Parametric correlations of the energy levels of ray-splitting billiards.

Parameter-dependent statistical properties of the spectra of ray-splitting billiards are studied experimentally and theoretically. The autocorrelation functions c(x) and c(omega,x) of level velocities as well as the generalized conductance C(0) are calculated for two different classically chaotic ray-splitting billiards. Experimentally a modified Sinai ray-splitting billiard is studied consisting of a thin microwave rectangular cavity with two quarter-circle-shaped Teflon inserts. The length of the cavity serves as the experimentally adjustable parameter. For the theoretical estimates of the parametric correlations we compute the quantum spectrum of a scaling triangular ray-splitting billiard. Our experimental and numerical results are compared with each other and with the predictions of random matrix theory.

Use of the relative phase in a bichromatic field pulse to control a quasienergy gap.

We show experimentally and theoretically how the relative phase in a short, linearly polarized microwave pulse consisting of two phase-locked frequencies is effective for strong-field quantum control of He Rydberg atoms when the frequency ratio p:q is 3:1. It is also effective when p:q = 2:1 but less effective for 3:2. Parameters in our experiment are similar to those investigating quantum control of tightly bound atoms or molecules with ultrashort pulsed lasers.

Experimental investigation of a regime of Wigner ergodicity in microwave rough billiards.

We study experimentally a new regime of Wigner ergodicity [K.M. Frahm and D.L. Shepelyansky, Phys. Rev. Lett. 79, 1833 (1997)] in a microwave rough billiard. We show that in the Wigner regime, eigenstates are extended over the whole energy surface but have a strongly peaked nonergodic structure. The Shannon width of the eigenstate distributions is calculated to estimate their spreads and to find their departure from the ergodic distributions.

Autocorrelation function of level velocities for ray-splitting billiards

We study experimentally and theoretically the autocorrelation function of level velocities c(x) and the generalized conductance C(0) for classically chaotic ray-splitting systems. Experimentally, a Sinai ray-splitting billiard was simulated by a thin microwave rectangular cavity with a quarter-circle Teflon insert. For the theoretical estimates of the autocorrelator c(x) and the conductance C(0) we made parameter-dependent quantum calculations of eigenenergies of an annular ray-splitting billiard. Our experimental and numerical results are compared to theoretical predictions of systems based on the Gaussian orthogonal ensemble in random matrix theory.