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Physical Review A

Rydberg-state mixing in the presence of an external electric field: Comparison of the hydrogen and antihydrogen spectra

Dmitry A. Solovyev, Elena V. Solovyeva

Published Apr 16, 2015• 7 citations

Abstract

We analyze the influence of an external electric field on the $ns$ and $np$ 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 $(\text{H})$ and antihydrogen $(\overline{\text{H}})$ 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.

DOI: 10.1103/physreva.91.042506

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Physical Review A•Sep 1, 1979•14 citations

We analyze the influence of an external electric field on the

ns

and

np

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

(\text{H})

and antihydrogen

(\overline{\text{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.

The probabilities of two-photon decay for hydrogen (H) and antihydrogen (

\bar H

) 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

\bar H

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.

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.

The technique of electric field ionization has been used to study molecular Rydberg states of

{\mathrm{H}}_{2}

and

{\mathrm{D}}_{2}

formed by electron capture of

{\mathrm{H}}_{2}^{+}

or

{\mathrm{D}}_{2}^{+}

beams in

{\mathrm{H}}_{2}

. The neutral molecules were passed through two intense electric field ionization regions in tandem, separated by an \ensuremath{\sim} ${10}^{\ensuremath{-}7}$-sec drift region. Up to 15% of the Rydberg population removed by the first ionization region was repopulated during transit through the drift region. This result has been interpreted in terms of nonadiabatic state mixing of nearly degenerate adiabatic molecular states. A difference in the state repopulation between Rydberg states of

{\mathrm{H}}_{2}

and

{\mathrm{D}}_{2}

was observed, indicating the importance of the rovibrational spectrum on the repopulation mechanism. By comparison, similar studies on atomic Rydberg states showed no difference between H and D. Moreover, the atoms exhibited only a small repopulation effect, consistent with the contribution due to $\stackrel{\ensuremath{\rightarrow}}{1}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{s}}$ coupling.