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Physical Review A

Model for collisions in ultracold-atom mixtures

Marco Anderlini, D. Ciampini, D. Cossart, E. Courtade, Matteo Cristiani, Carlo Sias, O. Morsch, E. Arimondo

Published Sep 14, 2005• 16 citations
Publisher

Abstract

We present a model for the collisional properties of a mixture of $^{133}\mathrm{Cs}$ and $^{87}\mathrm{Rb}$ atoms in a magnetic trap at $\ensuremath{\mu}\mathrm{K}$ temperatures. The experimental sequence we model corresponds to a selective evaporation of the Rb atoms using a radio-frequency field, leading to sympathetic cooling of the Cs atoms or, if selective evaporation is carried out fast, to a difference in temperature between the two atomic species. In the latter case, the two atomic clouds reached an equilibrium temperature starting from an Rb temperature lower than that of Cs. By supposing that each atomic cloud was in thermal equilibrium we modeled this rethermalization process through differential equations for the two atomic temperatures. An alternative approach was based on the Monte Carlo simulations of the individual collisional processes. The sympathetic cooling and the rethermalization were analyzed in terms of the inter-species collisional cross-section.

DOI
10.1103/physreva.72.033408

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A cold atomic gas formed by two different species represents an intriguing system for a deeper understanding of atom-atom interactions at ultralow temperatures. We present experiments on a mixture of atomic lithium and cesium which are of particular interest regarding the formation of heteronuclear molecules on the one hand, and the prospects for sympathetic cooling of atomic gases through mutual thermalization on the other hand. A first series of experiments on interaction in presence of a near-resonant light field is performed in a two-species magneto-optical trap. The collisional properties of the lithium-cesium mixture are investigated through detailed analysis of trap-loss processes induced by the trap light. Photoassociation in an additional near-resonant laser field yields high-resolution spectra of the excited Cs_2 dimers, but shows no unambiguous indication of LiCs molecule formation. A second series of experiments on pure ground-state collisional properties utilizes an optical dipole trap formed by light that is detuned extremely far below atomic resonance (quasi-electrostatic trap). Storage times of many minutes are achieved in a particularly simple and versatile setup for both atomic species. Cooling of cesium through evaporation and thermalization by elastic collisions is observed. The evolution of temperature and particle number is compared with model simulations of evaporative cooling. Direct laser cooling of trapped cesium in the absolute energetic ground state is demonstrated. Homonuclear spin-changing collisions of ground-state cesium and lithium atoms are analyzed, and first evidence for pure ground-state collisions between atoms of different species is found. Based on the current achievements, prospects for future experiments are discussed. (orig.)

