Quantum chaos in Feshbach resonances of the ErYb system

Abstract

We investigate ultracold magnetic-field-assisted collisions in the so far unexplored ErYb system. The nonsphericity of the Er atom leads to weakly anisotropic interactions that provide the mechanism for Feshbach resonances to emerge. The resonances are moderately sparsely distributed with a density of 0.1-0.3 G −1 and exhibit chaotic statistics characterized by a Brody parameter η≈0.5-0.7. The chaotic behaviour of Feshbach resonances is accompanied by strong mixing of magnetic and rotational quantum numbers in near-threshold bound states. We predict the existence of broad resonances at fields < 300 G that may be useful for the precise control of scattering properties and magnetoassociation of ErYb molecules. The high number of bosonic Er-Yb isotopic combinations gives many opportunities for mass scaling of interactions. Uniquely, two isotopic combinations have nearly identical reduced masses (differing by less than 10 −5 relative) that we expect to have strikingly similar Feshbach resonance spectra, which would make it possible to experimentally measure their sensitivity to hypothetical variations of proton-to-electron mass ratio. behaviour can be analyzed instead (see pioneering work of Porter and coworkers e.g. [24,25]) and the tools for such analysis include the Random Matrix Theory developed by Wigner [26] and Dyson [27]. 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. Ytterbium, alongside Sr, is the most widely used spin-singlet atom with applications for optical clocks, quantum gases and quantum simulation [32][33][34][35]. ErYb should also be very attractive due to the fantastic mass-scalability of both Yb [36,37] and Er (as shown here). Three of the bosonic Yb isotopes, 168 Yb [38] and 170 Yb [39] and 174 Yb [40] form stable Bose-Einstein condensates, and several Fermi and Bose-Fermi and Bose-Bose gases [41, 42] have also been demonstrated experimentally. Er and Yb atoms could form many isotopic mixtures, including two fermion-fermion mixtures with nearly equal masses and very close polarizabilities (hence, trapping properties). While an Er-Yb quantum degenerate mixture has not been achieved yet, it is clearly within the reach of present state-of-the-art techniques. Our predictions could be tested by forming a dual Mott insulator of Er and Yb atoms...

Feshbach resonances of large-mass-imbalance Er-Li mixtures

“…Considering in particular a similar kind of mixture of heavy 167 Er fermions and light 7 Li bosons, this opens the road to three-body Efimov states with both reduced scaling constants and nonvanishing angular momenta [2] and chiral p-wave superfluids in mixed dimensions. Additionally, ultracold mixtures of Yb and Er should allow for a detailed study of mass-scaling effects in Yb-Er Feshbach resonances [24]. Ultracold triple-species quantum gas mixtures of ytterbium, erbium, and lithium are also within reach.…”

Feshbach resonances of large mass-imbalance Er-Li mixtures

“…Considering in particular a similar kind of mixture of heavy 167 Er fermions and light 7 Li bosons this opens the road to three-body Efimov states with both reduced scaling constants and non-vanishing angular momenta [2], and chiral p-wave superfluids in mixed dimensions. Additionally, ultracold mixtures of Yb and Er should allow for a detailed study of mass-scaling effects in Yb-Er Feshbach resonances [24]. Ultracold triplespecies quantum gas mixtures of Ytterbium, Erbium and Lithium are also within reach.…”

Prospects of Forming High-Spin Polar Molecules from Ultracold Atoms

“…Note added.-Recently, we learned of parallel work on the related system Er þ Yb that also predicts many resonances at low field [103].…”