Quantum chaos in ultracold collisions betweenYb(1S0)andYb(3P2)

Abstract

We calculate and analyze Feshbach resonance spectra for ultracold Yb( 1 S0) + Yb( 3 P2) collisions as a function of an interatomic potential scaling factor λ and external magnetic field. We show that, at zero field, the resonances are distributed randomly in λ, 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 in magnetic field in the experimentally accessible range 400 to 2000 G are chaotically distributed, with strong level repulsion that is characteristic of quantum chaos.

Approach to chaos in ultracold atomic and molecular physics: Statistics of near-threshold bound states for Li+CaH and Li+CaF

“…A re-analysis of the erbium results [30] showed that the deviations from chaotic predictions might arise because some narrow resonances are not observed in the experiment. A comparable degree of chaos has recently been found in coupled-channel calculations on the remarkably simple system Yb( 1 S)+Yb( 3 P) [31]. However, similar calculations on Li+Er found statistics consistent with a random but non-chaotic level distribution [32].…”

Magnetically tunable Feshbach resonances in ultracold gases of europium atoms and mixtures of europium and alkali-metal atoms

“…6(a) and 6(b) raise a question of whether the investigated systems exhibit a quantum chaotic behavior. For ultracold collisions of Dy and Er atoms it was measured [16,25] and theoretically confirmed [16,44,[64][65][66][67] that the interplay of anisotropic electronic and dipolar interactions leads to the chaotic spectra of Feshbach resonances being the signature of the level repulsion following the predictions of the Gaussian Orthogonal Ensemble of random matrices [68]. Similar results were predicted for atom-molecule collisions [69][70][71].…”

Quantum chaos in Feshbach resonances of the ErYb system

“…In our analysis of the chaotic behaviour of resonance spacings we take into account the slow variation of resonance density by following the standard 'unfolding' procedure [28,73]. resonance every 3G.…”

“…Thus, η becomes a quantitative measure of chaotic behaviour where η close to zero indicates a lack of chaos, while η near unity shows strong level repulsion. Following Greenet al [28] we calculate the Brody parameter η through max-likelihood estimation: η can be found by maximizing the log-likelihood ( )…”

“…For ultracold gases the first evidence of chaos in a Feshbach resonance spectrum was reported in Er dimer by Frisch et al [19]. Since then, the chaotic character of bound states and Feshbach resonances in ultracold collisions was also found for several other systems, for example, in mixtures of Yb atoms in 1 S 0 and 3 P 2 states at large magnetic fields [28], and molecular collisions of Li atom with CaH and CaF [29]. On the other hand, the resonance spacings in collisions of Er and Li atoms in a magnetic field [30], and of highly magnetic europium ( 7 S) with alkali metal atoms [31] have both been shown to follow the non-chaotic poissonian distribution.Here we investigate the interactions and Feshbach spectra between weakly anisotropic lanthanides and heavy spin-singlet atoms using ErYb as a prime example.…”