Scattering lengths for collisions of ground state and metastable state hydrogen atoms

Jamieson, M. J.; Dalgarno, A.; Doyle, John M.

doi:10.1080/00268979600100541

Cited by 21 publications

(15 citation statements)

References 28 publications

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“…We have used the theoretical value of a 1S−1S = 0.0648 nm [22], which constitutes only a small contribution to χ. The value calculated by Jamieson et al [6], a 1S−2S = −2.3 nm, is in fair agreement with this measurement.…”

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confidence: 79%

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Cold Collision Frequency Shift of the1S-2STransition in Hydrogen

et al. 1998

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We have observed the cold collision frequency shift of the 1S-2S transition in trapped spin-polarized atomic hydrogen. We find ∆ν 1S−2S = −3.8 ± 0.8 × 10 −10 n Hz cm 3 , where n is the sample density. From this we derive the 1S-2S s-wave triplet scattering length, a 1S−2S = −1.4 ± 0.3 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.

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confidence: 79%

“…This allows us to deduce the 1S-2S triplet scattering length, which has been calculated by Jamieson, Dalgarno, and Doyle [6]. The frequency shift also provides a probe of the density distribution of our trapped sample, and constitutes a valuable tool for the study of Bose-Einstein condensation.…”

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confidence: 99%

Cold Collision Frequency Shift of the1S-2STransition in Hydrogen

et al. 1998

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“…Second, the above derivation of the sum rule assumes coherence of the excitation described by (4). One can see, however, that the results (14), (16), (18) hold as well for an incoherent excitation field of the form A(r)e iωt+iφ(t) with a fluctuating phase φ(t). Also, it is straightforward to generalize the results for the excitation field with different spatial dependence of different frequency components.…”

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confidence: 99%

“…The atoms are spin polarized and interact in the triplet channel. Calculated values of the 1S−1S and 1S−2S triplet scattering lengths are a 11 = 0.0648 nm [14] and a 12 = −2.3 nm [18]. We neglect 2S − 2S scattering because the excitation rate is assumed low (in the experiment typically 10 −4 of the atoms are excited) so the background gas is essentially pure 1S.…”

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Sum rule for the optical spectrum of a trapped gas

et al. 2002

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We develop an exact sum rule that relates the spectral shift of a trapped gas undergoing cold collisions to measurable quantities of the system. The method demonstrates the dependence of the cold collision frequency shift on the quantum degeneracy of the gas and facilitates extracting scattering lengths from the data. We apply the method to analyzing spectral data for magnetically trapped hydrogen atoms and determine the value of the 1S − 2S scattering length. PACS: 03.75.Fi, 32.80.Pj The broadening and shifting of spectral lines of a gas by collisions was among the earliest discoveries in the development of high precision spectroscopy [1]. The pressure shift, which originates in interatomic perturbations [2], is particularly simple to interpret at low temperatures where the thermal de Broglie wavelength1/2 is much larger than the scattering length a [3] and the interactions arise only through s-wave scattering. In this cold collision regime, the frequency shift is much larger than the level broadening.The theory of the cold collision shift has been developed to interpret hyperfine transitions in cryogenic hydrogen masers and laser cooled atomic fountains [4]. In this work we study the shift for optical excitation in a system that can be quantum degenerate, and apply the results to data on 1S−2S two-photon excitation of trapped atomic hydrogen [5].For the case of a homogeneous sample of density n, and a coherent, weak excitation that couples two inner states of the atoms, we findHere g 2 is the equal point value of the second order correlation function [6], g 2 ≡ g (2) ( r = 0), the state 1(2) is the ground(excited) state, and a αβ is the s-wave scattering length for α − β collisions.Equation (1) shows that quantum correlations in the system are manifest in the collision shift. For a uniform Bose gas in thermal equilibrium, where n BEC is the density of condensed atoms. Above the condensation temperature, when n BEC = 0, g 2 equals 2, in which case Eq.(1) is in agreement with previous work [4]. At zero temperature, for a pure condensate with n BEC = n, the collision shift is half of the shift for a noncondensed gas. Equation (1) generalizes the result [4] to T < T BEC and relates the spectral shift to the condensate fraction.It is quite remarkable that the factor g 2 in Eq.(1) multiplies both λ 12 and λ 11 . This results from correlations between an excited atom and other atoms. During the excitation, the internal states of the atoms are rotated: cos θ(t)|1S + e −iφ(t) sin θ(t)|2S . The angles θ(t), φ(t) depend on laser power and on the atom's trajectory in the laser field, specific for each atom. However, for small excitation power, the angle θ(t) is small, and thus the internal states of all atoms remain nearly identical while the laser is on, even if the excitation field is spatially nonuniform. Therefore, during the excitation the atoms interact as identical particles. This causes the short range statistical correlations in the initial state to be replicated in the excited state of the gas, which results ...

