Peter M. Koch

Experimental investigation of Wigner's reaction matrix for irregular graphs with absorption

We use tetrahedral microwave networks consisting of coaxial cables and attenuators connected by T-joints to make an experimental study of Wigners reaction K matrix for irregular graphs in the presence of absorption. From measurements of the scattering matrix S for each realization of the microwave network, we obtain distributions of the imaginary and real parts of K. Our experimental results are in good agreement with theoretical predictions.

Ray-Splitting Billiards

Ray splitting is a universal phenomenon that occurs with appreciable amplitude in all wave systems when the properties of the system change on a scale smaller than the wave length. We study the quantum implications of ray splitting theoretically and experimentally with the help of ray-splitting billiards in one and two dimensions. We show that Gutzwillers trace formula works even in the context of ray-splitting systems provided reflection and transmission of waves at ray-splitting boundaries is properly included.

Observation of dynamical localization in a rough microwave cavity

Abstract We measure the angular momentum content of modes in a flat, near-circular microwave cavity with a rough perimeter and demonstrate localization in angular momentum space. Because Schrodingers wave mechanics and Maxwells electrodynamics are equivalent for a 2d cavity, we compare our experimental results directly with the quantum theory of rough 2d cavities [K.M. Frahm and D.L. Shepelyansky, Phys. Rev. Lett. 78 (1997) 1440]. Introducing the concept of effective roughness we find good qualitative agreement.

Microwave “ionization” of excited hydrogen atoms: how nonclassical local stability brought about by scarred separatrix states is affected by broadband noise and by varying the pulse envelope

Abstract Studies of the microwave “ionization” of excited hydrogen atoms have shonn (so far) six regimes of dynamical behavior as one changes the scaled frequency, which is the ratio of the driving frequency ω and the classical Kepler frequency ω k . After a brief description of each regime, we focus on the results of recent experiments probing the detailed semiclassical behavior in two of them. Observed nonclassical local stability that, nevertheless, classically scales has been explained theoretically as being brought about by scarred quantal wavefunctions anchored semiclassically to the (broken) separatrix regions in the classical phase space above and below the main nonlinear resonance zone centered near ω ω k = 1 1 . The experimental data show that the upper and lower separatrix states states are affected differently by broadband noise added to the coherent microwave field and by variations in the microwave pulse envelope. Implications of these results for future work are discussed.

Chaotic ionization of highly excited hydrogen atoms

Recent experimental measurements of the microwave ionization of highly excited hydrogen atoms with principal quantum numbers ranging from n = 30 to 90 are well described by a classical treatment of the nonlinear electron dynamics. In particular, the predictions of the threshold field for the onset of significant ionization is found to coincide with the onset of classical chaos in a one-dimesional model of the experiment. In this brief note I emphasize that this excellent agreement between the theoretical and experimental ionization thresholds requires a proper theoretical treatment of the slow, adiabatic turn-on of the microwave perturbation in which the persistence on nonlinear resonances in the chaotic phase space plays a crucial role.

Beyond (1D p time) dynamics in the microwave ionization of excited atoms: surprises from experiments with collinear static and linearly polarized electric fields

Abstract We begin with a brief review of the ionization of 3D hydrogen atoms with large principal quantum number n0, first by a static electric field Fs and then by linearly polarized (LP) electric field. Near its onset, LP ionization can be understood with (1D + time) theory. Various kinds of resonant phenomena are important. We continue with a brief review of the polarization dependence. When the dynamics is dominated by the main pendulum-like resonance zone, a separation of timescales leads to ionization near onset that is independent of polarization. In other parameter ranges, polarization-dependent effects occur that can be understood only in higher dimensions, minimally (2D + time). Finally, we present preliminary results from new experiments using collinear LP and Fs fields, both of which can be strong. The data show the importance of (a) multiphoton resonances driven between Stark substates of the initial n0 manifold and (b) striking, regular oscillations recorded for fixed microwave parameters as a function of Fs. The mechanisms responsible for (a) are understood. Those responsible for (b) are not, but the oscillations exhibit empirical scaling behavior that will help to unravel the wave packet dynamics.

Dependence on relative phase for bichromatically driven atoms

We consider the interaction of atoms with a pulse of a linearly polarized electric field consisting of two phase-locked frequencies whose ratio ωH/ωL is the ratio of arbitrary integers h/l, with h>l. If the electric amplitudes vary in time, they do so with the same slow envelope. The relative phase can be used as a control parameter via variation of the phase H of ωH or L of ωL. We derive the physically important ranges of relative phase for total-yield processes as a function of h:l; they depend on whether h,l are both odd or only one is odd. We tabulate a variety of relevant phase-dependent results for all h:l from 2:1 through 8:7. We use calculations and experimental data for helium and hydrogen Rydberg atoms driven by a bichromatic microwave field to confirm the physically important ranges of H and L for a few h:l ratios. Two experimental examples taken from the literature for the interactions of atoms with sub-picosecond, bichromatic laser pulses also confirm our conclusions.

Ionization and excitation of hydrogen and helium Rydberg atoms by microwaves

We have used the interaction of hydrogen Rydberg atoms with microwave fields to study multiphoton ionization. The minimum number of photons absorbed in the experiments ranges from about 300 to only 15. A brief overview is given of the extensive theoretical work that is under development to explain experimental data, including various observed structures. Similarly we report on ionization of helium Rydberg atoms, qualitatively explained in terms of a static picture. Finally we show selective excitation of He triplet s‐state to higher angular momentum states, via absorption of several photons from the field. Using the Floquet method a close analogy between the microwave problem and slow atomic collisions can be made. Sharp resonant structures in the spectra can be linked to individual avoided crossings of calculated Floquet quasi‐energy curves. Our theory that exploits a separation of timescales explains very well the positions, depths, and shapes of the observed structures, but a discrepancy still remains ...

Exploring swollen atoms

Near the end of the 19th century the Swede Johannes Rydberg gave science the physical constant now identified by his name. Searching for patterns among wavelength-dispersed atomic spectra, early spectroscopists found empirical formulae that gave the inverse wavelength of some spectral lines. For the simplest atom, hydrogen, the formula involves differences of the inverse square of integers and an empirical constant of proportionality, R, now known as the Rydberg constant.

Microwave Excitation and Ionization of H Atoms at High Scaled Frequencies: Comparisons of Experiments and Theories

A hydrogen atom with principal quantum number n0»1 in a strong microwave electric field A(t)Fsin(ωt+ o) is a periodically driven, deterministic, Hamiltonian system that exhibits a transition to classical chaos. (Here F is the electric amplitude, A(t) is a slowly varying envelope function, ω is the angular frequency, and o is a phase averaged by all experiments described below) Because experiments, analytical theory, and numerical simulations can be carried out,1-11 it is an important testing ground for quantum chaos (the study of a quantal system whose classical counterpart is chaotic.) The values of scaled frequency ω and scaled fieldF largely govern the behavior of the dynamics. (Relative to the state with initial principal actionI 0 = n0ħ, the first is the ratio of ω) and the Kepler orbital frequency, and the second is the ratio of F and the mean, initial Coulomb binding field.)