imaging resolution along one dimension. We then dynamically prepared our ultracold bosons in several different initial states, which allowed us to observe edge and bulk properties in two ways: (1) we directly imaged the edge states (associated with quantized conductance in IQHE systems) and the localized bulk states (associated with the insulating bulk of IQHE systems); (2) we then created excitations, those on the edge were analogues to edge magnetoplasmons in quantum Hall systems and directly follow their chirally oriented skipping orbits.