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Chinese Physics B

The influence of collision energy on magnetically tuned 6Li-6Li Feshbach resonance

Rong Zhang, Yong‐Chang Han, Shu‐Lin Cong, Maksim B. Shundalau

Published Jan 19, 2022• 7 citations
Publisher

Abstract

The effect of collision energy on the magnetically tuned 6Li–6Li Feshbach resonance (FR) is investigated theoretically by using the coupled-channel (CC) method for the collision energy ranging from 1 μK ⋅ k B to 100 μK ⋅ k B. At the collision energy of 1 μK ⋅ k B, the resonance positions calculated are 543.152 Gs (s wave, the unit 1 Gs = 10−4 T), 185.109 Gs (p wave |ml | = 0), and 185.113 Gs (p wave |ml | = 1), respectively. The p-wave FR near 185 Gs exibits a doublet structure of 4 mGs, associated with dipole–dipole interaction. With the increase of the collision energy, it is found that the splitting width remains the same (4 mGs), and that the resonance positions of s and p waves are shifted to higher magnetic fields with the increase of collision energy. The variations of the other quantities including the resonance width and the amplitude of the total scattering section are also discussed in detail. The thermally averaged elastic rate coefficients at T = 10, 15, 20, 25 K are calculated and compared.

DOI
10.1088/1674-1056/ac4cc3

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The effect of collision energy on the magnetically tuned 6Li–6Li Feshbach resonance (FR) is investigated theoretically by using the coupled-channel (CC) method for the collision energy ranging from 1 μK ⋅ k B to 100 μK ⋅ k B. At the collision energy of 1 μK ⋅ k B, the resonance positions calculated are 543.152 Gs (s wave, the unit 1 Gs = 10−4 T), 185.109 Gs (p wave |ml | = 0), and 185.113 Gs (p wave |ml | = 1), respectively. The p-wave FR near 185 Gs exibits a doublet structure of 4 mGs, associated with dipole–dipole interaction. With the increase of the collision energy, it is found that the splitting width remains the same (4 mGs), and that the resonance positions of s and p waves are shifted to higher magnetic fields with the increase of collision energy. The variations of the other quantities including the resonance width and the amplitude of the total scattering section are also discussed in detail. The thermally averaged elastic rate coefficients at T = 10, 15, 20, 25 K are calculated and compared.
Abstract Taking the ultracold 85 Rb– 87 Rb collision system as an example, we investigated the Feshbach resonances of nonzero partial waves above the threshold. The self-energy at the threshold, which represents the coupling strength between open and closed channels, is considered a critical parameter to quantitatively describe the properties of Feshbach resonances. The total elastic and inelastic cross sections are calculated as functions of the magnetic field B and collision energy E col , ranging from 0.1 to 600 μ K. For a large absolute value of the self-energy at the threshold, the resonance decays rapidly with increasing collision energy, and narrow resonances of nonzero partial waves can be clearly resolved in the contour plot of the inelastic cross section versus the collision energy and magnetic field. It was found that the resonance tail appeared at the given magnetic field when the cross section decreased from the maximal value of the resonance peak to the minimum value, where a long resonance tail indicates an appreciable resonance in a relatively large region of collision energy. This relationship between the self-energy and the properties of Feshbach resonances still exists in the thermally averaged inelastic rate coefficient. The bound-state energies for nonzero partial waves split owing to the spin–spin interaction, which results in multiple nearly-overlapping resonances. Both the spin–spin and second-order spin–orbit effects are included. However, multiple nearly-overlapping resonances for nonzero partial waves are difficult to resolve in thermally averaged rate coefficients.
The effects of an electric field on the magnetically induced 6{}^{6}6Li-40{}^{40}40K Feshbach resonances are investigated theoretically by using the asymptotic bound-state model. We calculate the positions and widths of the Feshbach resonances observed in the experiments in the presence of an electric field and give a detailed analysis. An electric field can change the relative magnetic moment and the coupling strength to a different extent. The variation of resonant width caused by a strong electric field mainly depends on the coupling strength, and the sss-wave scattering cross section in an electric field is sensitive to the temperature of the colliding system and the magnetic-field intensity. The maximum of the thermal average scattering rate constant can be changed by several factors by applying an electric field.
We present a theoretical model for investigating the magnetically tuned Feshbach resonance (MTFR) of alkali metal atoms using the separable potential method (SPM). We discuss the relationship and difference between the SPM and the asymptotic bound state model. To demonstrate the validity of the SPM, we use it to calculate the weakly bound state energy and magnetically tuned scattering length for the 6Li–40K, 7Li2, and 6Li2 systems with narrow and broad Feshbach resonances. The results of the SPM calculations are in good agreement with those of coupled channel calculations and with experimental measurements for all three systems. The SPM, by simplifying the calculation of the two-body MTFR, is expected to simplify numerical computations for three-atom collisions in a magnetic field and the Feshbach-optimized photoassociation process.
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We use a full coupled-channels method to calculate collisional properties of magnetically or optically trapped ultracold 6Li.{}^{6}\mathrm{Li}.6Li. The magnetic-field dependence of the sss-wave scattering lengths of several mixtures of hyperfine states are determined, as are the decay rates due to exchange collisions. In one case, we find Feshbach resonances at B=0.08TB=0.08\mathrm{T}B=0.08T and B=1.98T.B=1.98\mathrm{T}.B=1.98T. We show that the exact coupled-channels calculation is well approximated over the entire range of magnetic fields by a simple analytical calculation.
We analyze, within the generalized multichannel quantum defect theory framework, atomic binary collision cross sections over the $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$ to 10mK10\phantom{\rule{0.3em}{0ex}}\mathrm{mK}10mK energy range just above the entrance channel threshold, a domain where the Wigner threshold law should apply. By adjusting the strength of a constant external magnetic field a Feshbach resonance is tuned at will over this energy range. In the threshold regime, the quasibound state interacts with an opening continuum whose wave function presents a strong energy dependence which reflects the breakdown of the WKB approximation. The effective discrete-continuum interactions become very sensitive to the energy. The consequences of these variations have been investigated by including threshold effects in the analysis of the Fano configuration-interaction theory [Phys. Rev. 124, 1866 (1961)] in terms of quantum defect theory quantities proposed by [Lecomte J. Phys. B 20, 3645 (1987)]. This analysis shows that the energy variations are in general so important that it becomes meaningless to associate a width with a Feshbach resonance. However, it is still possible to define the resonance energy, as long as the energy variation of the shift of the resonance, induced by the effective discrete-continuum interaction, remains linear over an energy range corresponding to the magnitude of the shift.