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Physical Review Letters

Resonant Magnetic Field Control of Elastic Scattering in Cold R 85 b

Jacob Roberts, N. R. Claussen, James P. Burke, Chris H. Greene, Eric Cornell, Carl Wieman

Published Dec 7, 1998• 499 citations
Publisher

Abstract

A magnetic field-dependent Feshbach resonance has been observed in the elastic scattering collision rate between atoms in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2$ state of ${}^{85}\mathrm{Rb}$. Changing the magnetic field by several Gauss caused the collision rate to vary by a factor of 1${0}^{4}$, and the sign of the scattering length could be reversed. The resonance peak is at 155.2(4) G and its width is 11.6(5) G. From these results we extract much improved values for the three quantities that characterize the interaction potential: The van der Waals coefficient ${C}_{6}$, the singlet scattering length ${a}_{S}$, and the triplet scattering length ${a}_{T}$.

DOI
10.1103/physrevlett.81.5109

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A magnetic field-dependent Feshbach resonance has been observed in the elastic scattering collision rate between atoms in the F=2,M=\ensuremath−2F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2,M\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2F=2,M=\ensuremath−2 state of 85Rb{}^{85}\mathrm{Rb}85Rb. Changing the magnetic field by several Gauss caused the collision rate to vary by a factor of 104{0}^{4}04, and the sign of the scattering length could be reversed. The resonance peak is at 155.2(4) G and its width is 11.6(5) G. From these results we extract much improved values for the three quantities that characterize the interaction potential: The van der Waals coefficient C6{C}_{6}C6​, the singlet scattering length aS{a}_{S}aS​, and the triplet scattering length aT{a}_{T}aT​.
A magnetic field dependent Feshbach resonance has been observed in the elastic scattering collision rate between atoms in the F = 2, M = -2 state of 85 Rb. Changing the magnetic field by several Gauss caused the collision rate to vary by a factor of 10,000, and the sign of the scattering length could be reserved. The resonance peak is at 155.2(4) G and its width is 11.6(5) G. From these results we extract much improved values for the three quantities that characterize the interaction porential: the van der Waals coefficient C6, the singlet scattering length, and the triplet scattering length.
We report extensions and corrections to the measurement of the Feshbach resonance in 85Rb{}^{85}\mathrm{Rb}85Rb cold atom collisions reported earlier [J. L. Roberts et al., Phys. Rev. Lett. 81, 5109 (1998)]. In addition to a better determination of the position of the resonance peak [154.9(4) G] and its width [11.0(4) G], improvements in our techniques now allow the measurement of the absolute size of the elastic-scattering rate. This provides a measure of the s-wave scattering length as a function of magnetic field near the Feshbach resonance and constrains the Rb-Rb interaction potential.
We present a theoretical analysis of numerous magnetically tunable Feshbach resonances measured by Chin et al. [preceding Letter, Phys. Rev. Lett. 85, 2717 (2000)] at fields of up to 25mT25\mathrm{mT}25mT. This analysis provides the most accurate characterization of the collisional properties of ground state Cs atoms currently available and clearly shows, in contrast to previous work, that Bose-Einstein condensation of 133Cs{}^{133}\mathrm{Cs}133Cs cannot be ruled out. The ${X}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and ${a}^{3}{\ensuremath{\Sigma}}_{u}$ scattering lengths are constrained to $(280\ifmmode\pm\else\textpm\fi{}10){a}_{0}$ and $(2400\ifmmode\pm\else\textpm\fi{}100){a}_{0}$, respectively ( 1a0=0.0529177nm{1a}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.0529177\mathrm{nm}1a0​=0.0529177nm), and the van der Waals C6{C}_{6}C6​ coefficient to $6890\ifmmode\pm\else\textpm\fi{}35\mathrm{a}.\mathrm{u}.(1\mathrm{a}.\mathrm{u}.\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.0957345\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\mathrm{J}\ifmmode \dot{}\else \.{}\fi{}{\mathrm{nm}}^{6})$.
The s-wave scattering length for elastic collisions between 87Rb{}^{87}\mathrm{Rb}87Rb atoms in the state ∣f,mf〉=∣1,1〉|{f,m}_{f}〉=|1,1〉∣f,mf​〉=∣1,1〉 is measured in the vicinity of a Feshbach resonance near 1007 G. Experimentally, the scattering length is determined from the mean-field-driven expansion of a Bose-Einstein condensate in a homogeneous magnetic field. The scattering length is measured as a function of the magnetic field and agrees with the theoretical expectation. The width of the resonance is determined to be 0.20(3) G, the position of the zero crossing of the scattering length is found at 1007.60(3) G.
In this paper we briefly review the basic steps that allow the calculation of the scattering length in the collision of two alkali-metal atoms in a well defined magnetic polarization state, and in the presence of a static magnetic field. Calculations are actually done for the low-field seeking state $F=1, {\ensuremath{\mu}}_{F}=\ensuremath{-}1$ of bosonic potassium atoms. The electrostatic potentials obtained through Rydberg-Klein-Rees data are connected to a dispersive, long range tail in which the dominant dipole-dipole C6{C}_{6}C6​ term may take different values within a specified range. We show the occurrence of Feshbach resonances in the ultra cold collision of two identical atoms, belonging either to the bosonic species 39K{}^{39}\mathrm{K}39K or 41K.{}^{41}\mathrm{K}.41K. Our results demonstrate that there is a range of C6{C}_{6}C6​ values for which the collision of two 39K{}^{39}\mathrm{K}39K atoms displays a single resonance, while for other values of C6{C}_{6}C6​ no resonance occurs. On the other hand, Feshbach resonances are present in the collision of two 41K{}^{41}\mathrm{K}41K atoms for almost all values of the dispersion coefficient C6{C}_{6}C6​ in that range. We also show the origin of the different types of Feshbach resonances that occur in the cold collision of two 41K{}^{41}\mathrm{K}41K atoms. The detection of such resonances can help establish the actual value of the dispersive coefficient.
We study elastic collisions in an optically trapped spin mixture of fermionic lithium atoms in the presence of magnetic fields up to 1.5 kG by measuring evaporative loss. Our experiments confirm the expected magnetic tunability of the scattering length by showing the main features of elastic scattering according to recent calculations. We measure the zero crossing of the scattering length at 530(3) G which is associated with a predicted Feshbach resonance at approximately 850 G. Beyond the resonance we observe the expected large cross section in the triplet scattering regime.