Multichannel quantum-defect theory (MQDT) provides a powerful toolkit for describing and understanding collisions of cold alkali-metal atoms. Various MQDT approximations differ primarily in how they characterize the so-called short-ranged $K$ matrix ${\mathbf{K}}_{\text{sr}}$ , which encapsulates the short-ranged physics into a handful of low-energy parameters that exhibit simple and smooth dependence on energy and field. Here, we compare three different methods for computing ${\mathbf{K}}_{\text{sr}}$ for homonuclear collisions of alkali-metal atoms, from lithium to cesium. The MQDT calculations are benchmarked against numerically converged coupled-channels calculations that use a log-derivative propagator out to the asymptotic region. We study how well these approximations reproduce positions of $s$ -wave magnetic Feshbach resonances, comparing with experiment where possible, and identify the limitations of various approximations.Multichannel quantum-defect theory (MQDT) provides a powerful toolkit for describing and understanding collisions of cold alkali-metal atoms. Various MQDT approximations differ primarily in how they characterize the so-called short-ranged $K$ matrix ${\mathbf{K}}_{\text{sr}}$, which encapsulates the short-ranged physics into a handful of low-energy parameters that exhibit simple and smooth dependence on energy and field. Here, we compare three different methods for computing ${\mathbf{K}}_{\text{sr}}$ for homonuclear collisions of alkali-metal atoms, from lithium to cesium. The MQDT calculations are benchmarked against numerically converged coupled-channels calculations that use a log-derivative propagator out to the asymptotic region. We study how well these approximations reproduce positions of $s$-wave magnetic Feshbach resonances, comparing with experiment where possible, and identify the limitations of various approximations.

Physical Review AOct 16, 20231 citation

A quantum defect theory of near-threshold molecular Feshbach resonance states

Paul S. Julienne, Cheng Chin, Eite Tiesinga

Bulletin of the American Physical SocietyMay 28, 20080 citations

Broad Feshbach resonances in ultracold alkali-metal systems

Yue Cui, Min Deng, Li You +2 more

A comprehensive search for broad Feshbach resonances (FRs) in all possible combinations of stable alkali-metal atoms is carried out, using a multichannel quantum-defect theory assisted by the analytic wave functions for a long-range van der Waals potential. A number of broad $s$ -, $p$ -, and $d$ -wave FRs in the lowest-energy scattering channels, which are stable against two-body dipolar spin-flip loss, are predicted and characterized. Our results also show that broad FRs of $p$ - or $d$ -wave type that are free of two-body loss do not exist between fermionic alkali-metal atoms for a magnetic field up to 1000 G. These findings constitute helpful guidance on efforts towards the experimental study of high-partial-wave coupling-induced many-body physics.A comprehensive search for broad Feshbach resonances (FRs) in all possible combinations of stable alkali-metal atoms is carried out, using a multichannel quantum-defect theory assisted by the analytic wave functions for a long-range van der Waals potential. A number of broad $s$-, $p$-, and $d$-wave FRs in the lowest-energy scattering channels, which are stable against two-body dipolar spin-flip loss, are predicted and characterized. Our results also show that broad FRs of $p$- or $d$-wave type that are free of two-body loss do not exist between fermionic alkali-metal atoms for a magnetic field up to 1000 G. These findings constitute helpful guidance on efforts towards the experimental study of high-partial-wave coupling-induced many-body physics.

