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Physical Review Letters

Determination of the s -Wave Scattering Length and the C6 van der Waals Coefficient of Yb174 via Photoassociation Spectroscopy

Katsunari Enomoto, Masaaki Kitagawa, Kentaro Kasa, S. Tojo, Yoshiro Takahashi

Published May 16, 2007• 43 citations
Publisher

Abstract

We report photoassociation spectroscopy of $^{174}\mathrm{Yb}$ for the $^{1}S_{0}\mathrm{\text{\ensuremath{-}}}^{1}P_{1}$ transition at $1\text{ }\text{ }\ensuremath{\mu}\mathrm{K}$, where only the $s$-wave scattering state contributes to the spectra. The wave function of the $s$-wave scattering state is obtained from the photoassociation efficiency, and we determine that the ${C}_{6}$ potential coefficient is $2300\ifmmode\pm\else\textpm\fi{}250\text{ }\text{ }\mathrm{a}.\mathrm{u}.$ and the $s$-wave scattering length is $5.53\ifmmode\pm\else\textpm\fi{}0.11\text{ }\text{ }\mathrm{nm}$. Based on these parameters, we discuss the scattering properties of $s$- and $d$-wave states.

DOI
10.1103/physrevlett.98.203201

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We report photoassociation spectroscopy of 174Yb^{174}\mathrm{Yb}174Yb for the 1S0\ensuremath-1P1^{1}S_{0}\mathrm{\text{\ensuremath{-}}}^{1}P_{1}1S0​\ensuremath-1P1​ transition at 1  \ensuremathμK1\text{ }\text{ }\ensuremath{\mu}\mathrm{K}1  \ensuremathμK, where only the sss-wave scattering state contributes to the spectra. The wave function of the sss-wave scattering state is obtained from the photoassociation efficiency, and we determine that the C6{C}_{6}C6​ potential coefficient is 2300\ifmmode±\else\textpm\fi250  a.u.2300\ifmmode\pm\else\textpm\fi{}250\text{ }\text{ }\mathrm{a}.\mathrm{u}.2300\ifmmode±\else\textpm\fi250  a.u. and the sss-wave scattering length is 5.53\ifmmode±\else\textpm\fi0.11  nm5.53\ifmmode\pm\else\textpm\fi{}0.11\text{ }\text{ }\mathrm{nm}5.53\ifmmode±\else\textpm\fi0.11  nm. Based on these parameters, we discuss the scattering properties of sss- and ddd-wave states.
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We report the use of photoassociative spectroscopy to determine the ground-state sss-wave scattering lengths for the main bosonic isotopes of strontium, 86Sr^{86}\mathrm{Sr}86Sr and 88Sr^{88}\mathrm{Sr}88Sr. Photoassociative transitions are driven with a laser red detuned by up to 1400 GHz from the $^{1}S_{0}\mathrm{\text{\ensuremath{-}}}^{1}P_{1}$ atomic resonance at 461 nm. A minimum in the transition amplitude for 86Sr^{86}\mathrm{Sr}86Sr at $\ensuremath{-}494\ifmmode\pm\else\textpm\fi{}5\text{ }\text{ }\mathrm{GHz}$ allows us to determine the scattering lengths 610a0<a86<2300a0610{a}_{0}<{a}_{86}<2300{a}_{0}610a0​<a86​<2300a0​ for 86Sr^{86}\mathrm{Sr}86Sr and a much smaller value of $\ensuremath{-}1{a}_{0}<{a}_{88}<13{a}_{0}$ for 88Sr^{88}\mathrm{Sr}88Sr.
In photoassociation spectroscopy, the line intensities of a given vibrational progression exhibit zero-signal modulation reflecting the node structure of the sss-wave ground state wave function of two free colliding atoms. This leads to the determination of the scattering length. We performed photoassociation of cold Cs atoms polarized in the Zeeman sublevel f=4f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4f=4, mf=4{m}_{f}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4mf​=4. We analyzed the intensities of the lines associated with the Cs2{\mathrm{Cs}}_{2}Cs2​ ${0}_{g}^{\ensuremath{-}}$ state dissociating to the 6s1/2+6p3/2{6s}_{1/2}{+6p}_{3/2}6s1/2​+6p3/2​ asymptote. This yields a value of the Cs triplet state scattering length, ${a}_{T}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}530a}_{0}$, while consistency requirements impose a value of the multipole ground state molecular coefficient, C6=6510{C}_{6}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}6510C6​=6510 a.u.
We have investigated the photoassociation (PA) spectra of ultracold 88^{88}88Sr atoms near the $5s^2 ^1S_0+5s5p ^1P_1$ atomic asymptote. The intensity modulation of the PA lines was used to reconstruct the ground-state scattering wave function, whose nodal point inferred the s-wave scattering length of a=1.1(2)a=1.1(2)a=1.1(2) nm. The observed PA resonances also determined a precise lifetime of the 1P1^1P_11P1​ state to be 5.263(4) ns.
The properties of bosonic ytterbium photoassociation spectra near the intercombination transition ${^{1}S}_{0}\ensuremath{-}{^{3}P}_{1}$ are studied theoretically at ultralow temperatures. We demonstrate how the shapes and intensities of rotational components of optical Feshbach resonances are affected by mass tuning of the scattering properties of the two colliding ground-state atoms. Particular attention is given to the relationship between the magnitude of the scattering length and the occurrence of shape resonances in higher partial waves of the van der Waals system. We develop a mass-scaled model of the excited-state potential that represents the experimental data for different isotopes. The shape of the rotational photoassociation spectrum for various bosonic Yb isotopes can be qualitatively different.
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