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Physical Review A

Calculations of resonant multiphoton population transfer in potassium atoms at long wavelengths

Mette B. Gaarde, Kenneth J. Schäfer

Published Oct 18, 2000• 6 citations
Publisher

Abstract

We study the interplay between resonant multiphoton population transfer and strong field ionization in potassium atoms, by calculating their response to intense, midinfrared (MIR) radiation. We use wavelengths close to the three or five photon resonance between the ground $4s$ state and the first excited $4p$ state, and find that the amount of population transferred to the excited state as a function of wavelength and intensity shows clear signatures of these resonances. The ionization yield also shows moderate resonant enhancement for intermediate intensities. We can further distinguish between population transfer to and ionization of the $4p$ state by using a chirped laser pulse to temporally separate the two processes. We find that the amount of population remaining in the $4p$ state at the end of the pulse shows a pronounced sensitivity to the sign of the chirp whereas the total amount of ionization does not. From this we conclude that direct, nonresonant ionization of the ground state competes strongly with the resonant process.

DOI
10.1103/physreva.62.053411

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We study the interplay between resonant multiphoton population transfer and strong field ionization in potassium atoms, by calculating their response to intense, midinfrared (MIR) radiation. We use wavelengths close to the three or five photon resonance between the ground 4s4s4s state and the first excited 4p4p4p state, and find that the amount of population transferred to the excited state as a function of wavelength and intensity shows clear signatures of these resonances. The ionization yield also shows moderate resonant enhancement for intermediate intensities. We can further distinguish between population transfer to and ionization of the 4p4p4p state by using a chirped laser pulse to temporally separate the two processes. We find that the amount of population remaining in the 4p4p4p state at the end of the pulse shows a pronounced sensitivity to the sign of the chirp whereas the total amount of ionization does not. From this we conclude that direct, nonresonant ionization of the ground state competes strongly with the resonant process.
When exposed to intense light of \ensuremath{\sim}580 nm, the ground state of K shifts up in energy, passing through two photon resonances with Rydberg states, and finally crossing the two-photon ionization limit. We have used laser pulses of varying duration to study the nature of the population transfer from the ground state to the excited state due to the intensity-tuned resonances encountered during the rising edge of the pulse. A dynamic Floquet approach in which the resonances are treated as avoided crossings of the Floquet energy levels is used to model the population transfer and gives excellent agreement with the data. The model is extended into the strong-coupling regime where the ground state interacts with many excited states simultaneously, and we show that this model can be used to describe multiphoton ionization as a series of avoided crossings with the continuum.
In the strong-field regime a single multiphoton resonance can enhance many harmonics of the fundamental laser frequency simultaneously. We demonstrate that an alkali-metal atom driven by an intense, ultrafast midinfrared pulse is an ideal system for observing this effect by calculating the response of potassium atoms to radiation that is nearly three or five photon resonant with the $4s\ensuremath{-}4p$ transition. We find that all the harmonics through at least the 17th are enhanced over a wide range of intensities, and that the resonance width of the enhanced harmonics is governed by the lifetime of the multiphoton resonance.
We have studied two-photon resonant three-photon ionization of atomic sodium vapor. A dye laser tuned to either the 4d or 5s two-photon allowed transition was used to excite the atom and a second more intense laser (λ = 7000 Å) was used for ionization. The ion yield was measured as a function of resonant laser intensity and detuning, the nonresonant laser intensity, and the temporal overlap of the exciting and ionizing laser pulses. We have found1 that at high laser intensities the photoionization yield decreases as the nonresonant laser intensity is increased. When tuned to the 5s level a value of ~−0.6 was obtained for the exponential index even with the resonant laser tuned to maximize the ion yield. A theoretical model including the effects of Stark shift of the ground state, power broadening of the intermediate level due to saturation of the two-photon transition and by rapid transitions to the ionization continuum was used to predict the experimental results. Good agreement between theory and experiment required the use of a photoionization cross section for the 5s level which was ~20 times greater than the accepted value. Results for photoionization from the 4d level are also presented.
We report on the single and double multiphoton ionization of ground state Sr atoms observed in an atomic beam experiment with laser pulses of ∼5 ns duration, maximum intensity ∼4 × 10 11 W cm −2 and within the 710–740 nm wavelength range. The Sr + spectrum consists of two strong lines originating from three-photon resonant four-photon ionization of bound states, a number of weak autoionizing resonances and a broad line due to four-photon excitation of the doubly excited 5p 2 1 S 0 state. The latter, along with a strong, broad and structured spectral feature, is also evident in the wavelength dependence of the doubly charged Sr 2+ ion. A weakly evident but reproducible inflection point ('knee' structure) appears in the intensity dependence of the Sr 2+ yield at the location of the 5p 2 1 S 0 resonance. A complementary fluorescence experiment revealed the accumulation of population in the 5p 1/2 , 3/2 , 6s 1/2 and 5d 3/2 , 5/2 excited Sr + states during the laser pulse. All fluorescence signals depend on laser wavelength in a manner similar to the recorded Sr + spectrum. The population accumulation in the 5p 1/2 , 3/2 ionic states unambiguously proves the absorption of two photons above the first 5s 1/2 atomic threshold while that of the 5d 3/2 , 5/2 and 6s 1/2 ones suggest the absorption of at least two more. Since under our laser pulse duration and intensity the absorption of such a number of photons in an unstructured continuum is highly improbable, it may be concluded that the process is mediated by dense manifolds of near- resonant doubly excited states, their role in the dynamics of laser–atom interaction under our conditions being far more crucial than in studies conducted using intense ultrashort pulses.
It has been widely believed that short-pulse multiphoton ionization is dominated by a resonance process: excited states of the atom are shifted by the radiation field into multiphoton resonance with the ground state, are populated, and then rapidly ionized. A recent experiment, shows significant population remaining in excited states at the end of the laser pulse, and this result has been interpreted as indicating that ionization proceeds slowly out of these states. We investigate this issue in the framework of Floquet theory, supplemented by direct numerical solution of the time-dependent Schrodinger equation. In this framework, the standard picture is portrayed as an adiabatic transition between Floquet eigenstates, which occurs as the amplitude of the laser field is ramped through the resonance value (i.e. through an avoided crossing of Floquet quasienergies). Thus it follows that the same type of transition must occur as the field is turned off. This mechanism can yield significant populations of excited states that do not suffer appreciable ionization. We exhibit this effect by numerical studies of a model atom with two bound states and two continua.