arXiv:0903.0884 · Physical Review A

Prediction of Feshbach resonances from three input parameters

Thomas M. Hanna, Eite Tiesinga, Paul S. Julienne

Published Apr 30, 2009• 39 citations

Abstract

We have developed a model of Feshbach resonances in gases of ultracold alkali-metal atoms using the ideas of multichannel quantum-defect theory. Our model requires just three parameters describing the interactions---the singlet and triplet scattering lengths, and the long-range van der Waals coefficient---in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to $^{6}\text{L}\text{i-}^{40}\text{K}$ and $^{40}\text{K}\text{\ensuremath{-}}^{87}\text{R}\text{b}$ scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique.

DOI: 10.1103/physreva.79.040701

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arXiv:0903.0884 · Physical Review A

Prediction of Feshbach resonances from three input parameters

Thomas M. Hanna, Eite Tiesinga, Paul S. Julienne

Published Apr 30, 2009• 39 citations

arXiv HTML PDF

Abstract

^{6}\text{L}\text{i-}^{40}\text{K}

and

^{40}\text{K}\text{\ensuremath{-}}^{87}\text{R}\text{b}

scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique.

DOI: 10.1103/physreva.79.040701

Related papers

Prediction of Feshbach resonances using an analytical quantum-defect matrix

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Physical Review AMar 14, 201210 citations

Broad Feshbach resonances in ultracold alkali-metal systems

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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.

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Georg M. Bruun, Andrew David Jackson, Evgeni E. Kolomeitsev

A low-energy effective theory based on a microscopic multichannel description of the atom-atom interaction is derived for the scattering of alkali-metal atoms in different hyperfine states. This theory describes all scattering properties, including medium effects, in terms of the singlet and triplet scattering lengths and the range of the atom-atom potential and provides a link between a microscopic description of Feshbach scattering and more phenomenological approaches. It permits the calculation of medium effects on the resonance coming from the occupation of closed channel states. The examination of such effects is demonstrated to be of particular relevance to an experimentally important Feshbach resonance for $^{40}\mathrm{K}$ atoms. We analyze a recent rethermalization rate experiment on $^{40}\mathrm{K}$ and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multichannel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.A low-energy effective theory based on a microscopic multichannel description of the atom-atom interaction is derived for the scattering of alkali-metal atoms in different hyperfine states. This theory describes all scattering properties, including medium effects, in terms of the singlet and triplet scattering lengths and the range of the atom-atom potential and provides a link between a microscopic description of Feshbach scattering and more phenomenological approaches. It permits the calculation of medium effects on the resonance coming from the occupation of closed channel states. The examination of such effects is demonstrated to be of particular relevance to an experimentally important Feshbach resonance for $^{40}\mathrm{K}$ atoms. We analyze a recent rethermalization rate experiment on $^{40}\mathrm{K}$ and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multichannel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.

arXiv:cond-mat/0501407Physical Review AMay 26, 200544 citations

^{6}\text{L}\text{i-}^{40}\text{K}

and

^{40}\text{K}\text{\ensuremath{-}}^{87}\text{R}\text{b}

scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique.

1/{R}^{6}

model potential, and threshold behaviors of the quantum-defect parameters are discussed. The model allows us to predict the Feshbach resonances when the singlet and triplet scattering lengths are known or to fit the scattering lengths when a couple of Feshbach resonances is located experimentally. As an illustrative example, we investigate the

{}^{6}

Li-

{}^{40}

K scattering. The theoretical results agree quite well with experimental values.

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.

{a}^{\mathrm{S}}

and

{a}^{\mathrm{T}}

, as well as an adjustable parameter ${\ensuremath{\gamma}}_{\mathrm{sr}}$, this model can be used to reliably predict FRs. An application example of $^{6}\mathrm{Li}\ensuremath{-}^{40}\mathrm{K}$ collision shows that the results given by the simple model agree quite well with both the relevant experimental data and the coupled-channel calculations.

^{40}\mathrm{K}

atoms. We analyze a recent rethermalization rate experiment on

^{40}\mathrm{K}

and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multichannel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.