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Optics and Spectroscopy

Probabilities of single-photon 2s–1s transition in hydrogen and antihydrogen atoms in an external electric field

D. A. Solov’ev, V. Sharipov, L. N. Labzovskiǐ, G. Plunien

Published Apr 1, 2008• 5 citations
Publisher

Abstract

The probabilities of single-photon 2s–1s transition in hydrogen (H) and antihydrogen ( $$ \bar H $$ ) atoms in an external electric field are calculated. These quantities are different for H and $$ \bar H $$ due to the presence of a T odd term linearly dependent on the electric field strength. The relative difference between the probabilities of the considered process for hydrogen and antihydrogen is given, and the conditions under which this difference can be measured are discussed.

DOI
10.1134/s0030400x0804005x

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The probabilities of single-photon 2s–1s transition in hydrogen (H) and antihydrogen ( Hˉ\bar HHˉ ) atoms in an external electric field are calculated. These quantities are different for H and Hˉ\bar HHˉ due to the presence of a T odd term linearly dependent on the electric field strength. The relative difference between the probabilities of the considered process for hydrogen and antihydrogen is given, and the conditions under which this difference can be measured are discussed.
The probabilities of two-photon decay for hydrogen (H) and antihydrogen ( Hˉ \bar H Hˉ ) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabilities for 2s and 2p levels differ for H and Hˉ \bar H Hˉ atoms because of interference terms linear in field. Coulomb Green’s function method is used for summing over intermediate states.
One- and two-photon transitions in the hydrogen atom are analytically evaluated in the absence and in the presence of an external electric field. The emission probabilities are different for the hydrogen and anti-hydrogen atoms due to the existence of contributions, linear in electric field. The magnitude of these contributions is evaluated within the nonrelativistic limit. The Coulomb Green function method is applied. Different nonrelativistic "forms" for the decay probabilities in combination with different gauge choices are considered. The three-photon E1E1E1 2p-1s transition probability is also evaluated and possible applications of the results are discussed.
We analyze the influence of an external electric field on the nsnsns and npnpnp Rydberg states. The impact of an electric field leads to a significant modification of the decay rate. Namely, the additional (linear and quadratic in the field) terms arise in the differential transition probabilities. In contrast to the quadratic term, the linear summand leads to a difference of the hydrogen (H)(\text{H})(H) and antihydrogen (H‾)(\overline{\text{H}})(H) spectra. However, this difference vanishes after the integration over photon-emission directions and does not contribute to the total emission probability. The quadratic term results in the significant change of the total decay rate and level width, respectively. The analysis of the linear and quadratic terms depending on the field strength is discussed.
Theoretical calculations for the 1S → 2S two- photon transition rate in atomic hydrogen are reviewed. They are compared with two experiments via the saturation effects that are observed when three-photon ionization is enhanced by two- photon resonance with the metastable 2S state. There is a significant disagreement between theoretical and experimental results. The disagreement is illustrated by determining the transition rate as a function of intensity for experimental laser profiles: (1) using parameters that give rates in agreement with experimental data, and (2) using theoretical values for the parameters. Finally, experiments that would involve direct observation of the 2S metastable state are considered. It is shown that single-longitudinal-mode laser experiments would provide an accurate measurement of the Rabi frequency for this transition and yield a definitive value for the rate. A Monte Carlo simulation method is used to consider practical effects associated with such an experiment, for example, chirp and ASE noise in the laser. Also, simulations of the multiphoton ionization process in multimode and wide band laser fields are presented.