Periodically Driven Quantum Systems: Effective Hamiltonians and Engineered Gauge Fields

By Nathan Goldman, J. Dalibard. 2014

683 citations recorded by the source corpus.

Topological effects can result from a material's intrinsic properties, or can be generated by external electromagnetic fields or mechanical deformations. Researchers analyze how driven quantum systems can lead to new topological states of matter.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4da44a520bfa6c3ad3dfe11c5a89457411693769

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Artificial gauge fields in materials and engineered systems (2017, neutral): “[55], the effective Hamiltonian Heff of such a “quantum walk” can be approximated by”
QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains (2016, methodology): “Such multi-spin operators are often times generated by the nested commutators typically appearing in higher-order terms of perturbative expansions, such as the Schrieffer-Wolff transformation [19–21] and the inverse-frequency expansion [22, 23].”
Floquet topological transitions in a driven one-dimensional topological insulator (2015, background): “…[19–21] and theories are being developed to unveil the states’ ﬁngerprint of their topology [8,22–25], e.g., the bulk boundary correspondence [26–28], their dynamics [29,30], occupation [31,32], transport properties [33–36], and the connection between the Hall response and the edge states [37].”
Topological bands for ultracold atoms (2018, positive): “Writing the Hamiltonian in terms of its harmonics Ĥ(t) = ∞∑ m=−∞ Ĥme imωt = Ĥ0+ ∞∑ m=1 Ĥme imωt+Ĥ−me −imωt (B4) where Ĥ†m = Ĥ−m, the Magnus expansion leads to (Goldman and Dalibard, 2014) Ĥeff = Ĥ0 + 1 ~ω ∞∑ m=1 1 m [Ĥm, Ĥ−m] + 1 2(~ω)2 ∞∑ m=1 1 m2 [ [Ĥm, Ĥ0], Ĥm ] + [ [Ĥ−m, Ĥ0],…”
Floquet engineering with quasienergy bands of periodically driven optical lattices (2015, background): “Here the concept of coarse graining comes into play: If one may safely neglect all “small” quasienergy anticrossings, it may be possible to describe the driven system by an effective time-independent Hamiltonian within the subspace considered [25].”
Microwave-engineering of programmable XXZ Hamiltonians in arrays of Rydberg atoms (2021, methodology): “This Floquet-engineering technique [10], initially introduced in the context of NMR”
Realization of an anomalous Floquet topological system with ultracold atoms (2020, background): “Floquet engineering [1–3] has found widespread applications for the realization of out-of-equilibrium manybody systems with novel properties in systems of ultracold atoms [4, 5], photonics [6, 7], superconducting qubits [8] and graphene [9].”