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“…This error is also added to the error budget. According to [13], the interaction cross section for atomic hydrogen in the 2S state is different for triplet and singlet states, and the pressure shift of the 2S hyperfine interval is comparable to the pressure shift of the 2S triplet level. The previous 2S hyperfine interval measurement [2] indicates for a pressure shift of −31(24) MHz/mbar, which is of the same order of magnitude as the pressure shift of the 1S(F = 1, m F = ±1) → 2S(F = 1, m F = ±1) transition in hydrogen which is −8(2) MHz/mbar [11,12].…”

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High-Precision Optical Measurement of the2SHyperfine Interval in Atomic Hydrogen

et al. 2004

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We have applied an optical method to the measurement of the 2S hyperfine interval in atomic hydrogen. The interval has been measured by means of two-photon spectroscopy of the 1S − 2S transition on a hydrogen atomic beam shielded from external magnetic fields. The measured value of the 2S hyperfine interval is equal to 177 556 860(15) Hz and represents the most precise measurement of this interval to date. The theoretical evaluation of the specific combination of 1S and 2S hyperfine intervals D21 is in moderately good agreement with the value for D21 deduced from our measurement. PACS numbers: 12.20.Fv, 32.10.Fn, 32.30.Jc, 42.62.Fi The frequency of the 2S hyperfine interval f HFS (2S) has been measured twice during the last 50 years by driving the magnetic-dipole radio-frequency transition in a hydrogen thermal beam [1,2]. The relative accuracy of these measurements (150−300 ppb) exceeds the accuracy of the theoretical prediction for the 2S hyperfine interval which is restricted by an insufficient knowledge of the proton structure. However, the specific combination of the 1S and 2S hyperfine intervalscan be calculated with high precision due to significant cancellations of nuclear structure effects (see [3] For the measurement of the 2S hyperfine interval in atomic hydrogen we have applied 1S − 2S two-photon spectroscopy to a cold hydrogen atomic beam which is shielded from magnetic fields. Using a high-finesse cavity as a frequency flywheel we deduce the 2S hyperfine interval as the frequency difference between two extremely stable laser light fields which excite the respective transitions between the different hyperfine sublevels of the 1S and 2S states in atomic hydrogen. The differential measurement cancels some important systematic effects typical for two-photon spectroscopy on atomic beams. Applying this optical method, we achieve a level of accuracy which is nearly 2 times better than the accuracy of the recent radio-frequency measurement [2]. Along with the previous optical Lamb shift measurement [6], our present measurement demonstrates the perspectives of precision optical methods in fields where traditionally radio-frequency techniques have been used.The hydrogen spectrometer setup, described in detail elsewhere [7], has been modified by magnetic compensation and shielding systems and an optional differential pumping system [8]. A dye laser operating near 486 nm is locked to an ultra-stable reference cavity made from ULE by means of the Pound-Drever-Hall lock. The drift of the cavity, suspended in a vacuum chamber with a two-stage active temperature stabilization system, is typically 0.5 Hz/s.The frequency of the dye laser light is doubled in a β-barium borate crystal, and the resulting UV radiation near 243 nm is coupled into a linear enhancement cavity inside a vacuum chamber. Atomic hydrogen, produced in a radio-frequency discharge at a pressure of around 1 mbar, flows through teflon tubes to a copper nozzle cooled to 5 K with a helium flow-through cryostat. Hydrogen atoms thermalize in inelast...

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Scattering lengths for collisions of ground state and metastable state hydrogen atoms

Cited by 21 publications

References 28 publications

Cold Collision Frequency Shift of the1S-2STransition in Hydrogen

Cold Collision Frequency Shift of the1S-2STransition in Hydrogen

Sum rule for the optical spectrum of a trapped gas

High-Precision Optical Measurement of the2SHyperfine Interval in Atomic Hydrogen

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