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arXiv:0811.4282 · Physical Review A

Feshbach resonance in d -wave collisions

Quentin Beaufils, A. Crubellier, T. Zanon-Willette, B. Laburthe-Tolra, É. Maréchal, L. Vernac, O. Gorceix

Published Mar 16, 2009• 38 citations
arXivHTMLPDF

Abstract

We analyze a narrow Feshbach resonance with ultracold chromium atoms colliding in $d$ wave. The resonance is made possible by dipole-dipole interactions, which couple an incoming $l=2$ collision channel with a bound molecular state with $l=0$. 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.

DOI
10.1103/physreva.79.032706

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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.
We study atom losses associated to a previously unreported magnetic Feshbach resonance in 39K^{39}\mathrm{K}39K. This resonance is peculiar in that it presents ddd-wave character both in the open and closed channels, directly coupled by the dominant spin-exchange interaction. The losses associated to a ddd-wave open-channel resonance present specific signatures such as strong temperature dependance and anisotropic line shapes. The resonance strength and position depend on the axial projection of the orbital angular momentum of the system and are extracted from rigorous multichannel calculations. A two-step model, with an intermediate collision complex being ejected from the trap after collisions with free atoms, permits us to reproduce the observed dependance of the loss rate as a function of temperature and magnetic field.
We report on experiments with ultracold chromium atoms. Preparing a cloud of 52Cr atoms in a crossed optical dipole trap (CODT) and applying magnetic fields between 4 and 600 G, we observe 14 Feshbach resonances by the occurrence of increased atom loss at distinct magnetic field values. A comparison with theory taking only dipole–dipole coupling into account shows very good agreement between experimental and theoretical resonance positions and allows us to extract the s-wave scattering lengths a 6=112(14) a 0, a 4= 58(6) a 0, a 2=−7(20) a 0 of the involved molecular potentials as well as the dispersion coefficients C 6= 733(70) au and au. The strongest resonance at 589 G has a calculated width of 1.7 G and reveals a three-body loss coefficient below L 3, max∼3×10−36 m6 s−1. Further evaporative cooling within the CODT leads to the formation of a Bose–Einstein condensate (BEC) with up to 100 000 condensed atoms. The magnetic dipole–dipole interaction between the Cr atoms is so strong that, as a first mechanical manifestation of dipole–dipole interaction, we observe a modification of the condensate expansion which depends on the alignment of the atomic magnetic dipoles with respect to the axis of the CODT. This magnetostrictive effect is in very good agreement with the theory of dipolar quantum gases and shows that a Cr-BEC is an excellent model system to study dipole–dipole interactions in degenerate quantum gases.
We study atom losses associated to a previously unreported magnetic Feshbach resonance in potassium 39. This resonance is peculiar in that it presents ddd-wave character both in the open and in the closed channels, directly coupled by the dominant spin-exchange interaction. The losses associated to a ddd-wave open-channel resonance present specific signatures such as strong temperature dependance and anisotropic line shapes. The resonance strength and position depend on the axial projection of the orbital angular momentum of the system and are extracted from rigorous multichannel calculations. A two-step model, with an intermediate collision complex being ejected from the trap after collisions with free atoms, permits to reproduce the observed dependance of the loss rate as a function of temperature and magnetic field.
We study collisions in an optically trapped, pure sample of ultracold Cs 2 molecules in various internal states. The molecular gas is created by Feshbach association from a near-degenerate atomic gas, with adjustable temperatures in the nanokelvin range. We identify several narrow loss resonances, which point to the coupling to more complex molecular states and may be interpreted as Feshbach resonances in dimerdimer interactions. Moreover, in some molecular states we observe a surprising temperature dependence in collisional loss. This shows that the situation cannot be understood in terms of the usual simple threshold behavior for inelastic two-body collisions. We interpret this observation as further evidence for a more complex molecular structure beyond the well-understood dimer physics.
By applying a magnetic field across a trapped ultracold gas of alkali metal atoms, it is possible to alter the binding energies of near threshold molecular states. The proximity of molecular states to the scattering threshold has a strong effect on the threshold scattering characteristics. Because of this the magnetic field strength can be used to control low energy scattering within the gas. This resonant phenomena is referred to as a magnetically tuneable Feshbach resonance. This thesis looks at these and related phenomena in the context of trapped potassium atoms. First, we perform coupled-channels calculations in order to characterise a group of previously unreported Feshbach resonances, occurring in a host of different collision channels. Next, we compare these characterisations to empirical data, and more simplified models. Second, a detailed investigation into the photodissociation of weakly bound Feshbach molecules is carried out. This allows us to gain new insights into the structure of the exit channel interaction. We make semi-classical arguments which enable experimentalists to directly measure the height of potential barriers. We also perform detailed numerical calculations which, in conjunction with experimental data, allow us to develop a fine-tuned potential model for the exit state. Third, we model weakly bound triatomic states and their impact on near threshold scattering. Then, we discuss the use of three body recombination as a tool for observing Efimov states. Furthermore, we model the three body recombination rate using a simplified two channel model. Finally we suggest a method intended to provide the basis for numerical calculations using realistic Born-Oppenheimer potentials. It could also be used to analytically study near threshold three body physics.
Inelastic collision rates for ultracold 85Rb{}^{85}\mathrm{Rb}85Rb atoms in the F=2F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2F=2, ${m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2$ state have been measured as a function of magnetic field. At 250 gauss (G), the two- and three-body loss rates were measured to be ${K}_{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(1.87\ifmmode\pm\else\textpm\fi{}0.95\ifmmode\pm\else\textpm\fi{}0.19)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\mathrm{cm}}^{3}/\mathrm{s}$ and ${K}_{3}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({4.24}_{\ensuremath{-}0.29}^{+0.70}\ifmmode\pm\else\textpm\fi{}0.85)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}{\mathrm{cm}}^{6}/\mathrm{s}$, respectively. As the magnetic field is decreased from 250 G towards a Feshbach resonance at 155 G, the inelastic rates decrease to a minimum and then increase dramatically, peaking at the Feshbach resonance. Both two- and three-body losses are important, and individual contributions have been compared with theory.