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arXiv:1910.03077 · New Journal of Physics

Quantum chaos in Feshbach resonances of the ErYb system

Maciej B. Kosicki, Mateusz Borkowski, Piotr Szymon Żuchowski

Published Jan 15, 2020• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1367-2630/ab6c36

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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.
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.
We explore the magnetic Feshbach spectra of ultracold ground-state Li+Er systems. Our calculations predict many tunable resonances at fields below 1000 G that could be stably tuned in ultracold experiments. We show that Li+Er spectra are much less congested than those of systems involving heavier highly magnetic atoms and exhibit nonchaotic properties. These features would facilitate identifying and addressing individual resonances. We derive a simple model for the mass-scaling shifting of low-field resonances that may simplify designing experiments with different Er bosonic isotopes. Our work establishes Li+Er as very promising systems for quantum simulation, precision measurements and the formation of polar paramagnetic molecules.
We investigate magnetically tunable Feshbach resonances between ultracold europium atoms and between europium and alkali-metal atoms using multichannel quantum scattering calculations. For ultracold gases of europium atoms both homonuclear 153Eu+153Eu^{153}\mathrm{Eu}+^{153}\mathrm{Eu}153Eu+153Eu and heteronuclear 151Eu+153Eu^{151}\mathrm{Eu}+^{153}\mathrm{Eu}151Eu+153Eu systems are studied. Calculations for mixtures of europium and alkali-metal atoms are carried out for prototype systems of 153Eu+87Rb^{153}\mathrm{Eu}+^{87}\mathrm{Rb}153Eu+87Rb and 153Eu+7Li^{153}\mathrm{Eu}+^{7}\mathrm{Li}153Eu+7Li. We analyze the prospects for the control of scattering properties, observation of quantum chaotic behavior, and magnetoassociation into ultracold polar and paramagnetic molecules. We show that favorable resonances can be expected at experimentally feasible magnetic-field strengths below 1000G1000\phantom{\rule{0.28em}{0ex}}\mathrm{G}1000G for all investigated atomic combinations. For Eu atoms, a rich spectrum of resonances is expected as a result of the competition between relatively weak short-range spin-exchange and strong long-range magnetic dipole-dipole interactions, where the dipolar interaction induces measurable resonances. A high density of resonances is expected at magnetic-field strengths below 200G200\phantom{\rule{0.28em}{0ex}}\mathrm{G}200G without pronounced quantum chaos signatures. The present results may be useful for the realization and application of dipolar atomic and molecular quantum gases based on europium atoms in many-body physics.
We have investigated magnetically tunable Feshbach resonances in ultracold collisions of Rb with Yb in its metastable 3P2{}^{3}{P}_{2}3P2​ and 3P0{}^{3}{P}_{0}3P0​ states, using coupled-channel scattering and bound-state calculations. For the 3P2{}^{3}{P}_{2}3P2​ state, we find sharp resonances when both atoms are in their lowest Zeeman sublevels. However, these resonances are decayed by inelastic processes that produce Yb atoms in 3P1{}^{3}{P}_{1}3P1​ and 3P0{}^{3}{P}_{0}3P0​ states. The molecules that might be produced by magnetoassociation at the 3P2{}^{3}{P}_{2}3P2​ thresholds can decay by similar pathways and would have lifetimes no more than a few microseconds. For the 3P0{}^{3}{P}_{0}3P0​ state, by contrast, there are resonances that are promising for magnetoassociation. There are resonances due to both rotating and nonrotating molecular states that are significantly stronger than the analogous resonances for Yb(1S\mathrm{Yb}{(}^{1}SYb(1S). The ones due to rotating states are denser in magnetic field; in contrast to Yb(1S\mathrm{Yb}{(}^{1}SYb(1S), they exist even for bosonic isotopes of Yb(3P0\mathrm{Yb}{(}^{3}{P}_{0}Yb(3P0​).
We investigate the possibility of forming Li+Yb ultracold molecules by magnetoassociation in mixtures of ultracold atoms. We find that magnetically tunable Feshbach resonances exist, but are extremely narrow for even-mass ytterbium isotopes, which all have zero spin. For odd-mass Yb isotopes, however, there is a new mechanism due to hyperfine coupling between the electron spin and the Yb nuclear magnetic moment. This mechanism produces Feshbach resonances for fermionic Yb isotopes that can be more than 2 orders of magnitude larger than for the bosonic counterparts.
With the creation of ultracold atoms and molecules, a new type of chemistry---``resonance'' chemistry---emerges: chemical reactions can occur when the energy of colliding atoms and molecules matches a bound state of the combined molecule (Feshbach resonance). This chemistry is rather similar to reactions that take place in nuclei at low energies. In this paper we suggest some problems for future experimental and theoretical work related to the resonance chemistry of ultracold molecules. Molecular Bose-Einstein condensates are particularly interesting because in this system collisions and chemical reactions are extremely sensitive to weak fields; also, a preferred reaction channel may be enhanced due to a finite number of final states. The sensitivity to weak fields arises due to the high density of narrow compound resonances and the macroscopic number of molecules with kinetic energy E=0E=0E=0 (in the ground state of a mean-field potential). The high sensitivity to the magnetic field may be used to measure the distribution of energy intervals, widths, and magnetic moments of compound resonances and study the onset of quantum chaos. A difference in the production rate of right-handed and left-handed chiral molecules may be produced by external electric E\mathbf{E}E and magnetic B\mathbf{B}B fields and the finite width $\ensuremath{\Gamma}$ of the resonance (correlation $\ensuremath{\Gamma}\mathbf{E}∙\mathbf{B}$). The same effect may be produced by the parity-violating energy difference in chiral molecules.