•Jan 1, 2000•1 citation
We present a model for the collisional properties of a mixture of 133Cs^{133}\mathrm{Cs}133Cs and 87Rb^{87}\mathrm{Rb}87Rb atoms in a magnetic trap at \ensuremathμK\ensuremath{\mu}\mathrm{K}\ensuremathμK temperatures. The experimental sequence we model corresponds to a selective evaporation of the Rb atoms using a radio-frequency field, leading to sympathetic cooling of the Cs atoms or, if selective evaporation is carried out fast, to a difference in temperature between the two atomic species. In the latter case, the two atomic clouds reached an equilibrium temperature starting from an Rb temperature lower than that of Cs. By supposing that each atomic cloud was in thermal equilibrium we modeled this rethermalization process through differential equations for the two atomic temperatures. An alternative approach was based on the Monte Carlo simulations of the individual collisional processes. The sympathetic cooling and the rethermalization were analyzed in terms of the inter-species collisional cross-section.
We report on measurements of the collisional properties of a mixture of 133Cs^{133}\mathrm{Cs}133Cs and 87Rb^{87}\mathrm{Rb}87Rb atoms in a magnetic trap at $\ensuremath{\mu}\mathrm{K}$ temperatures. By selectively evaporating the Rb atoms using a radio-frequency field, we achieved sympathetic cooling of Cs down to a few $\ensuremath{\mu}\mathrm{K}$. The interspecies collisional cross section was determined through rethermalization measurements, leading to good agreement with a theoretical prediction of 595a0595{a}_{0}595a0​ for the triplet sss-wave scattering length for Rb in the $\ensuremath{\mid}F=2,{m}_{F}=2⟩$ and Cs in the $\ensuremath{\mid}F=4,{m}_{F}=4⟩$ magnetic states. We briefly speculate on the prospects for reaching the Bose-Einstein condensation of Cs inside a magnetic trap through sympathetic cooling.
We model sympathetic cooling of ground-state CaF molecules by ultracold Li and Rb atoms. The molecules are moving in a microwave trap, while the atoms are trapped magnetically. We calculate the differential elastic cross sections for CaF-Li and CaF-Rb collisions, using model Lennard-Jones potentials adjusted to give typical values for the sss-wave scattering length. Together with trajectory calculations, these differential cross sections are used to simulate the cooling of the molecules, the heating of the atoms, and the loss of atoms from the trap. We show that a hard-sphere collision model based on an energy-dependent momentum transport cross section accurately predicts the molecule cooling rate but underestimates the rates of atom heating and loss. Our simulations suggest that Rb is a more effective coolant than Li for ground-state molecules, and that the cooling dynamics is less sensitive to the exact value of the sss-wave scattering length when Rb is used. Using realistic experimental parameters, we find that molecules can be sympathetically cooled to $100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ in about 10 s. By applying evaporative cooling to the atoms, the cooling rate can be increased and the final temperature of the molecules can be reduced to $1 \ensuremath{\mu}\mathrm{K}$ within 30 s.
We determine the interspecies sss-wave triplet scattering length a3{a}_{3}a3​ for all K-Rb isotopic mixtures by measuring the elastic cross section for collisions between 41K^{\mathrm{41}}\mathrm{K}41K and 87Rb^{87}\mathrm{R}\mathrm{b}87Rb in different temperature regimes. The positive value ${a}_{3}=+{163}_{\ensuremath{-}12}^{+57}{a}_{0}$ ensures the stability against collapse of binary $^{41}\mathrm{K}\ensuremath{-}^{87}\mathrm{R}\mathrm{b}$ Bose-Einstein condensates. For the fermion-boson mixture $^{40}\mathrm{K}\ensuremath{-}^{87}\mathrm{R}\mathrm{b}$, we obtain a large and negative scattering length which implies an efficient sympathetic cooling of the fermionic species down to the degenerate regime.
This thesis reports the formation of a dual-species Bose-Einstein condensate of 87^{87}87Rb and 133^{133}133Cs in the same trapping potential. Quantum degenerate mixtures exhibit rich physics inaccessible to single species experiments and provide an ideal starting point for the creation of ultracold dipolar molecules. These molecules offer a wealth of new research avenues including precision metrology, quantum simulation and computation. The experimental method exploits the efficient sympathetic cooling of 133^{133}133Cs via elastic collisions with 87^{87}87Rb, initially in a magnetic quadrupole trap and subsequently in a levitated optical trap. Evaporative cooling in the dipole trap must compete against a high interspecies three-body inelastic collision rate \mbox{∼10−25−10−26\sim10^{-25}-10^{-26}∼10−25−10−26~cm6/^{6}/6/s}. The two condensates each contain up to \mbox{2×1042\times10^{4}2×104} atoms and exhibit a striking phase separation, revealing the mixture to be immiscible due to strong repulsive interspecies interactions. Sacrificing all the 87^{87}87Rb during the cooling leads to the creation of single-species 133^{133}133Cs condensates of up to \mbox{6×1046\times10^{4}6×104} atoms. In addition this thesis reports the observation of an interspecies Feshbach resonance at 181.7(5)~G and the creation of a pure sample of Cs2_{2}2​ molecules via magneto-association on the 4(g)4 resonance at 19.8~G. These results represent important steps towards the creation of ultracold polar RbCs molecules.
A cold atomic gas formed by two different species represents an intriguing system for a deeper understanding of atom-atom interactions at ultralow temperatures. We present experiments on a mixture of atomic lithium and cesium which are of particular interest regarding the formation of heteronuclear molecules on the one hand, and the prospects for sympathetic cooling of atomic gases through mutual thermalization on the other hand. A first series of experiments on interaction in presence of a near-resonant light field is performed in a two-species magneto-optical trap. The collisional properties of the lithium-cesium mixture are investigated through detailed analysis of trap-loss processes induced by the trap light. Photoassociation in an additional near-resonant laser field yields high-resolution spectra of the excited Cs_2 dimers, but shows no unambiguous indication of LiCs molecule formation. A second series of experiments on pure ground-state collisional properties utilizes an optical dipole trap formed by light that is detuned extremely far below atomic resonance (quasi-electrostatic trap). Storage times of many minutes are achieved in a particularly simple and versatile setup for both atomic species. Cooling of cesium through evaporation and thermalization by elastic collisions is observed. The evolution of temperature and particle number is compared with model simulations of evaporative cooling. Direct laser cooling of trapped cesium in the absolute energetic ground state is demonstrated. Homonuclear spin-changing collisions of ground-state cesium and lithium atoms are analyzed, and first evidence for pure ground-state collisions between atoms of different species is found. Based on the current achievements, prospects for future experiments are discussed. (orig.)