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A realisation of a periodically driven microwave system is presented. The principal element of the scheme is a variable capacity, i.e. a varicap, introduced as an element of the resonant circuit. Sideband structures corresponding to different driving signals, have been measured experimentally. In the linear regime we observed sideband structures with specific shapes. The main peculiarities of these shapes can be explained within a semiclassical approximation. A good agreement between experimental data and theoretical expectations has been found.
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We present an experimental and numerical study of missing-level statistics of chaotic three-dimensional microwave cavities. The nearest-neighbor spacing distribution, the spectral rigidity, and the power spectrum of level fluctuations were investigated. We show that the theoretical approach to a problem of incomplete spectra does not work well when the incompleteness of the spectra is caused by unresolved resonances. In such a case the fraction of missing levels can be evaluated by calculations based on random matrix theory.
We study the dynamics of a two-level quantum system under the influence of sinusoidal driving in the intermediate frequency regime. Analyzing the Floquet quasienergy spectrum, we find combinations of the field parameters for which population transfer is optimal and takes place through a series of well defined steps of fixed duration. We also show how the corresponding evolution operator can be approximated at all times by a very simple analytical expression. We propose this model as being specially suitable for treating periodic driving at avoided crossings found in complex multi-level systems, and thus show a relevant application of our results to designing a control protocol in a realistic molecular model
We report on the experimental investigation of the dependence of the elastic enhancement, i.e., enhancement of scattering in backward direction over scattering in other directions of a wave-chaotic system with partially violated time-reversal (T ) invariance on its openness. The elastic enhancement factor is a characteristic of quantum chaotic scattering which is of particular importance in experiments, like compound-nuclear reactions, where only cross sections, i.e., the moduli of the associated scattering matrix elements are accessible. In the experiment a quantum billiard with the shape of a quarter bow-tie, which generates a chaotic dynamics, is emulated by a flat microwave cavity. Partial T-invariance violation of varying strength 0 < xi < 1 is induced by two magnetized ferrites. The openness is controlled by increasing the number M of open channels, 2 < M < 9, while keeping the internal absorption unchanged. We investigate the elastic enhancement as function of xi and find that for a fixed M it decreases with increasing time-reversal invariance violation, whereas it increases with increasing openness beyond a certain value of xi > 0.2. The latter result is surprising because it is opposite to that observed in systems with preserved T invariance (xi = 0). We come to the conclusion that the effect of T -invariance violation on the elastic enhancement then dominates over the openness, which is crucial for experiments which rely on enhanced backscattering, since, generally, a decrease of the openness is unfeasible. Motivated by these experimental results we, furthermore, performed theoretical investigations based on random matrix theory which confirm our findings.
Three dimensional Weyl semimetals exhibit open Fermi arcs on their sample surfaces connecting the projection of bulk Weyl points of opposite chirality. The canonical interpretation of these surfaces states is in terms of chiral edge modes of a layer quantum Hall effect: The two-dimensional momentum-space planes perpendicular to the momentum connecting the two Weyl points are characterized by a non-zero Chern number. It might be interesting to note, that in analogy to the known two-dimensional Floquet anomalous chiral edge states, one can realize open Fermi arcs in the absence of Chern numbers in periodically driven system. Here, we present a way to construct such anomalous Fermi arcs in a concrete model.
Time-periodic (Floquet) topological phases of matter exhibit bulk-edge relationships that are more complex than static topological insulators and superconductors. Finding the edge modes unique to driven systems usually requires numerics. Here we present a minimal two-band model of Floquet topological insulators and semimetals in two dimensions where all the bulk and edge properties can be obtained analytically. It is based on the extended Harper model of quantum Hall effect at flux one half. We show that periodical driving gives rise to a series of phases characterized by a pair of integers. The model has a most striking feature: the spectrum of the edge modes is always given by a single cosine function, $omega(k_y)propto cos k_y$ where $k_y$ is the wave number along the edge, as if it is freely dispersing and completely decoupled from the bulk. The cosine mode is robust against the change in driving parameters and persists even to semi-metallic phases with Dirac points. The localization length of the cosine mode is found to contain an integer and in this sense quantized.
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