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arXiv:1506.06347 · Physical Review A

Chaotic scattering in the presence of a dense set of overlapping Feshbach resonances

Krzysztof Jachymski, Paul S. Julienne

Published Aug 26, 2015• 11 citations
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Abstract

Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by random matrix theory. Scattering resonances observed in ultracold atomic and molecular systems exhibit similar features as a consequence of their energy level structure. We study how the overlap between Feshbach resonances affects the distribution of resonance spacings. The spectrum of strongly overlapping resonances turns out to be non-Poisson even when the assumptions of random matrix theory are not fulfilled, but the spectrum is also not completely chaotic and tends towards being semi-Poisson.

DOI
10.1103/physreva.92.020702

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Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by random matrix theory. Scattering resonances observed in ultracold atomic and molecular systems exhibit similar features as a consequence of their energy level structure. We study how the overlap between Feshbach resonances affects the distribution of resonance spacings. The spectrum of strongly overlapping resonances turns out to be non-Poisson even when the assumptions of random matrix theory are not fulfilled, but the spectrum is also not completely chaotic and tends towards being semi-Poisson.
Strongly dipolar gases, such as dysprosium, erbium and thulium, exhibit dense Feshbach spectra whose level statistics have been associated with quantum chaos arising from couplings among many molecular channels. Here, we combine a precise calibration of the Feshbach spectrum of 162^{162}162Dy with spectroscopic measurements of the differential magnetic moments of bound states associated with more than 80 resonances between 0 and 30 G. These magnetic moments provide an eigenstate-sensitive probe of the molecular states underlying the resonance spectrum. We find that the level statistics are not uniform: resonances associated with states near the center of the magnetic-moment distribution display enhanced level repulsion, whereas those near the lower edge remain close to Poisson statistics. Our results reveal hidden structure within the chaotic dysprosium Feshbach spectrum and identify molecular-state composition as a key ingredient in the emergence of quantum chaos in strongly dipolar scattering.
We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive atom-loss measurements of their dense magnetic Feshbach-resonance spectra, analyze their statistical properties, and compare to predictions from a random-matrix-theory-inspired model. Furthermore, theoretical coupled-channels simulations of the anisotropic molecular Hamiltonian at zero magnetic field show that weakly bound, near threshold diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zero-energy bound states with nearest-neighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field. Finally, we show that the extreme temperature sensitivity of a small, but sizable fraction of the resonances in the Dy and Er atom-loss spectra is due to resonant nonzero partial-wave collisions. Our threshold analysis for these resonances indicates a large collision-energy dependence of the three-body recombination rate.
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We calculate and analyze Feshbach resonance spectra for ultracold Yb(1S0)+Yb(3P2)\mathrm{Yb}({}^{1}{S}_{0})+\mathrm{Yb}({}^{3}{P}_{2})Yb(1S0​)+Yb(3P2​) collisions as a function of an interatomic potential scaling factor $\ensuremath{\lambda}$ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in $\ensuremath{\lambda}$, but that signatures of quantum chaos emerge as a field is applied. The random zero-field distribution arises from superposition of structured spectra associated with individual total angular momenta. In addition, we show that the resonances with respect to magnetic field in the experimentally accessible range of 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.
We review random matrix approaches to chaotic wave scattering and transport in open systems. Starting from the effective non-Hermitian Hamiltonian formulation, we discuss the scattering matrix, reaction matrix, time delays, and complex resonances as complementary probes of open chaotic dynamics. We emphasize universal statistics governed by symmetry, openness, and channel coupling. Topics include the maximum-entropy description of fixed-energy scattering and its applications to quantum transport, energy correlations, resonance and eigenfunction statistics, and selected wave-chaotic phenomena induced by finite absorption. The focus throughout is on non-perturbative methods and universal structures underlying open quantum and wave chaotic systems.