Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1907.12722

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

Kunpeng Wang, Xiaodong He, Xiang Gao, Ruijun Guo, Xu, Peng, Jun Zhuang, Runbing Li, Min Liu, Jin Wang, Li, Jiaming, Mingsheng Zhan

Published Jul 30, 2019• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1907.12722

Related papers

Homonuclear ultracold elastic s -wave collisions of alkali-metal atoms via multichannel quantum defect theory

Alyson Laskowski, Nirav P. Mehta

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 A•Oct 16, 2023•1 citation

Homonuclear ultracold elastic $s$-wave collisions of alkali atoms via multichannel quantum defect theory

Alyson Laskowski, Nirav P. Mehta

Multichannel quantum defect theory (MQDT) provides a powerful toolkit for describing and understanding collisions of cold alkali 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, high-energy 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 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 to experiment where possible, and identify the limitations of various approximations.

arXiv:2307.16654•Jul 31, 2023•0 citations

Multichannel quantum defect theory for cold molecular collisions

James F. E. Croft, Alisdair O. G. Wallis, Jeremy M. Hutson +1 more

Multichannel quantum defect theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics and is only weakly dependent on energy and magnetic field. Once this has been produced, calculations at additional energies and fields can be performed at a computational cost that is proportional to the number of channels $N$ and not to ${N}^{3}$. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy dependence and the field dependence is currently impractical.

arXiv:1105.4483•Physical Review A•Oct 6, 2011•47 citations

Cold molecular collisions : efficient methods for quantum calculations

James F. E. Croft

Multichannel Quantum Defect Theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics. Multichannel quantum defect theory can provide an efficient alternative to full coupled-channel calculations for low-energy molecular collisions. However, the efficiency relies on interpolation of the Y matrix that encapsulates the short-range dynamics. It is shown how the phases of the MQDT reference functions may be chosen so as to remove such poles from the vicinity of a reference energy and dramatically increase the range of interpolation. For the test cases of Mg+NH and Li+NH, the resulting optimized Y matrix may be interpolated smoothly over an energy range of several Kelvin and a magnetic field range of over 1000G. Calculations at additional energies and fields can then be performed at a computational cost that is proportional to the number of channels N and not to N cubed. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy and the field dependence is currently impractical.

•Jan 1, 2012•0 citations

Quantum defect theory description of weakly bound levels and Feshbach resonances in LiRb

Jesús Pérez‐Ríos, Sourav Dutta, Yong P Chen +1 more

The multichannel quantum defect theory (MQDT) in combination with the frame transformation (FT) approach is applied to model the Fano–Feshbach resonances measured for 7 Li 87 Rb and 6 Li 87 Rb Marzok et al (2009 Phys. Rev. A 79 012717 ). The MQDT results show a level of accuracy comparable to that of previous models based on direct, fully numerical solutions of the the coupled channel Schrödinger equations. Here, energy levels deduced from 2-photon photoassociation (PA) spectra for 7 Li 85 Rb are assigned by applying the MQDT approach, obtaining the bound state energies for the coupled channel problem. Our results confirm that MQDT yields a compact description of PA observables as well as the Fano–Feshbach resonance positions and widths.

arXiv:1412.4295•New Journal of Physics•Apr 27, 2015•7 citations

Quantum defect theory for high-partial-wave cold collisions

Brandon Ruzic, Chris H. Greene, John L. Bohn

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:1301.1370•Physical Review A•Mar 11, 2013•41 citations
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−p-p− and d−d-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.
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 KKK matrix Ksr{\mathbf{K}}_{\text{sr}}Ksr​, 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 Ksr{\mathbf{K}}_{\text{sr}}Ksr​ 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 sss-wave magnetic Feshbach resonances, comparing with experiment where possible, and identify the limitations of various approximations.
Homonuclear ultracold elastic sss-wave collisions of alkali atoms via multichannel quantum defect theory
Multichannel quantum defect theory (MQDT) provides a powerful toolkit for describing and understanding collisions of cold alkali atoms. Various MQDT approximations differ primarily in how they characterize the so-called short-ranged KKK-matrix, Ksr{\mathbf K}_{\text{sr}}Ksr​, which encapsulates the short-ranged, high-energy 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 Ksr{\mathbf K}_{\text{sr}}Ksr​ for homonuclear collisions of alkali 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 sss-wave magnetic Feshbach resonances, comparing to experiment where possible, and identify the limitations of various approximations.
Multichannel quantum defect theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics and is only weakly dependent on energy and magnetic field. Once this has been produced, calculations at additional energies and fields can be performed at a computational cost that is proportional to the number of channels NNN and not to N3{N}^{3}N3. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy dependence and the field dependence is currently impractical.
Multichannel Quantum Defect Theory (MQDT) is shown to be capable of producing quantitatively accurate results for low-energy atom-molecule scattering calculations. With a suitable choice of reference potential and short-range matching distance, it is possible to define a matrix that encapsulates the short-range collision dynamics. Multichannel quantum defect theory can provide an efficient alternative to full coupled-channel calculations for low-energy molecular collisions. However, the efficiency relies on interpolation of the Y matrix that encapsulates the short-range dynamics. It is shown how the phases of the MQDT reference functions may be chosen so as to remove such poles from the vicinity of a reference energy and dramatically increase the range of interpolation. For the test cases of Mg+NH and Li+NH, the resulting optimized Y matrix may be interpolated smoothly over an energy range of several Kelvin and a magnetic field range of over 1000G. Calculations at additional energies and fields can then be performed at a computational cost that is proportional to the number of channels N and not to N cubed. MQDT thus provides a promising method for carrying out low-energy molecular scattering calculations on systems where full exploration of the energy and the field dependence is currently impractical.
The multichannel quantum defect theory (MQDT) in combination with the frame transformation (FT) approach is applied to model the Fano–Feshbach resonances measured for 7 Li 87 Rb and 6 Li 87 Rb Marzok et al (2009 Phys. Rev. A 79 012717 ). The MQDT results show a level of accuracy comparable to that of previous models based on direct, fully numerical solutions of the the coupled channel Schrödinger equations. Here, energy levels deduced from 2-photon photoassociation (PA) spectra for 7 Li 85 Rb are assigned by applying the MQDT approach, obtaining the bound state energies for the coupled channel problem. Our results confirm that MQDT yields a compact description of PA observables as well as the Fano–Feshbach resonance positions and widths.
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 LLL. 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−−10000--10000−−1000 G for the scattering of 40K+87Rb{}^{40}\mathrm{K}{+}^{87}\mathrm{Rb}40K+87Rb in their lowest hyperfine states. Moreover, we derive analytic expressions for our universal set of MQDT parameters in the threshold regime.