Topological Characterization of Periodically-Driven Quantum Systems

By Takuya Kitagawa, Erez Berg, Mark Rudner, E. Demler. 2010

890 citations recorded by the source corpus.

Topological properties of physical systems can lead to robust behaviors that are insensitive to microscopic details. Such topologically robust phenomena are not limited to static systems but can also appear in driven quantum systems. In this paper, we show that the Floquet operators of periodically driven systems can be divided into topologically distinct (homotopy) classes, and give a simple physical interpretation of this classification in terms of the spectra of Floquet operators. Using this picture, we provide an intuitive understanding of the well-known phenomenon of quantized adiabatic pumping. Systems whose Floquet operators belong to the trivial class simulate the dynamics generated by time-independent Hamiltonians, which can be topologically classified according to the schemes developed for static systems. We demonstrate these principles through an example of a periodically driven two--dimensional hexagonal lattice model which exhibits several topological phases. Remarkably, one of these phases supports chiral edge modes even though the bulk is topologically trivial.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a9dc9a101a2b8b2e08011692c77d7a95551456eb

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Engineered Open Systems and Quantum Simulations with Atoms and Ions (2012, background): “The ”loss” of topology at θ = θs can be viewed as a non-equilibrium topological phase transition(Rudner and Levitov, 2009; Lindner et al., 2011; Kitagawa et al., 2010) as a result of changing the Liouville parameters: θ = θs also implies a clos-”
Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice (2011, methodology): “Topological order could be achieved by introducing artificial gauge fields, either via Raman transitions [25] or time-dependent lattice modulation [26].”
Realization of an anomalous Floquet topological system with ultracold atoms (2020, methodology): “[25] using amplitude modulation.”
Periodic table for Floquet topological insulators (2016, background): “[30] Takuya Kitagawa, Erez Berg, Mark Rudner, and Eugene Demler, “Topological characterization of periodically driven quantum systems,” Phys.”
Topological bands for ultracold atoms (2018, positive): “One finds that finitesize systems can have protected edge states, at quasienergies between the bulk bands, even if the topological invariants constructed from the Floquet Hamiltonian ĤFq are trivial for all of the bulk energy bands (Kitagawa et al., 2010).”