Topology from Quantum Dynamics of Ultracold Atoms

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Reid, Graham Hair
Rolston, Steven L
Spielman, Ian B
Ultracold atoms are a versatile platform for studying quantum physics in the lab. Usingcarefully chosen external fields, these systems can be engineered to obey a wide range of effective Hamiltonians, making them an ideal system for quantum simulation experiments studying exotic forms of matter. In this work, we describe experiments using 87Rb Bose–Einstein condensates (BECs) to study exotic topological matter based on out-of-equilibrium effects. The topological states are prepared through the quantum dynamics of the ultracold atom system subjected to a highly tunable lattice potential described by the bipartite Rice–Mele (RM) model, created by combining dressing from a radiofrequency (RF) magnetic field and laser fields driving Raman transitions. We describe a form of crystal momentum-resolved quantum state tomography, which functions by diabatically changing the lattice parameters, used to reconstruct the full pseudospin quantum state. This allows us to calculate topological invariants characterizing the system. We apply these techniques to study out-of-equilibrium states of our lattice system, described by various combinations of sublattice, time-reversal and particle-hole symmetry. Afterquenching between lattice configurations, we observe the resulting time-evolution and follow the Zak phase and winding number. Depending on the symmetry configuration, the Zak phase may evolve continuously. In contrast, the winding number may jump between integer values when sublattice symmetry is transiently present in the time-evolving state. We observe a scenario where the winding number changes by ±2, yielding values that are not present in the native RM Hamiltonian. Finally, we describe a modulation protocol in which the configuration of the bipartite latticeis periodically switched, resulting in the Floquet eigenstates of the system having pseudospin-momentum locked linear dispersion, analogous to massless particles described by the Dirac equation. We modulate our lattice configuration to experimentally realize the Floquet system and quantify the drift velocity associated with the bands at zero crystal momentum. The linear dispersion of Floquet bands derives from nontrivial topology defined over the micromotion of the system, which we measure using our pseudospin quantum state tomography, in very good agreement with theory.