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Physical Review A

Magnetic relaxation in dysprosium-dysprosium collisions

Bonna K. Newman, Nathan Brahms, Yat Shan Au, Cort Johnson, Colin B. Connolly, John M. Doyle, Daniel Kleppner, Thomas J. Greytak

Published Jan 31, 2011• 14 citations
Publisher

Abstract

The collisional magnetic reorientation rate constant ${g}_{R}$ is measured for magnetically trapped atomic dysprosium (Dy), an atom with large magnetic dipole moments. Using buffer gas cooling with cold helium, large numbers ($>{10}^{11}$) of Dy are loaded into a magnetic trap and the buffer gas is subsequently removed. The decay of the trapped sample is governed by collisional reorientation of the atomic magnetic moments. We find ${g}_{R}=1.9\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ cm${}^{3}$ s${}^{\ensuremath{-}1}$ at 390 mK. We also measure the magnetic reorientation rate constant of holmium (Ho), another highly magnetic atom, and find ${g}_{R}=5\ifmmode\pm\else\textpm\fi{}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ cm${}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$ at 690 mK. The Zeeman relaxation rates of these atoms are greater than expected for the magnetic dipole-dipole interaction, suggesting that another mechanism, such as an anisotropic electrostatic interaction, is responsible. Comparison with estimated elastic collision rates suggests that Dy is a poor candidate for evaporative cooling in a magnetic trap.

