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arXiv:physics/9809016 · Physical Review Letters

Cold Collision Frequency Shift of the 1S - 2S Transition in Hydrogen

T. C. Killian, Dale G. Fried, Lorenz Willmann, David Landhuis, Stephen C. Moss, Thomas J. Greytak, Daniel Kleppner

Published Nov 2, 1998• 172 citations
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Abstract

We have observed the cold collision frequency shift of the $1S$- $2S$ transition in trapped spin-polarized atomic hydrogen. We find $\ensuremath{\Delta}{\ensuremath{\nu}}_{1S\ensuremath{-}2S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}3.8\ifmmode\pm\else\textpm\fi{}0.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}n\mathrm{Hz}{\mathrm{cm}}^{3}$, where $n$ is the sample density. From this we derive the $1S$- $2S$ $s$-wave triplet scattering length, ${a}_{1S\ensuremath{-}2S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1.4\ifmmode\pm\else\textpm\fi{}0.3\mathrm{nm}$, which is in fair agreement with a recent calculation. The shift provides a valuable probe of the distribution of densities in a trapped sample.

DOI
10.1103/physrevlett.81.3807

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We have observed the cold collision frequency shift of the 1S1S1S- 2S2S2S transition in trapped spin-polarized atomic hydrogen. We find \ensuremathΔ\ensuremathν1S\ensuremath−2S=\ensuremath−3.8\ifmmode±\else\textpm\fi0.8\ifmmode×\else\texttimes\fi10\ensuremath−10nHzcm3\ensuremath{\Delta}{\ensuremath{\nu}}_{1S\ensuremath{-}2S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}3.8\ifmmode\pm\else\textpm\fi{}0.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}n\mathrm{Hz}{\mathrm{cm}}^{3}\ensuremathΔ\ensuremathν1S\ensuremath−2S​=\ensuremath−3.8\ifmmode±\else\textpm\fi0.8\ifmmode×\else\texttimes\fi10\ensuremath−10nHzcm3, where nnn is the sample density. From this we derive the 1S1S1S- 2S2S2S sss-wave triplet scattering length, a1S\ensuremath−2S=\ensuremath−1.4\ifmmode±\else\textpm\fi0.3nm{a}_{1S\ensuremath{-}2S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}1.4\ifmmode\pm\else\textpm\fi{}0.3\mathrm{nm}a1S\ensuremath−2S​=\ensuremath−1.4\ifmmode±\else\textpm\fi0.3nm, which is in fair agreement with a recent calculation. The shift provides a valuable probe of the distribution of densities in a trapped sample.
Atomic hydrogen has been loaded into a 1-K deep magnetic trap through the use of a dilution refrigerator. Evaporative cooling has been used to cool the trapped hydrogen into the submillikelvin temperature regime. These techniques have produced a sample with density of 8 × 1013 cm-3 at a temperature of 100 μK. At this density a transition to a Bose-Einstein condensate is predicted to occur at a temperature of 30 μK. These results have been obtained with a magnetic trap that has been constructed to accommodate upcoming experiments based on laser spectroscopy of the 1S-2S two photon transition in the trapped hydrogen. A frequency doubled narrow linewidth cw dye laser system has been constructed to excite the 1S-2S transition. The excitation will be detected by the observation of electric field-induced Lyman-alpha fluorescence. The optical detection system should yield improved sample density and temperature diagnostic capabilities that will facilitate a closer approach to the quantum degenerate regime. Additionally the cold, confined hydrogen gas offers the possibility of improving the level of resolution of Doppler-free hydrogen 1S-2S laser spectroscopy by several orders of magnitude.
We have measured electron spin resonance line shifts due to collisions in atomic hydrogen gas compressed to densities approximately 10(18) cm(-3) in a strong magnetic field (4.6 T). The shift in a doubly polarized gas is negligible, in contrast with a mixture of two hyperfine states. This difference is explained by properly including effects of quantum statistics in atomic collisions and magnetic dipolar effects. We report on the first direct measurement of the difference between the triplet and singlet s-wave scattering lengths a(t) - a(s) = 60(10) pm, which is in agreement with existing theories.
We show that a correct formulation of the cold collision frequency shift for two photon spectroscopy of Bose-condensed and cold non-Bose-condensed hydrogen is consistent with experimental data. Our treatment includes transport and inhomogeneity into the theory of a non-condensed gas, which causes substantial changes in the cold collision frequency shift for the ordinary thermal gas, as a result of the very high frequency (3.9 kHz) of the transverse trap mode. For the condensed gas, we find substantial corrections arise from the inclusion of quasiparticles, whose number is very large because of the very low frequency (10.2 Hz) of the longitudinal trap mode. These two effects together account for the apparent absence of a `factor of two' between the two possibilities. Our treatment considers only the Doppler-free measurements, but could be extended to Doppler-sensitive measurements. For Bose-condensed hydrogen, we predict a characteristic `foot' extending into higher detunings than can arise from the condensate alone, as a result of a correct treatment of the statistics of thermal quasiparticles.
In this Comment, we reanalyze the experiments on the collision frequency shift of the b-c and a-d hyperfine transitions in three-dimensional atomic hydrogen in the presence of, respectively, a and b-state atoms. Accurate consideration of the symmetry of the spatial and spin part of the diatomic wavefunction yields the difference a_T-a_S=0.30(5) Åbetween the triplet and singlet s-wave scattering lengths of hydrogen atoms. This corrects the factor-of two error of the commented work [Phys. Rev. Lett. 101, 263003 (2008)].
The experimental results on the collision frequency shift of ESR in diluted two-and three-dimensional atomic hydrogen at ultralow temperature have been analyzed. The apparent contradiction between experiment and theory is resolved by taking into account the relation between the symmetry of the state of two atoms and their total electron spin S . For example, transitions between symmetric and antisymmetric states of a pair of atoms induced by a symmetric perturbation are forbidden. If symmetric and antisymmetric states are, respectively, pure electronic triplets ( S = 1) and singlets ( S = 0), this results in the cancellation of the singlet-triplet transitions. Thus, the collision frequency shift of b → c and b → a transitions vanishes in a completely electron and nuclear spin-polarized gas (hyperfine state b ). The comparison is performed with experiments in ultracold alkali vapors.