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arXiv:physics/0302094 · Physical Review Letters

Multichannel Cold Collisions between Metastable Sr Atoms

Viatcheslav Kokoouline, Robin Santra, Chris H. Greene

Published Jun 23, 2003• 49 citations
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Abstract

We present a multichannel-scattering calculation of elastic and inelastic cold collisions between two low-field seeking, metastable 88Sr [(5s5p)3P2] atoms in the presence of an external magnetic field. The scattering physics is governed by strong anisotropic long-range interactions, which lead to pronounced coupling among the partial waves of relative motion. As a result, nonadiabatic transitions are shown to trigger a high rate of inelastic losses. At relatively high energies, T>100 microK, the total inelastic collision rate is comparable with the elastic rate. However, at lower collisional energy, the elastic rate decreases, and at T approximately 1 microK, it becomes substantially smaller than the inelastic rate. Our study suggests that magnetic trapping and evaporative cooling of 88Sr [(5s5p)3P2] atoms, as well as 40Ca [(4s4p)3P2], in low-field seeking states will prove difficult to achieve experimentally.

DOI
10.1103/physrevlett.90.253201

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•Jan 1, 2011•0 citations
We present a multichannel-scattering calculation of elastic and inelastic cold collisions between two low-field seeking, metastable 88Sr [(5s5p)3P2] atoms in the presence of an external magnetic field. The scattering physics is governed by strong anisotropic long-range interactions, which lead to pronounced coupling among the partial waves of relative motion. As a result, nonadiabatic transitions are shown to trigger a high rate of inelastic losses. At relatively high energies, T>100 microK, the total inelastic collision rate is comparable with the elastic rate. However, at lower collisional energy, the elastic rate decreases, and at T approximately 1 microK, it becomes substantially smaller than the inelastic rate. Our study suggests that magnetic trapping and evaporative cooling of 88Sr [(5s5p)3P2] atoms, as well as 40Ca [(4s4p)3P2], in low-field seeking states will prove difficult to achieve experimentally.
Ultracold collisions between metastable bosonic 88{}^{88}88Sr [(5s5p)3P2(5s5p){\phantom{\rule{0.16em}{0ex}}}^{3\phantom{\rule{-0.16em}{0ex}}}\phantom{\rule{-0.16em}{0ex}}{P}_{2}(5s5p)3P2​] and fermionic 87{}^{87}87Sr [(5s5p)3P2(5s5p){\phantom{\rule{0.16em}{0ex}}}^{3\phantom{\rule{-0.16em}{0ex}}}\phantom{\rule{-0.16em}{0ex}}{P}_{2}(5s5p)3P2​ (i=9/2)(i=9/2)(i=9/2)] atoms are investigated based on an approach of tensorial analysis. The scattering physics of two atoms in fully polarized sss-wave entrance channels is studied in detail. In the Born-Oppenheimer approximation, the strong anisotropic interatomic interaction is demonstrated to induce formations of long-range molecular potential wells. However, besides significantly modifying the elastic scattering, the anisotropic interatomic interaction leads to the strong multichannel coupling between different partial waves, which triggers a high rate of inelastic losses. By applying an external static magnetic field B0=B0ez{\mathbf{B}}_{0}={\mathcal{B}}_{0}{\mathbf{e}}_{\mathrm{z}}B0​=B0​ez​, the inelastic scattering can be suppressed while the elastic scattering is significantly enhanced. Additionally, the energy-dependent complex sss-wave scattering lengths at a given relative collision energy strongly depend on the strength of magnetic field. We, moreover, self-consistently investigate ultracold collisions of two atoms at low temperatures in an optical lattice site. In the $\ensuremath{\delta}$-function pseudopotential approximation, we derive the effective sss-wave scattering lengths, energy eigenvalues, elastic and inelastic scattering rates, and their dependence on the external magnetic field. We find that (i) the effective scattering lengths of ultracold atoms in entrance channels of interest display resonance behavior at certain values of magnetic field and (ii) the extra Zeeman interaction not only leads to the suppression of inelastic scattering but also enlarges the elastic scattering rates.
Recent theoretical work indicates that collisions between metastable alkaline-earth atoms (AEAs) in the presence of external magnetic fields should be largely determined by partial waves with large angular momenta even at very low temperatures. Unusually large inelastic collision cross sections were predicted and doubts have been raised regarding the feasibility of evaporative cooling of metastable AEAs in magnetic traps. Here we present experimental data for 40Ca[4s4p]3 P2 clearly confirming the asserted multichannel character of the collision mechanism. While elastic cross sections are found to be similar to the predicted values, inelastic cross sections exceed the calculations by an order of magnitude. Our results substantiate the expectation of inefficient evaporative cooling.
