Statistical periodicity in driven quantum systems: General formalism and application to noisy Floquet topological chains

Abstract

Much recent experimental effort has focused on the realization of exotic quantum states and dynamics predicted to occur in periodically driven systems. But how robust are the sought-after features, such as Floquet topological surface states, against unavoidable imperfections in the periodic driving? In this work, we address this question in a broader context and study the dynamics of quantum systems subject to noise with periodically recurring statistics. We show that the stroboscopic time evolution of such systems is described by a noise-averaged Floquet superoperator. The eigenvectors and -values of this superoperator generalize the familiar concepts of Floquet states and quasienergies and allow us to describe decoherence due to noise efficiently. Applying the general formalism to the example of a noisy Floquet topological chain, we re-derive and corroborate our recent findings on the noise-induced decay of topologically protected end states. These results follow directly from an expansion of the end state in eigenvectors of the Floquet superoperator.

arXiv comment13 pages, 5 figures. This is the final, published version

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Cited by in corpus (10)

• Edge and bulk localization of Floquet topological superconductors
• `Muhammad Ali effect' and incoherent destruction of Wannier-Stark localization in a stochastic field
• Quantized Floquet topology with temporal noise
• Dynamical transitions in aperiodically kicked tight-binding models
• Simulating Floquet topological phases in static systems
• Transport signatures of symmetry protection in 1D Floquet topological insulators
• Topological reflection matrix
• Quantized charge transport in disordered Floquet topological insulators in the absence of Anderson localization
• Fractionalized Prethermalization in the One-Dimensional Hubbard Model
• Noise resilience of two-dimensional Floquet topological phases