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Australian Journal of Physics

Nonlinear Effects in Single-photon Resonant Excitation of Atomic Hydrogen

K. Unnikrishnan

Published Jun 1, 1996• 0 citations
Publisher

Abstract

The first nonperturbative calculation of the amplitude for the excitation of a discrete atomic state by a classical electrornagnetic field is described. Specifically, the excitation amplitude for the H(ls) ? H(2p) transition involving the net absorption of only one photon is shown to exhibit a nonlinear dependence on the field amplitude beyond an intensity I ˜ 1013 W cm-2 In this region, the rate of change of the transition amplitude decreases with increasing field strength, finally becoming negative after I ˜ 4 X 1014 W cm-2. Degeneracy of the excited state is shown to be largely responsible for the early onset of such behaviour, thereby picking out atomic hydrogen as the most suitable target for experimental observations.

DOI
10.1071/ph960669

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The first nonperturbative calculation of the amplitude for the excitation of a discrete atomic state by a classical electrornagnetic field is described. Specifically, the excitation amplitude for the H(ls) ? H(2p) transition involving the net absorption of only one photon is shown to exhibit a nonlinear dependence on the field amplitude beyond an intensity I ˜ 1013 W cm-2 In this region, the rate of change of the transition amplitude decreases with increasing field strength, finally becoming negative after I ˜ 4 X 1014 W cm-2. Degeneracy of the excited state is shown to be largely responsible for the early onset of such behaviour, thereby picking out atomic hydrogen as the most suitable target for experimental observations.
Using the hydrogenic model for the helium atom, the amplitude of transition from states He(ls) to He(ls, nl) by absorption of N photons of an intense field together with the emission of one Raman photon is evaluated. From the general expression for the transition amplitude, the particular case of transition from He(ls) to He(ls, 2p) is considered. The 'reduced' transition amplitude is plotted against the number of photons N involved and against the intensity parameter y st;parately. It is found that the s wave contributes maximaly to the transition amplitude. An important feature of the calculations is the appearance of nonlinear behaviour at high intensity. The dominance of higher order processes over lower ones at high intensity is also found.
The dependence on the ellipticity of the incident laser field of the harmonics generated by atoms of hydrogen in the multiphoton regime is examined for two fundamental wavelengths, 532 and 1064 nm. The single atom response is calculated nonperturbatively using the Floquet method in conjunction with basis sets of complex Sturmian functions. The results are compared with those obtained using lowest order perturbation theory. Nonperturbative effects modify the strength and polarization of the harmonics at the highest intensities investigated, particularly, for the threshold harmonics and in the vicinity of Stark-shift-induced resonances. No anomalous dependence of the rate of harmonic generation on the ellipticity of the fundamental field is found.
We have observed second-harmonic generation in atomic hydrogen in the Lyman-α region, with and without an applied dc electric field, Ea. Experiments with a continuous atomic beam were carried out by using a pulsed dye laser tuned to 243 nm for excitation of the n = 2-1 transition. The laser beam was focused 0.4 mm below the H-source nozzle, where the H-atom density was estimated to be 5 × 1013 cm-3. Measurements of second-harmonic generation (SHG) at ~122 nm were made at various electric fields up to ~27 kV/cm. It was shown that the SH signal produced at E a = 0 occurs because of a charge-separation field of ~800 V/cm that is caused by three-photon ionization. Measurements of the SHG and ion current were found to vary as I2 L and I3 L , respectively. At high fields (E a > 10 kV/cm) the SH signal at the center of the Stark-split components decreased somewhat from the peak value, but the ion current (corresponding to photon absorption) approached zero. This observation is a clear demonstration of a similar effect, predicted by Harris et al.1 of efficient nonlinear conversion with induced transparency, and it suggests the possibility of obtaining intense Lyman-a radiation.
We investigate resonant strong field ionization of atomic hydrogen with respect to the 1s–2p transition. By 'strong' we understand that Rabi periods are executed on a femtosecond time scale. Ionization and AC Stark shifts modify the bound state dynamics severely, leading to nonperturbative signatures in the photoelectron spectra. We introduce an analytical model, capable of predicting qualitative features in the photoelectron spectra such as the positions of the Autler–Townes peaks for modest field strengths. Ab initio solutions of the time-dependent Schrödinger equation show a pronounced shift and broadening of the left Autler–Townes peak as the field strength is increased. The right peak remains rather narrow and shifts less. This result is analysed and explained with the help of exact AC Stark shifts and ionization rates obtained from Floquet theory. Finally, it is demonstrated that in the case of finite pulses as short as 20 fs the Autler–Townes duplet can still be resolved. The fourth generation light sources under construction worldwide will provide bright, coherent radiation with photon energies ranging from a tenth of an meV up to tens of keV, hence covering the regime studied in the paper so that measurements of nonperturbative, relative AC Stark shifts should become feasible with these new light sources.