Abstract
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.
- Received 7 June 2015
DOI:https://doi.org/10.1103/PhysRevX.5.041029
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Published by the American Physical Society
Popular Summary
Quantum chaos theory describes the states of a quantum system from a probabilistic point of view rather than from microscopic simulations. Chaos imprints its presence on a wide variety of physically distinct systems, and it manifests itself as a complex resonant response to external excitations in which the spacings between resonances satisfy distinct and characteristic distributions. For example, in atomic physics, laser radiation can bring atoms into highly excited states whose spectra are chaotic as a function of laser color. The origin of chaos is attributed to collective phenomena arising from strong mixing between many electrons. Here, we experimentally and theoretically introduce nanokelvin collisions between neutral magnetic rare-earth atoms in an external magnetic field as a controllable system to study quantum chaos.
We investigate the underlying origin of the chaotic scattering and its universality by comparatively studying nanokelvin collisions in an external magnetic field for two neutral magnetic rare-earth atoms, erbium (Er) and dysprosium (Dy). We focus on ultracold, trapped ensembles of Dy and Er atoms, which have an unprecedentedly dense spectrum of collisional Fano-Feshbach resonances. We experiment with 10,000 magnetic-field values ranging from 0 to 70 G, and we analyze the results with coupled channels and bound-state calculations based on physical angular-momentum couplings and interaction potentials. We find that the presence of weakly bound levels with complex superposition states containing multiple rotational diatomic molecular states lie at the heart of the chaotic resonance distribution in collisions between magnetic atoms. These novel weakly bound levels, containing orbital angular momenta up to , exist solely because of strong anisotropic, orientation- and spin-dependent atom-atom interactions. In particular, we identify the anisotropic interactions occurring at short range as being primarily responsible for the chaotic behavior. Finally, based on a resonant model of three-body combination—in which three ultracold atoms combine to form a diatomic molecule and another atom, both of which are lost from the trap—we are able to explain the rapid increase in the resonance density with increasing temperature.
We expect that our results will pave the way for other studies of chaotic behavior in nuclear and atomic physics and provide a basis for understanding the scattering behavior of complex matter.