Geometrical pumping with a Bose-Einstein condensate
We realized a quantum "charge" pump for a Bose-Einstein condensate (BEC) in a 1D bipartite magnetic lattice, whose bands are characterized by non-trivial topological invariants: the Zak phases.
For each band, the Zak phase is determined by that band's aggregate Berry curvature, a geometric quantity defined at each crystal momentum. We probed this Berry curvature in an adiabatic charge pump experiment, by periodically driving the system. Our BEC occupied just a single crystal momentum state, allowing us to access its band's local geometry. For each pump cycle we observed an overall displacement (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. The non-quantized displacement of the BEC is solely determined by the underlying Berry curvature, differing from that of the lattice motion in our periodic drive.
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