Abtract:

"Ultracold atoms in optical lattices provide a unique setting for experimentally studying concepts that lie at the heart of theoretical condensed matter physics, but are out of reach of current condensed matter experiments. Here we focus on using a Bose-Einstein condensate (BEC) to realize a geometric pump in a new bipartite magnetic lattice [1] and visualize the edge states of a synthetic lattice in the quantum Hall regime [2]. In the geometric pump experiment, the magnetic lattice is characterized by non-trivial topological invariants for its bands: the Zak phases. For each band, the Zak phase is determined by that band's integrated Berry curvature, a geometric quantity defined at each crystal momentum. We probed this Berry curvature by periodically and adiabatically driving the system (a ``charge'' pump experiment). Unlike topological charge pumps in filled bands that yield quantized pumping, our BEC occupied just a single crystal momentum state allowing us to access its band's local geometry. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wavepacket's position in each unit cell, i.e., the polarization. Our magnetic lattice enabled us to observe this modulation by measuring the BEC's magnetization. While our periodic drive shifted the lattice potential by one unit cell per cycle, the displacement of the BEC, solely determined by the underlying Berry curvature, was always less than the lattice's displacement. In the second experiment, we engineered an effective magnetic field in a two-dimensional lattice with an elongated strip geometry, consisting of the sites of an optical lattice in the long direction and three internal atomic spin states in the short direction. We imaged the localized static states of BECs in this strip; by exciting dynamics, we further observed the skipping orbits of excited atoms traveling down the system’s edges, analogous to edge magnetoplasmons in two-dimensional electron systems."

[1] Lu et al., arXiv:1508.04480 (2015).
[2] Stuhl et al., arXiv:1502.02496 (2015).