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arXiv:1706.08926 · Physical Review A

In situ realization of particlelike scattering states in a microwave cavity

Julian Böhm, André Brandstötter, Philipp Ambichl, Stefan Rotter, Ulrich Kuhl

Published Feb 6, 2018• 26 citations
arXivHTMLPDF

Abstract

We realize scattering states in a lossy and chaotic two-dimensional microwave cavity which follow bundles of classical particle trajectories. To generate such particlelike scattering states, we measure the system's complex transmission matrix and apply an adapted Wigner-Smith time-delay formalism to it. The necessary shaping of the incident wave is achieved in situ using phase- and amplitude-regulated microwave antennas. Our experimental findings pave the way for establishing spatially confined communication channels that avoid possible intruders or obstacles in wave-based communication systems.

DOI
10.1103/physreva.97.021801

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The Journal of Chemical Physics•Dec 15, 1985•0 citations
We realize scattering states in a lossy and chaotic two-dimensional microwave cavity which follow bundles of classical particle trajectories. To generate such particlelike scattering states, we measure the system's complex transmission matrix and apply an adapted Wigner-Smith time-delay formalism to it. The necessary shaping of the incident wave is achieved in situ using phase- and amplitude-regulated microwave antennas. Our experimental findings pave the way for establishing spatially confined communication channels that avoid possible intruders or obstacles in wave-based communication systems.
In this work several aspects of quantum chaos are studied in the time domain. The wave equation for flat microwave cavities is equivalent to the Schrödinger equation in quantum mechanics. Therefore microwave measurements provide an experimental approach to quantum chaos. The experiments are described in terms of scattering theory, to take the coupling of the antennas to the system as well as the dissipation in the cavity walls into account. In the first part the scattering matrix of several microwave cavities is analyzed in the regime of overlapping resonances. The difference between regular and chaotic systems can be observed both in the autocorrelation functions of the same S-matrix elements, and in the cross-correlation functions of different S-matrix elements. In accordance with literature, this difference is more pronounced in the cross-correlation functions. To describe the experimental correlation functions, the absorption in the cavity walls is modeled by an infinite number of weak decay channels. In the second part the focus is shifted to the stability of quantum time-evolution. The fidelity amplitude is a standard benchmark for the stability of a quantum system against a change of the Hamiltonian. It is defined as the overlap of the perturbed and unperturbed time-evolution of the same initial state. Exact theoretical results for a random matrix model are compared with numerical simulations and the linear-response results. For strong perturbations a partial recovery of the fidelity amplitude is found, and an intuitive explanation for this behavior is given in terms of a spectral Debye-Waller factor. Further, in the third part, experimental results for the fidelity amplitude are presented for two microwave cavities with classically chaotic dynamics. The perturbation of the systems is realized by applying small changes to their geometry. The results are well described by the linear-response expression, and the perturbation strength can be related to the change of the geometry of the cavities. In the fourth part microwave measurements on dielectric quadrupole billiards with mixed phase space are discussed. The internal dynamics is analyzed by means of Husimi distributions, while for the outer region the Poynting vector is determined to obtain the emission pattern. The emission pattern of the quadrupole billiard is strongly influenced by the structures of its mixed phase space.
The present doctoral thesis is concerned, on the one hand, with the investigation of the decay probability in a quantum billiard, and, on the other, the realization of the double-slit experiment in microwave billiards. For both purposes transmission elements of the scattering matrix are experimentally measured in microwave cavities with regular and chaotic dynamics. One or more pieces of the billiards' boundary are removed and the leaked outward eld is investigated. The general aim is to distinguish the eect of the billiard dynamics on the temporal decay behaviour and on the interference patterns. The decay probability in an open quantum billiard can be explored by means of the scattering matrix formalismus derived in the framework of nuclear physics. In a circular billiard, archetype of regular systems, the opening breaks the spatial symmetry causing a splitting of the degenerate states observable at low frequencies. One state of the doublet remains unaected contributing to the long-time behavior inside the cavity (survival probability), while the short-lived one is strongly influenced by the opening and decays much faster. The case of chaotic dynamics is studied by means of a tilted stadium billiard. For sufficiently long times the decay probability shows an essentially nonexponential behaviour. Agreement with theoretical results derived by Harney, Dittes and Muller is obtained for a few of the open channels and intermediate times. For both, the circle and the stadium,the short time decay resembles the classical behaviour. Furthermore, a double-slit experiment is performed with a wave packet starting inside a microwave billiard domain, both for regular and chaotic dynamics. Stationary and temporal patterns formed by the leaking of the wave packet are experimentally determined. The evolution of a directed initial state is constructed by means of the electromagnetic propagator. Also single-slit experiments are carried out and compared with the corresponding double-slit experiments. The present work sheds light on the fundamental question of the decay of open quantum systems and provides plentiful information about the structure of the diracted eld from microwave billards with a double-slit on the boundary connecting classical properties with the corresponding quantum features in both cases.
We present experimental studies of geometry-specific quantum scattering in microwave billiards of a given shape. We perform full quantum-mechanical scattering calculations and find excellent agreement with experimental results. We also carry out semiclassical calculations where the conductance is given as a sum over all classical trajectories between the leads, each of the trajectories carrying a quantum-mechanical phase. We unambiguously demonstrate that the characteristic frequencies of the oscillations in the transmission and reflection amplitudes t and r are related to the length distribution of the classical trajectories between the leads, whereas the frequencies of the probabilities T=/t/(2) and R=/r/(2) can be understood in terms of the length difference distribution in the pairs of classical trajectories. We also discuss the effect of nonclassical "ghost" trajectories, i.e., trajectories that include classically forbidden reflection off the lead mouths.
The scattering matrix S linearly relates the vector of incoming waves to outgoing wave excitations, and contains an enormous amount of information about the scattering system and its connections to the scattering channels. Time delay is one way to extract information from S, and the transmission time delay τ_{T} is a complex (even for Hermitian systems with unitary scattering matrices) measure of how long a wave excitation lingers before being transmitted. The real part of τ_{T} is a well-studied quantity, but the imaginary part of τ_{T} has not been systematically examined experimentally, and theoretical predictions for its behavior have not been tested. Here we experimentally test the predictions of Asano et al. [Nat. Commun. 7, 13488 (2016)NCAOBW2041-172310.1038/ncomms13488] for the imaginary part of transmission time delay in a nonunitary scattering system. We utilize Gaussian time-domain pulses scattering from a two-port microwave graph supporting a series of well-isolated absorptive modes to show that the carrier frequency of the pulses is changed in the scattering process by an amount in agreement with the imaginary part of the independently determined complex transmission time delay, Im[τ_{T}], from frequency-domain measurements of the subunitary S matrix. Our results also generalize and extend those of Asano et al., establishing a means to predict pulse propagation properties of non-Hermitian systems over a broad range of conditions.
A formalism to calculate the time delay experienced by a particle undergoing scattering is presented. The formalism is a natural extension of Wigner’s delay time to wave packets which do not exhibit a well defined angular momentum. The delay depends only on the partial wave phase shifts characterizing the scattering event. The formalism is tested by applying it to the 3D square well. The results are shown to agree with the known properties of resonant scattering as deduced from a study of the poles of the scattering matrix in the complex energy plane.