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arXiv:1002.1534 · Physical Review Letters

Comment on “Clock Shift in High Field Magnetic Resonance of Atomic Hydrogen”

A. I. Safonov, I. I. Safonova, Igor Stanislavovich Yasnikov

Published Mar 4, 2010• 5 citations
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Abstract

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)].

DOI
10.1103/physrevlett.104.099301

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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)].
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.
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.
We present an experimental study of the quantum gas of atomic hydrogen in a strong magnetic field (4.6 T). The gas is compressed to densities of ~1018 cm−3 at temperatures of 0.2–0.5 K. We observed shifts of the electron spin resonance (ESR) lines caused by the exchange interaction in atomic collisions (clock shift) and the long-range dipolar interactions. The clock shift was found to be vanishingly small in a doubly polarized gas, in contrast to a mixture of two hyperfine states. The difference is explained by properly including quantum statistical effects in the treatment of atomic collisions. From our data, we extract the difference between the triplet and singlet s-wave scattering lengths, at−as=60(10) pm, in agreement with existing theories. At densities above 1017 cm−3, weakly resolved structures appeared in the ESR spectra, interpreted in terms of electron spin waves. We consider exchange and dipolar interactions to possibly induce the spin waves.
We have observed the cold collision frequency shift of the 1S1S1S- 2S2S2S 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 nnn is the sample density. From this we derive the 1S1S1S- 2S2S2S sss-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.
In this thesis three experiments with atomic hydrogen (H) at low temperatures T<1 K are presented. Experiments were carried out with two- (2D) and three-dimensional (3D) H gas, and with H atoms trapped in solid H2 matrix. The main focus of this work is on interatomic interactions, which have certain specific features in these three systems considered. A common feature is the very high density of atomic hydrogen, the systems are close to quantum degeneracy. Short range interactions in collisions between atoms are important in gaseous H. The system of H in H2 differ dramatically because atoms remain fixed in the H2 lattice and properties are governed by long-range interactions with the solid matrix and with H atoms. The main tools in our studies were the methods of magnetic resonance, with electron spin resonance (ESR) at 128 GHz being used as the principal detection method. For the first time in experiments with H in high magnetic fields and at low temperatures we combined ESR and NMR to perform electron-nuclear double resonance (ENDOR) as well as coherent two-photon spectroscopy. This allowed to distinguish between different types of interactions in the magnetic resonance spectra. Experiments with 2D H gas utilized the thermal compression method in homogeneous magnetic field, developed in our laboratory. In this work methods were developed for direct studies of 3D H at high density, and for creating high density samples of H in H2. We measured magnetic resonance line shifts due to collisions in the 2D and 3D H gases. First we observed that the cold collision shift in 2D H gas composed of atoms in a single hyperfine state is much smaller than predicted by the mean-field theory. This motivated us to carry out similar experiments with 3D H. In 3D H the cold collision shift was found to be an order of magnitude smaller for atoms in a single hyperfine state than that for a mixture of atoms in two different hyperfine states. The collisional shifts were found to be in fair agreement with the theory, which takes into account symmetrization of the wave functions of the colliding atoms. The origin of the small shift in the 2D H composed of single hyperfine state atoms is not yet understood. The measurement of the shift in 3D H provides experimental determination for the difference of the scattering lengths of ground state atoms. The experiment with H atoms captured in H2 matrix at temperatures below 1 K originated from our work with H gas. We found out that samples of H in H2 were formed during recombination of gas phase H, enabling sample preparation at temperatures below 0.5 K. Alternatively, we created the samples by electron impact dissociation of H2 molecules in situ in the solid. By the latter method we reached highest densities of H atoms reported so far, 3.5(5)x1019 cm-3. The H atoms were found to be stable for weeks at temperatures below 0.5 K. The observation of dipolar interaction effects provides a verification for the density measurement. Our results point to two different sites for H atoms in H2 lattice. The steady-state nuclear polarizations of the atoms were found to be non-thermal. The possibility for further increase of the impurity H density is considered. At higher densities and lower temperatures it might be possible to observe phenomena related to quantum degeneracy in solid.
We propose the explanation of a small yet finite frequency shift of a hyperfine transition in two-dimensional atomic hydrogen bound to the surface of superfluid helium at T < 0.1 K. The nonzero shift is caused, first, by the interaction between adsorbed atoms, which effectively reduces their binding energy to the helium surface by a value proportional to their density and, consequently, reduces the deviation of the hyperfine constant from the free-atom value. Second, the transition between the hyperfine states b and c is shifted owing to a difference in the interaction of the b and c atoms with the residual atoms in the state a that appear due to one and two-body nuclear relaxation. This shift is also linear in the density of the two-dimensional gas. The net effect of the two contributions qualitatively agrees with the experimentally observed value of the shift.