RECURRENCE SPECTROSCOPY - OBSERVATION AND INTERPRETATION OF LARGE-SCALE STRUCTURE IN THE ABSORPTION-SPECTRA OF ATOMS IN MAGNETIC-FIELDS

Measurements were made of the absorption spectrum of hydrogen atoms to levels near the ionization threshold in a strong magnetic field. Taki ng advantage of a classical scaling law, we varied the photon energy a nd the magnetic-field strength simultaneously, and measured absorption versus B--1/3 at fixed scaled energy, epsilon=E/(B/B-o)(2/3). The abs orption rate has sinusoidal fluctuations which are correlated with clo sed classical orbits of the electron. Fourier transformation of this s ignal gives peaks, which we interpret as ''recurrence strength,'' as a function of the classical action of the closed orbit. Closed-orbit th eory gives formulas for these recurrence strengths. We find that the f ormulas are in good agreement with the measurements. As the scaled ene rgy is increased, observed recurrences proliferate, consistent with a change from orderly to chaotic motion of the electron. Bifurcation the ory provides organizing principles for understanding this proliferatio n and for interpreting the data. New ''exotic'' orbits suddenly appear through saddle-node bifurcations. The ''main sequence'' of orbits is produced from an orbit parallel to B through a sequence of pitchfork a nd period-doubling bifurcations. Other, recurrences are created by per iod-tripling and higher-order bifurcations of existing orbits. These b ifurcations can have ''generic'' structure, or sometimes the structure s are modified by symmetries of the system. Focusing effects associate d with these bifurcations cause some recurrences to be particularly st rong.