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arXiv:2012.09223 · Physical Review A

Characterizing the temperature dependence of Fano-Feshbach resonances of ultracold polarized thulium

Vladimir Khlebnikov, V. V. Tsyganok, D. A. Pershin, E. T. Davletov, Elena Kuznetsova, Alexey V. Akimov

Published Feb 4, 2021• 10 citations
arXivHTMLPDF

Abstract

Recent studies demonstrated anomalous temperature shifts for some Fano-Feshbach resonances of thulium atoms. These anomalies were explained by the variation in light intensity in the optical dipole trap, which accompanied changes in temperature. In addition, a temperature-related transformation of the statistics of the inter-resonance spacing was demonstrated [Aikawa et al., Phys. Rev. Lett. 108, 210401 (2012)]. Here, we analyze the shifts of isolated $s$- and $d$-type Fano-Feshbach resonances of ultracold thulium atoms with temperature for a fixed depth of an optical dipole trap. The measurements are consistent with the three-body recombination-based theory of the temperature-related resonance shift and enable the extraction of the resonance parameters, particularly the magnetic moments of closed channel states. This parameter and the known polarizability of the open channel enable us to separate the contributions of the temperature and Stark shift to the overall shift of the resonances and show the dominant role of the Stark effect in the overall shift.

DOI
10.1103/physreva.103.023306

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Recent studies demonstrated anomalous temperature shifts for some Fano-Feshbach resonances of thulium atoms. These anomalies were explained by the variation in light intensity in the optical dipole trap, which accompanied changes in temperature. In addition, a temperature-related transformation of the statistics of the inter-resonance spacing was demonstrated [Aikawa et al., Phys. Rev. Lett. 108, 210401 (2012)]. Here, we analyze the shifts of isolated sss- and ddd-type Fano-Feshbach resonances of ultracold thulium atoms with temperature for a fixed depth of an optical dipole trap. The measurements are consistent with the three-body recombination-based theory of the temperature-related resonance shift and enable the extraction of the resonance parameters, particularly the magnetic moments of closed channel states. This parameter and the known polarizability of the open channel enable us to separate the contributions of the temperature and Stark shift to the overall shift of the resonances and show the dominant role of the Stark effect in the overall shift.
Recently, the transformation from random to chaotic behavior in the statistics of Fano-Feshbach resonances was observed in thulium atoms with rising ensemble temperature. We performed random matrix theory simulations of such spectra and analyzed the resulting statistics in an attempt to understand the mechanism of the transformation. Our simulations show that, when evaluated in terms of the Brody parameter, resonance statistics do not change or change insignificantly when higher temperature resonances are appended to the statistics. In the experiments evaluated, temperature was changed simultaneously with optical dipole trap depth. Thus, simulations included the Stark shift based on the known polarizability of the free atoms and assuming their polarizability remains the same in the bound state. Somewhat surprisingly, we found that, while including the Stark shift does lead to minor statistical changes, it does not change the resonance statistics and, therefore, is not responsible for the experimentally observed statistic transformation. This observation suggests that either our assumption regarding the polarizability of Feshbach molecules is poor or that an additional mechanism changes the statistics and leads to more chaotic statistical behavior.
Here, we report on the observation of a random to chaotic temperature transformation in the statistics of nearest-neighbor spacings of Fano-Feshbach resonances in the ultracold polarized gas of thulium-169 atoms. We associate this transformation to the appearance of so-called d resonances as well as the shift of other resonances with the temperature. In addition to this statistical change, it has been observed that the characters of s- and d-resonance temperature shifts are quite different: s resonances experience almost no shift or even negative shift with the temperature, while d resonances experience an obvious positive shift. The sign change was attributed to the difference in polarizability of Feshbach molecules and free thulium atoms. In addition, careful analysis of the broad Fano-Feshbach resonances enabled the determination of the sign of thulium's background scattering length. A rethermalization experiment made it possible to estimate a length value of a_{bg}=+144±38 a.u. This indicates that thulium atoms are suitable for achieving Bose-Einstein condensation.
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.
We report the observation of large anomalous shifts, up to +7.5 G, of the positions of the 33.6 G and 39.9 G Feshbach resonances in potassium-39 atoms confined in a 1063.9 nm optical dipole trap (ODT) at temperatures up to around 35 μK and trap depths up to about 136 μK. When the atom cloud is cooled to lower temperatures, by reducing the trap depth of the ODT, the shifts decrease proportionally with trap depth and approach zero at zero depth. We show that the large observed shifts originate from a large differential ac Stark shift between the incoming pair of potassium-39 atoms and the weakly bound Feshbach molecule, which in turn originates from an unexpectedly large dynamic polarizability of the Feshbach molecule. The polarizabilities of the Feshbach molecules extracted from the measured shifts of the 33.6 G and 39.9 G resonances are about four to seven times the sum of the polarizabilities of the two incoming potassium-39 atoms, that is, about four to seven times larger than the usual polarizability of weakly bound Feshbach molecules. The large polarizabilities of the Feshbach molecules are attributed to a near-coincidence between the frequency of the 1063.9 nm ODT laser and the frequency of a molecular transition from the last vibrational level of the lowest triplet a3Σ+u potential to a vibrational level of the excited b3Σ+g potential. Other potassium-39 Feshbach resonances we have studied exhibit a zero or very small shift, corresponding to molecular polarizabilities close to the sum of the polarizabilities of the two incoming potassium-39 atoms.
We analyze a narrow Feshbach resonance with ultracold chromium atoms colliding in ddd wave. The resonance is made possible by dipole-dipole interactions, which couple an incoming l=2l=2l=2 collision channel with a bound molecular state with l=0l=0l=0. We find that three-body losses associated with this resonance increase with temperature, and that the loss feature width as a function of magnetic field also increases linearly with temperature. The analysis of our experimental data shows that the Feshbach coupling is small compared both to the temperature and to the density limited lifetime of the resonant bound molecular state. One consequence is that the three-body loss rate is proportional to the square of the number of atoms, and that we can directly relate the amplitude of the losses to the Feshbach coupling parameter. We compare our measurement to a calculation of the coupling between the collisional channel and the molecular bound state by dipole-dipole interactions, and find a good agreement, with no adjustable parameter. An analysis of the loss line shape is also performed, which enables to precisely measure the position of the resonance.