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arXiv:1211.2270 · Physical Review A

Effective range from tetramer-dissociation data for cesium atoms

M. R. Hadizadeh, Marcelo Takeshi Yamashita, Lauro Tomio, A. Delfino, T. Frederico

Published Jan 17, 2013• 12 citations
arXivHTMLPDF

Abstract

The shifts in the four-body recombination peaks, due to an effective range correction to the zero-range model close to the unitary limit, are obtained and used to extract the corresponding effective range of a given atomic system. The approach is applied to an ultracold gas of cesium atoms close to broad Feshbach resonances, where deviations of experimental values from universal model predictions are associated with effective range corrections. The effective range correction is extracted with a weighted average given by $3.9\ifmmode\pm\else\textpm\fi{}0.8{R}_{\mathrm{vdW}}$, where ${R}_{\mathrm{vdW}}$ is the van der Waals length scale, which is consistent with the van der Waals potential tail for the Cs${}_{2}$ system. The method can be generally applied to other cold atom experimental setups to determine the contribution of the effective range to the tetramer dissociation position.

DOI
10.1103/physreva.87.013620

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The shifts in the four-body recombination peaks, due to an effective range correction to the zero-range model close to the unitary limit, are obtained and used to extract the corresponding effective range of a given atomic system. The approach is applied to an ultracold gas of cesium atoms close to broad Feshbach resonances, where deviations of experimental values from universal model predictions are associated with effective range corrections. The effective range correction is extracted with a weighted average given by 3.9\ifmmode±\else\textpm\fi0.8RvdW3.9\ifmmode\pm\else\textpm\fi{}0.8{R}_{\mathrm{vdW}}3.9\ifmmode±\else\textpm\fi0.8RvdW​, where RvdW{R}_{\mathrm{vdW}}RvdW​ is the van der Waals length scale, which is consistent with the van der Waals potential tail for the Cs2{}_{2}2​ system. The method can be generally applied to other cold atom experimental setups to determine the contribution of the effective range to the tetramer dissociation position.
We report a thorough investigation of finite-temperature effects on three-body recombination near a triatomic Efimov resonance in an ultracold gas of cesium atoms. Our measurements cover a wide range from a near-ideal realization of the zero-temperature limit to a strongly temperature-dominated regime. The experimental results are analyzed within a recently introduced theoretical model based on a universal zero-range theory. The temperature-induced shift of the resonance reveals a contribution that points to an energy dependence of the three-body parameter. We interpret this contribution in terms of the finite range of the van der Waals interaction in real atomic systems and we quantify it in an empirical way based on length scale arguments. A universal character of the corresponding resonance shift is suggested by observations related to other Efimov resonances and the comparison with a theoretical finite-temperature approach that explicitly takes the van der Waals interaction into account. Our findings are of importance for the precise determination of Efimov resonance positions from experiments at finite temperatures.
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At long distances, interactions between neutral ground-state atoms can be described by the van der Waals potential. In the ultracold regime, atom-atom scattering is dominated by sss-waves phase shifts given by an effective range expansion in terms of the scattering length ${\ensuremath{\alpha}}_{0}$ and the effective range r0{r}_{0}r0​. We show that while the scattering length cannot be predicted for these potentials, the effective range is given by the universal low-energy theorem ${r}_{0}=A+B/{\ensuremath{\alpha}}_{0}+C/{\ensuremath{\alpha}}_{0}^{2}$, where AAA, BBB, and CCC depend on the dispersion coefficients Cn{C}_{n}Cn​ and the reduced diatom mass. We confront this formula to about 100 determinations of r0{r}_{0}r0​ and ${\ensuremath{\alpha}}_{0}$ and show why the result is dominated by the leading dispersion coefficient C6{C}_{6}C6​. Universality and scaling extend much beyond naive dimensional analysis estimates.
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Quantum-mechanical scattering calculations of Feshbach resonances arising from van der Waals molecule formation are used to determine vibrational and rotational predissociation lifetimes. A multichannel effective range theory is used to establish the relationship between predissociation and the zero-temperature limit of collisional quenching for resonances lying close to the thresholds for dissociation. The elastic scattering Feshbach resonances may be measurable in ultracold atom-molecule experiments.
We revisit the basic properties of Fano-Feshbach resonances in two-body systems with van der Waals tail interactions, such as ultracold neutral atoms. Using a two-channel model and two different methods, we investigate the relationship between the width and shift of the resonances and their dependence on the low-energy parameters of the system. Unlike what was previously believed [C. Chin et al., Rev. Mod. Phys. 82, 1225 (2010)] for magnetic resonances, we find that the ratio between the width and the shift of a resonance does not depend only on the background scattering length, but also on a closed-channel scattering length. We obtain different limits corresponding to different cases of optical and magnetic resonances. Although the generalization of the theory to the multichannel case remains to be done, we found that our two-channel predictions are verified for a specific resonance of lithium-6.