The binary collision dynamics of 2Dg,3/2{}^{2}{D}_{g,3/2}2Dg,3/2​ ground state scandium atoms is studied from first principles. We employ 30 coupled diabatic ab initio potentials in a coupled-channels study of the scattering dynamics of cold and ultracold scandium atoms in external magnetic fields. Due to the long-ranged magnetic dipolar interaction, the field dependence of the cross section does not follow the threshold laws derived by Volpi and Bohn [Phys. Rev. A 65, 052712 (2002)]. In the field-free case, the near-threshold cross section is independent of the collision energy, and hence the cross section does not follow the well-established Wigner threshold laws. The observed threshold behavior is explained in the Born approximation. For energies above $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, inelastic collisions are driven by the anisotropic nonrelativistic electronic interaction. For energies below $100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, the ratio of elastic-to-inelastic collisions is likely to be favorable for evaporative cooling. Both anisotropy in the long-range interaction and in the short-range potential contribute to large cross sections for inelastic collisions at higher energies and lead to a small ratio of elastic-to-inelastic collisions. This is in agreement with the large rates for Zeeman relaxation of submerged-shell atoms observed experimentally. The effect of the uncertainty in the ab initio potential is sampled by scaling the reduced mass and is found to have little influence on the conclusions drawn from this work.
Ultracold collisions of spin-polarized 24Mg, 40Ca, and 88Sr in the metastable 3P2 excited state are investigated based on molecular potentials obtained from ab initio calculations. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 mT. A loss-rate model shows that losses should be smallest near zero magnetic field and for fields slightly larger than the resonance field, where the scattering length is also positive.
We measure the rates of elastic and inelastic two-body collisions of cold spin-polarized neon atoms in the metastable 3P2^{3}P_{2}3P2​ state for 20Ne^{20}\mathrm{Ne}20Ne and 22Ne^{22}\mathrm{Ne}22Ne in a magnetic trap. From particle loss, we determine the loss parameter of inelastic collisions $\ensuremath{\beta}=6.5(18)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for 20Ne^{20}\mathrm{Ne}20Ne and $\ensuremath{\beta}=1.2(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\text{ }\text{ }{\mathrm{cm}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for 22Ne^{22}\mathrm{Ne}22Ne. These losses are caused by ionizing (i.e., Penning) collisions and occur less frequently than for unpolarized atoms. This proves the suppression of Penning ionization due to spin polarization. From cross-dimensional relaxation measurements, we obtain elastic scattering lengths of $a=\ensuremath{-}180(40){a}_{0}$ for 20Ne^{20}\mathrm{Ne}20Ne and $a=+{150}_{\ensuremath{-}50}^{+80}{a}_{0}$ for 22Ne^{22}\mathrm{Ne}22Ne, where a0=0.0529  nm{a}_{0}=0.0529\text{ }\text{ }\mathrm{nm}a0​=0.0529  nm.
In this work we investigate the potential of controlling cold (O(K)−mK) and ultracold (mK-μK) atom-molecule collisions by tuning scattering states across Feshbach resonances using magnetic fields. We are interested in particular in the prospect of suppressing the often undesirable inelastic collisions. The He-O_2 system provides the vehicle for our study. We calculate bound and quasi-bound states of several isotopic combinations, including their Zeeman structure, to reveal the underlaying pattern for easier characterization of quasi-bound states in terms of rigorous and approximately good quantum numbers. These calculations also help us locate the fields at which zero-energy resonances will occur. Scattering calculations are then performed for collisions of 3^He and 4^He with {16}^O_2 at fixed (1 μK) energy but varying magnetic field. The field is varied to sweep the scattering state across resonance. At low and ultralow energies we enter the Wigner threshold regime where the S-partial wave dominates the wavefunction. The cross sections, and the real and imaginary parts of the scattering length, vary dramatically across resonance. Their profiles are used to analyze the resonances. In a highlight of our results we show that dramatic suppression of inelastic cross sections occur for 4^He-{16}^O_2 . The resonances are relatively wide (of order 100 Gauss), with suppression of inelastic scattering over a similarly wide range of fields and for temperatures ranging from 10 mK down to 1 μK. We conclude that under certain conditions it is possible to almost completely eliminate inelastic collisions. This is potentially very important for cooling techniques, such as evaporative and sympathetic cooling, that require efficient elastic cross sections. Suppression of inelastic collisions can not only increase thermalization efficiency but it can also result in longer trap-lifetimes by reducing transitions to untrapable states.