arXiv:1808.03917Physical Review AOct 24, 201824 citations

A Quantum Model of Feshbach Resonances

Raffaele Carlone, M. Correggi, D. Finco +1 more

arXiv:1901.08282Annales Henri PoincaréJun 4, 20193 citations

Quantum defect theory for the orbital Feshbach resonance

Yanting Cheng, Ren Zhang, Peng Zhang

In the ultracold gases of alkali-earth-metal-like atoms, a new type of Feshbach resonance, i.e., the orbital Feshbach resonance (OFR), has been proposed and experimentally observed in ultracold $^{173}\mathrm{Yb}$ atoms [R. Zhang et al., Phys. Rev. Lett. 115, 135301 (2015)]. When the OFR of the $^{173}\mathrm{Yb}$ atoms occurs, the energy gap between the open and closed channels is smaller by two orders of magnitude than the van der Waals energy. As a result, quantitative accurate results for the low-energy two-body problems can be obtained via multichannel quantum defect theory (MQDT), which is based on the exact solution of the Schr\"odinger equation with the van der Waals potential. In this paper we use MQDT to calculate the two-atom scattering length, effective range, and binding energy of two-body bound states for the systems with OFR. With these results we further study the clock-transition spectrum for the two-body bound states, which can be used to experimentally measure the binding energy. Our results are helpful for the quantitative theoretical and experimental research for the ultracold gases of alkali-earth-metal-like atoms with OFR.In the ultracold gases of alkali-earth-metal-like atoms, a new type of Feshbach resonance, i.e., the orbital Feshbach resonance (OFR), has been proposed and experimentally observed in ultracold $^{173}\mathrm{Yb}$ atoms [R. Zhang et al., Phys. Rev. Lett. 115, 135301 (2015)]. When the OFR of the $^{173}\mathrm{Yb}$ atoms occurs, the energy gap between the open and closed channels is smaller by two orders of magnitude than the van der Waals energy. As a result, quantitative accurate results for the low-energy two-body problems can be obtained via multichannel quantum defect theory (MQDT), which is based on the exact solution of the Schr\"odinger equation with the van der Waals potential. In this paper we use MQDT to calculate the two-atom scattering length, effective range, and binding energy of two-body bound states for the systems with OFR. With these results we further study the clock-transition spectrum for the two-body bound states, which can be used to experimentally measure the binding energy. Our results are helpful for the quantitative theoretical and experimental research for the ultracold gases of alkali-earth-metal-like atoms with OFR.

arXiv:1607.07513Physical Review AJan 23, 201712 citations

K

matrix

{\mathbf{K}}_{\text{sr}}

, which encapsulates the short-ranged physics into a handful of low-energy parameters that exhibit simple and smooth dependence on energy and field. Here, we compare three different methods for computing

{\mathbf{K}}_{\text{sr}}

for homonuclear collisions of alkali-metal atoms, from lithium to cesium. The MQDT calculations are benchmarked against numerically converged coupled-channels calculations that use a log-derivative propagator out to the asymptotic region. We study how well these approximations reproduce positions of

s

-wave magnetic Feshbach resonances, comparing with experiment where possible, and identify the limitations of various approximations.

s

p

-, and

d

-wave FRs in the lowest-energy scattering channels, which are stable against two-body dipolar spin-flip loss, are predicted and characterized. Our results also show that broad FRs of

p

- or

d

-wave type that are free of two-body loss do not exist between fermionic alkali-metal atoms for a magnetic field up to 1000 G. These findings constitute helpful guidance on efforts towards the experimental study of high-partial-wave coupling-induced many-body physics.

In the ultracold gases of alkali-earth-metal-like atoms, a new type of Feshbach resonance, i.e., the orbital Feshbach resonance (OFR), has been proposed and experimentally observed in ultracold

^{173}\mathrm{Yb}

atoms [R. Zhang et al., Phys. Rev. Lett. 115, 135301 (2015)]. When the OFR of the

^{173}\mathrm{Yb}

atoms occurs, the energy gap between the open and closed channels is smaller by two orders of magnitude than the van der Waals energy. As a result, quantitative accurate results for the low-energy two-body problems can be obtained via multichannel quantum defect theory (MQDT), which is based on the exact solution of the Schr\"odinger equation with the van der Waals potential. In this paper we use MQDT to calculate the two-atom scattering length, effective range, and binding energy of two-body bound states for the systems with OFR. With these results we further study the clock-transition spectrum for the two-body bound states, which can be used to experimentally measure the binding energy. Our results are helpful for the quantitative theoretical and experimental research for the ultracold gases of alkali-earth-metal-like atoms with OFR.