DOI
10.1103/physreva.83.012713

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The collisional magnetic reorientation rate constant gR{g}_{R}gR​ is measured for magnetically trapped atomic dysprosium (Dy), an atom with large magnetic dipole moments. Using buffer gas cooling with cold helium, large numbers (>1011>{10}^{11}>1011) of Dy are loaded into a magnetic trap and the buffer gas is subsequently removed. The decay of the trapped sample is governed by collisional reorientation of the atomic magnetic moments. We find gR=1.9\ifmmode±\else\textpm\fi0.5\ifmmode×\else\texttimes\fi10\ensuremath−11{g}_{R}=1.9\ifmmode\pm\else\textpm\fi{}0.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}gR​=1.9\ifmmode±\else\textpm\fi0.5\ifmmode×\else\texttimes\fi10\ensuremath−11 cm3{}^{3}3 s\ensuremath−1{}^{\ensuremath{-}1}\ensuremath−1 at 390 mK. We also measure the magnetic reorientation rate constant of holmium (Ho), another highly magnetic atom, and find gR=5\ifmmode±\else\textpm\fi2\ifmmode×\else\texttimes\fi10\ensuremath−12{g}_{R}=5\ifmmode\pm\else\textpm\fi{}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}gR​=5\ifmmode±\else\textpm\fi2\ifmmode×\else\texttimes\fi10\ensuremath−12 cm3{}^{3}3 s\ensuremath−1{\mathrm{s}}^{\ensuremath{-}1}s\ensuremath−1 at 690 mK. The Zeeman relaxation rates of these atoms are greater than expected for the magnetic dipole-dipole interaction, suggesting that another mechanism, such as an anisotropic electrostatic interaction, is responsible. Comparison with estimated elastic collision rates suggests that Dy is a poor candidate for evaporative cooling in a magnetic trap.
Ultracold dysprosium gases, with a magnetic moment 10 times that of alkali atoms and equal only to terbium as the most magnetic atom, are expected to exhibit a multitude of fascinating collisional dynamics and quantum dipolar phases, including quantum liquid crystal physics. We report the first laser cooling and trapping of half a billion Dy atoms using a repumper-free magneto-optical trap (MOT) and continuously loaded magnetic confinement, and we characterize the trap recycling dynamics for bosonic and fermionic isotopes. The first inelastic collision measurements in the few partial wave, 100 microK-1 mK, regime are made in a system possessing a submerged open electronic f shell. In addition, we observe unusual stripes of intra-MOT <10 microK sub-Doppler cooled atoms.
Spin relaxation due to atom--atom collisions is measured for magnetically trapped erbium and thulium atoms at a temperature near 500 mK. The rate constants for Er--Er and Tm--Tm collisions are $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ and $1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}$ cm3{}^{3}3 ${\mathrm{s}}^{\ensuremath{-}1}$, respectively, 2−−32--32−−3 orders of magnitude larger than those observed for highly magnetic SSS-state atoms. This is strong evidence for an additional, dominant, spin relaxation mechanism, electronic interaction anisotropy, in collisions between these ``submerged-shell,'' $L\ensuremath{\ne}0$ atoms. These large spin relaxation rates imply that evaporative cooling of these atoms in a magnetic trap will be highly inefficient.
The nature of the interaction between ultracold atoms with a large orbital and spin angular momentum has attracted considerable attention. It was suggested that such interactions can lead to the realization of exotic states of highly correlated matter. Here, we report on a theoretical study of the competing anisotropic dispersion, magnetic dipole-dipole, and electric quadrupole-quadrupole forces between two dysprosium atoms. Each dysprosium atom has an orbital angular momentum of L = 6 and a magnetic moment of μ = 10 μ(B). We show that the dispersion coefficients of the ground state adiabatic potentials lie between 1865 a.u. and 1890 a.u., creating a non-negligible anisotropy with a spread of 25 a.u. and that the electric quadrupole-quadrupole interaction is weak compared to the other interactions. We also find that for interatomic separations R < 50a(0) both the anisotropic dispersion and magnetic dipole-dipole potential are larger than the atomic Zeeman splittings for external magnetic fields of order 10 G to 100 G. At these separations the atomic angular momentum can be reoriented. We finish by describing two scattering models for these inelastic m-changing collisions. A universal scattering theory is used to model loss due to the anisotropy in the dispersion and a Born approximation is used to model losses from the magnetic dipole-dipole interaction for the (164)Dy isotope. These models find loss rates that are of the same order of magnitude as the experimental value.
We have magnetically trapped and evaporatively cooled atomic molybdenum. Using a cryogenic helium buffer gas, $2\ifmmode\times\else\texttimes\fi{}{10}^{10}$ molybdenum atoms are loaded into a magnetic trap at an initial temperature of 500 mK. The molybdenum atoms undergo two-body decay with a measured inelastic rate constant of ${g}_{\mathrm{in}}=(1.2\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for the initial conditions after loading. The molybdenum atoms are cooled by adiabatic expansion and forced evaporation to 200 mK.
We report a combined experimental and theoretical study of collision-induced dipolar relaxation in a cold spin-polarized gas of atomic nitrogen (N). We use buffer gas cooling to create trapped samples of 14N^{14}\mathrm{N}14N and 15N^{15}\mathrm{N}15N atoms with densities $(5\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}{10}^{12} {\mathrm{cm}}^{\ensuremath{-}3}$ and measure their magnetic relaxation rates at milli-Kelvin temperatures. These measurements, together with rigorous quantum scattering calculations based on accurate ab initio interaction potentials for the ${}^{7}{\ensuremath{\Sigma}}_{u}^{+}$ electronic state of N2{\mathrm{N}}_{2}N2​ demonstrate that dipolar relaxation in N+N\mathrm{N}+\mathrm{N}N+N collisions occurs at a slow rate of $~{10}^{\ensuremath{-}13} {\mathrm{cm}}^{3}$/s over a wide range of temperatures (1 mK to 1 K) and magnetic fields (10 mT to 2 T). The calculated dipolar relaxation rates are insensitive to small variations of the interaction potential and to the magnitude of the spin-exchange interaction, enabling the accurate calibration of the measured N atom density. We find consistency between the calculated and experimentally determined rates. Our results suggest that N atoms are promising candidates for future experiments on sympathetic cooling of molecules.
We investigate Zeeman relaxation in cold Sb(${}^{4}{S}_{3/2}^{\ensuremath{\circ}}$)--He collisions in a magnetic field. Ensembles of >>>1013{10}^{13}1013 laser-ablated Sb atoms are cooled in cryogenic 4{}^{4}4He buffer gas to 800 mK and inelastic collisions are observed to equilibrate the mJ{m}_{J}mJ​-state distribution to the translational temperature. The ratio $\ensuremath{\gamma}$ of momentum transfer to inelastic collision rates is measured to be $\ensuremath{\leqslant}9.1\ifmmode\times\else\texttimes\fi{}{10}^{2}$. We also perform quantum scattering calculations of Sb--4{}^{4}4He collisions, based on ab initio interaction potentials, that demonstrate significant anisotropy of the ground state induced by the spin-orbit interaction. Agreement is obtained between theory and experiment with a $\ensuremath{\approx}101010%$ increase in the ab initio potential depth. This work suggests that buffer-gas-cooled pnictogen atoms lighter than Sb can be loaded into a magnetic trap.