We introduce a choice of reference wave functions that allows multichannel quantum defect theory (MQDT) to describe ultracold collisions involving high-partial-wave quantum numbers $L$ . This requires a careful standardization of the MQDT reference wave functions at long range to ensure their linear independence. To illustrate the simplicity and accuracy of the resulting theory, we perform a comprehensive calculation of $L\ensuremath{\le}2$ Fano-Feshbach resonances in the range $0--1000$ G for the scattering of ${}^{40}\mathrm{K}{+}^{87}\mathrm{Rb}$ in their lowest hyperfine states. Moreover, we derive analytic expressions for our universal set of MQDT parameters in the threshold regime.We introduce a choice of reference wave functions that allows multichannel quantum defect theory (MQDT) to describe ultracold collisions involving high-partial-wave quantum numbers $L$. This requires a careful standardization of the MQDT reference wave functions at long range to ensure their linear independence. To illustrate the simplicity and accuracy of the resulting theory, we perform a comprehensive calculation of $L\ensuremath{\le}2$ Fano-Feshbach resonances in the range $0--1000$ G for the scattering of ${}^{40}\mathrm{K}{+}^{87}\mathrm{Rb}$ in their lowest hyperfine states. Moreover, we derive analytic expressions for our universal set of MQDT parameters in the threshold regime.

arXiv:1301.1370Physical Review AMar 11, 201341 citations

Revealing Energy Dependence of Quantum Defects via Two Heteronuclear Atoms in an Optical Tweezer

Kunpeng Wang, Xiaodong He, Xiang Gao +8 more

As a physically motivated and computationally simple model for cold atomic and molecular collisions, the multichannel quantum defect theory (MQDT) with frame transformation (FT) formalism provides an analytical treatment of scattering resonances in an arbitrary partial wave between alkali-metal atoms, leading to the experimental observation of $p-$ and $d-$ wave resonances. However, the inconsistency of quantum defects for describing scattering resonances shows up when compared with experiments. Here, with two heteronuclear atoms in the ground state of an optical tweezer, the energy dependence of quantum defects is obviously revealed by comparing the measured s-wave scattering length with the prediction of MQDT-FT. By dividing the quantum defects into energy sensitive and insensitive categories, the inconsistency is ultimately removed while retaining the analytic structure of MQDT-FT. This study represents a significant improvement in the analytical MQDT-FT and demonstrates that a clean two-particle system is valuable to the test of collisional physics.As a physically motivated and computationally simple model for cold atomic and molecular collisions, the multichannel quantum defect theory (MQDT) with frame transformation (FT) formalism provides an analytical treatment of scattering resonances in an arbitrary partial wave between alkali-metal atoms, leading to the experimental observation of $p-$ and $d-$wave resonances. However, the inconsistency of quantum defects for describing scattering resonances shows up when compared with experiments. Here, with two heteronuclear atoms in the ground state of an optical tweezer, the energy dependence of quantum defects is obviously revealed by comparing the measured s-wave scattering length with the prediction of MQDT-FT. By dividing the quantum defects into energy sensitive and insensitive categories, the inconsistency is ultimately removed while retaining the analytic structure of MQDT-FT. This study represents a significant improvement in the analytical MQDT-FT and demonstrates that a clean two-particle system is valuable to the test of collisional physics.

arXiv:1907.12722Jul 30, 20191 citation

We introduce a choice of reference wave functions that allows multichannel quantum defect theory (MQDT) to describe ultracold collisions involving high-partial-wave quantum numbers

L

. This requires a careful standardization of the MQDT reference wave functions at long range to ensure their linear independence. To illustrate the simplicity and accuracy of the resulting theory, we perform a comprehensive calculation of $L\ensuremath{\le}2$ Fano-Feshbach resonances in the range

0--1000

G for the scattering of

{}^{40}\mathrm{K}{+}^{87}\mathrm{Rb}

in their lowest hyperfine states. Moreover, we derive analytic expressions for our universal set of MQDT parameters in the threshold regime.

p-

and

d-

wave resonances. However, the inconsistency of quantum defects for describing scattering resonances shows up when compared with experiments. Here, with two heteronuclear atoms in the ground state of an optical tweezer, the energy dependence of quantum defects is obviously revealed by comparing the measured s-wave scattering length with the prediction of MQDT-FT. By dividing the quantum defects into energy sensitive and insensitive categories, the inconsistency is ultimately removed while retaining the analytic structure of MQDT-FT. This study represents a significant improvement in the analytical MQDT-FT and demonstrates that a clean two-particle system is valuable to the test of collisional physics.