Project Details
Projekt
Floquet engineering and control of topological optical-lattice systems
Applicant
Professor Dr. André Eckardt
Subject Area
Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
Term
from 2016 to 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 277974659
Recently, we saw tremendous progress in realizing artificial magnetic fields and topological band structures in optical lattices. This led, inter alia, to the observation of a quantized Hall response, the measurement of Chern numbers from the far-from equilibrium dynamics, and the detection of chiral edge modes. These studies are motivated by the unique properties of atomic quantum gases, which are complementary to those of electronic systems. These include the possibility to cleanly realize highly tunable minimal lattice models,single-lattice-site resolution for measuring and manipulating atoms, and the ability to study coherent many-body dynamics given by theexcellent isolation in combination with the capability to manipulate these systems on their intrinsic time scales. The latter is also used forthe creation of strong artificial magnetic fields (of up to a flux quantum per plaquette) via time-periodic driving (Floquet engineering).Extending these studies to interacting topological systems, is an important goal, for which we will address the following problems:Disorder-induced (many-body) localization is proposed as a way to suppress driving-induced heating and can induce also topologicallynon-trivial states (topological Anderson insulators). These effects were described, however, using low-energy models. Their robustnessagainst heating via multi-photon transitions to excited lattice bands is an open question, which we wish to address. Another strategy tocounteract driving-induced heating is the coupling to a bath, given, e.g., by a second atomic species. Therefore, we will investigate open Floquet systems and their non-equilibrium steady states. To this end, we will work out, how to use efficient quantum-trajectory simulations also beyond the typical secular approximation for very weak systembath coupling, which is hard to justify for Floquet systems. It is one question, whether a certain topological state can be stabilized as ground-state of an (approximate) Floquet Hamiltonian. Of equal importance is, however, also how this state can be prepared and probed. We will, therefore, study optimal preparation protocols for fractional Chern insulators and schemes for probing their fractional quasiparticle statistics. This includes also the study of magnetic-field ramps, which, so far, have not been implemented in optical lattices.We will numerically investigate the impact of interactions on the measurement of topological invariants, including also the winding numbers that characterize anomalous Floquet topological insulators beyond their Chern numbers. For an analytical description of these systems, we will also employ flow equations in Floquet space. Finally, we plan to derive lattice models for the recently proposed traid anyons and work out schemes for their quantum-gas implementation via engineering. We will pursue these goals in close collaboration with other experimental and theory teams of the Research Unit.
DFG Programme
Research Units
