Ericson Fluctuations in an Open Deterministic Quantum System: Theory Meets Experiment

We provide numerically exact photoexcitation cross sections of rubidium Rydberg states in crossed, static electric, and magnetic fields, in quantitative agreement with recent experimental results. Their spectral backbone underpins a clear transition towards the Ericson regime, associated with a universal, fluctuating behavior of the cross section of strongly coupled, fragmenting quantum systems.

Figure 1

Numerical photoexcitation cross sections, at magnetic and electric field strengths $B=2.0045\mathrm{T}$ and $F=22.4\mathrm{kV}/\mathrm{m}$, respectively, in the energy range $E=-70.0\dots -65.0{\mathrm{cm}}^{-1}$ (top), $E=-65.0\dots -60.0{\mathrm{cm}}^{-1}$ (middle), and $E=-60.0\dots -55.0{\mathrm{cm}}^{-1}$ (bottom). The latter completely covers the energy range probed in the experiments reported in 18, 19. While individual resonances are well resolved in the lower lying spectra, on top of a flat continuum background, a strongly fluctuating continuum structure in the bottom plot expresses the increasing contribution of overlapping resonances on the spectral level, see Fig. 2.

Figure 2

Distribution of the resonance widths ${\Gamma }_j$ contributing to the photoexcitation cross section, Eq. (2), in units of the local mean level spacing $\Delta =⟨E_j-E_{j-1}⟩$, over an energy range which spans the domain probed in the three plots of Fig. 1, for the same values of $F$ and $B$. The dashed line at ${\Gamma }_j/\Delta =1$ separates isolated (${\Gamma }_j/\Delta <1$) from overlapping resonances (${\Gamma }_j/\Delta >1$). Comparison with Fig. 1 shows how broad resonances on the spectral level induce a strongly fluctuating continuum background, in the photoexcitation cross section. The energy range $E=-60.0\dots -55.0{\mathrm{cm}}^{-1}$, where resonance overlap is most pronounced in this plot, covers the energy range probed in the experiments reported in 18, 19.

Figure 3

Top: (Normalized) autocorrelation functions $C(\Delta E)$ of the photoionization cross sections for magnetic field strengths $B=2.0045\mathrm{T}$ (full line), $B=1.49\mathrm{T}$ (dashed line), $B=0.9974\mathrm{T}$ (dotted line), and $B=0.563\mathrm{T}$ (dash-dotted line), at electric field strength $F=22.4\mathrm{kV}/\mathrm{m}$. The corresponding cross sections are shown in the subsequent panels, with increasing magnetic field strength from top to bottom. The characteristic correlation lengths $\gamma$ of $C(E)$ deduced from our—parameter-free—numerical treatment, for the three largest values of $B$, are in very good agreement with the experimentally reported values; see Table . Note that even for the smallest value of $B$ [not studied in 18 ] there is a largely fluctuating continuum background, as opposed to the purely Coulombic problem realized with hydrogen atoms [28].