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Physical Review A

Two-frequency excitation of hydrogen atoms

P. Stehle

Published Nov 1, 1982• 4 citations
Publisher

Abstract

When a hydrogen atom in a state with principal quantum number ${n}_{i}$ is irradiated simultaneously with light of frequency ${\ensuremath{\omega}}_{L}$, nearly that required to produce a transition to a higher state with principal quantum number ${n}_{f}$ and with microwave radiation of frequency $\ensuremath{\omega}$, the transition is very probable when the resonance condition ${\ensuremath{\omega}}_{L}+k\ensuremath{\omega}={E}_{f}\ensuremath{-}{E}_{i}$ is satisfied, the emission or absorption of the net number $k$ of microwave photons just compensating for the detuning of the light from the resonance. This process is analyzed with the use of a forward scattering method and the results are used to discuss the experiments of Bayfield et al. on the excitation of hydrogen.

DOI
10.1103/physreva.26.2711

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When a hydrogen atom in a state with principal quantum number ni{n}_{i}ni​ is irradiated simultaneously with light of frequency \ensuremathωL{\ensuremath{\omega}}_{L}\ensuremathωL​, nearly that required to produce a transition to a higher state with principal quantum number nf{n}_{f}nf​ and with microwave radiation of frequency \ensuremathω\ensuremath{\omega}\ensuremathω, the transition is very probable when the resonance condition \ensuremathωL+k\ensuremathω=Ef\ensuremath−Ei{\ensuremath{\omega}}_{L}+k\ensuremath{\omega}={E}_{f}\ensuremath{-}{E}_{i}\ensuremathωL​+k\ensuremathω=Ef​\ensuremath−Ei​ is satisfied, the emission or absorption of the net number kkk of microwave photons just compensating for the detuning of the light from the resonance. This process is analyzed with the use of a forward scattering method and the results are used to discuss the experiments of Bayfield et al. on the excitation of hydrogen.
Hydrogen atoms with principal quantum number n=10n=10n=10 have been laser excited to states between n=44and67n=44 \mathrm{and} 67n=44and67 in the presence of a strong microwave field whose frequency $\ensuremath{\omega}$ was adjustable between 5.9 and 8.0 GHz. The excitation probability has been studied as a function of nnn, $\ensuremath{\omega}$, microwave field strength and the number of microwave photons absorbed.
A previous theory of atomic transitions in ultrastrong electromagnetic fields is applied to the problem of the ionization of highly excited hydrogen atoms. The magnitude of the fields necessary for the validity of the theory is greatly reduced by using excited hydrogen in the initial state, and the requirement of only multiphoton ionization limits the application to lowfrequency (microwave) fields. The requirement can probably be satisfied with currently available equipment. A result of the calculation is that the average number of photons absorbed is twice the minimum number.
The results of semiclassical calculations on one-, two-, three-, and four-photon absorption in truncated models of the hydrogen atom are presented. The temporal behavior near "resonance" is confirmed to be Rabi-like, with a transition probability given by $P(t)={\frac{{\ensuremath{\gamma}}^{2}}{[{(\frac{{\ensuremath{\omega}}_{0}}{N}+\ensuremath{\delta}\ensuremath{-}\ensuremath{\omega})}^{2}+{\ensuremath{\gamma}}^{2}]}}{sin}^{2}{(\frac{\mathrm{Nt}}{2}){[{(\frac{{\ensuremath{\omega}}_{0}}{N}+\ensuremath{\delta}\ensuremath{-}\ensuremath{\omega})}^{2}+{\ensuremath{\gamma}}^{2}]}^{\frac{1}{2}}},$ where the resonance shift $\ensuremath{\delta}$ is proportional to the intensity of the monochromatic driving field with frequency $\ensuremath{\omega}$ and the power broadening $\ensuremath{\gamma}$ is proportional to the N2\frac{N}{2}2N​ power of intensity. NNN is the number of photons involved and $\mathrm{h}{\ensuremath{\omega}}_{0}$ is the energy separation between initial and final states. Calculated values of $\ensuremath{\delta}$ and $\ensuremath{\gamma}$ are given for several models; also, for the two-photon $1s\ensuremath{\rightarrow}2s$ absorption, $\ensuremath{\delta}$ and $\ensuremath{\gamma}$ are given which include the contributions of all bound ppp states.
Both experiments and quantum calculations have revealed some validity of classical predictions for the classically stochastic or "diffusive" many-photon excitation and ionization of hydrogen atoms with principal quantum number n near 60 in an intense microwave field. These processes partially arise from the relatively dense number of excited atomic states present near the continuum, and from the large radiative couplings between these states. The classical scaling relations are supplemented to predict approximate threshold conditions for "diffusion" and ionization. Diffusion occurs when an electron orbit changes during one orbit time, while ionization requires adequate energy absorption from the the external field. Indicated are interesting experiments at ten micron wavelengths, intensities of tens of gigawatts per square cm, and bound electrons such as in the helium ion with n=6. These values are similar to those predicted for n=1 electrons in quantum well structures, where the situation is somewhat different because of the inverted anharmonicity of the ladders of field-free atom energy levels.