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Journal of the Optical Society of America

Two-photon absorption spectroscopy of potassium Rydberg states*

C. D. Harper, S E Wheatley, M. D. Levenson

Published May 1, 1977• 17 citations
Publisher

Abstract

Highly excited S and D states of potassium were studied by two-photon absorption using a tuneable dye laser and fluorescence detection. Measurements were made of the term values, relative fluorescence signal levels, and fluorescence decay profiles. Using matrix elements determined from quantum defect wave functions, theoretical two-photon absorption cross sections were calculated.

DOI
10.1364/josa.67.000579

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Highly excited S and D states of potassium were studied by two-photon absorption using a tuneable dye laser and fluorescence detection. Measurements were made of the term values, relative fluorescence signal levels, and fluorescence decay profiles. Using matrix elements determined from quantum defect wave functions, theoretical two-photon absorption cross sections were calculated.
The intracavity laser spectroscopy method was used to determine the two-photon absorption of potassium vapor. The two-photon transitions from the ground state 4 2 S 1/2 to the states 6 2 S 1/2 and 4 2 D 3/2,5/2 were detected from absorption in the output spectrum of a wide-band dye laser emitting in the range 760–770 nm; the absorption occurred at a frequency corresponding to the difference between the energies of the upper state and the energy of a ruby laser photon. The ratio ofthe absorption cross section to the square ofthe field was σ 2 / E 2 = 1.5 × 10 −33 ,1.3 × 10 −35 ,and 2.8 × 10 −36 m 4 /V 2 , in satisfactory agreement with calculations carried out on the basis of perturbation theory.
Three-photon absorption spectroscopy allows determination of the nf2F52,720\mathrm{nf}^{2}F_{\frac{5}{2},\frac{7}{2}}^{0}nf2F25​,27​0​ energy levels of alkali metals ($\ensuremath{\Delta}L=+3$). The 3d2D32,523d^{2}D_{\frac{3}{2},\frac{5}{2}}3d2D23​,25​​ levels of KI were selectively excited using a narrow-band dye laser. The $3d^{2}D_{\frac{3}{2},\frac{5}{2}}\ensuremath{\rightarrow}\mathrm{nf}^{2}F_{\frac{5}{2},\frac{7}{2}}^{0}$ absorption lines were observed in the background spectrum of another dye laser, and the nf2F52,720\mathrm{nf}^{2}F_{\frac{5}{2},\frac{7}{2}}^{0}nf2F25​,27​0​ energy levels were deduced, from n=10n=10n=10 to n=14n=14n=14 inclusive, with an accuracy better than 0.1 ${\mathrm{cm}}^{\ensuremath{-}1}$. Previously, an experiment was performed for the 7f2F52,7207f^{2}F_{\frac{5}{2},\frac{7}{2}}^{0}7f2F25​,27​0​ levels in order to verify the method. Shifts and systematic errors were entirely negligible. For all lines, the relative intensities of the absorbed doublet peaks are in good agreement with the estimates of the $4s^{2}S_{\frac{1}{2}}\ensuremath{\rightarrow}3d^{2}D_{\frac{3}{2},\frac{5}{2}}$ probabilities.
We have observed fluorescence and ionization signals resulting from two-photon resonant excitation of thallium in an atomic beam. The output of a pulsed dye laser is used to excite the resonance between the ground state (6('2)P(,1/2)) and an excited n('2)P state of thallium. Both two-photon absorption and three-photon absorption occur simultaneously; the latter results in photoionization of the atom. The excited states populated by two-photon absorption decay via cascade fluorescence back to the ground state; one or more of these spectral components constitute our fluorescence signal. The lifetimes of the excited n('2)P states of thallium have been measured directly by observing the exponential decay of this fluorescence. Calculations are included to ascertain the time required for the fluorescence signal to reach within 2% of a simple exponential decay. This decay is a measure of the lifetime of the initial state, under the condition that none of the fluorescence components arise from states which are populated by cascade through longer-lived states. The lifetimes of the n('2)P(,1/2) and n('2)P(,3/2) states of thallium for n = 7 to 11 are determined in this manner and compared with the values deduced from semi-empirical calculations of oscillator strengths by various authors. For calculations employing the effects of core polarizability in the electron wavefunctions and in the transition matrix elements, the agreement is very good--to within our experimental uncertainty, which is typically(, )<5%. Our measurements are also compared to the four other known experimental values for such excited states of thallium. Some of these previous experiments and calculations were carried out in conjunction with parity non-conservation experiments in thallium. Our measurements may provide useful checks on the accuracy of some of the calculations performed in the evaluation of such experiments. The ionization and fluorescence signals are also studied under conditions of strong saturation of the two-photon resonance with the 7('2)P states. The manifestation of saturation in the ionization signal is a broadening of the excitation spectrum, which is found to greatly exceed that of the fluorescence signal. Furthermore, the ratio of the ionization signal to the fluorescence signal at the peak of the resonance is found to vary linearly at intensities below about 10('9) W/cm('2); this too saturates at higher intensities. Various models are employed to simulate the observed behavior, encompassing both rate equations as well as density matrix formulations. The numerical solutions to these models are compared with the observed behavior; the agreement is found to depend strongly on the assumed experi- mental conditions to which the ensemble of atoms is subjected.
Two-photon absorption cross sections of ground-state xenon atoms to the 2p5{p}_{5}p5​(J=0), 2p6{p}_{6}p6​(J=2), and 2p9{p}_{9}p9​(J=2) states in the 5${p}^{5}6pconfigurationandphotoionizationcrosssectionsat193and248nmfromthe26p configuration and photoionization cross sections at 193 and 248 nm from the 26pconfigurationandphotoionizationcrosssectionsat193and248nmfromthe2{p}_{5}$ and 2p6{p}_{6}p6​ states have been determined and are compared with previous experimental and theoretical values where such exist. Fluorescence depletion spectroscopy as a method for determining excited-state photoionization cross sections is described and discussed and shown to have many attractive features. Based on our cross-section measurements, we calculate that (2+1)-photon photoionization in Xe with a laser intensity of 30 MW/cm2{\mathrm{cm}}^{2}cm2 during 25 ns at 249.6 nm, using the 2p5{p}_{5}p5​(J=0) state as an intermediate state, can produce a fractional ionization of 10%.
Measurements of the absolute generalized cross sections for the non-resonant two-photon excitation of discrete states of barium atoms are presented. They are based on the detection of an ion current due to absorption of a third photon in two processes of both resonant and non-resonant two-photon excitation of the same discrete level. Also considered is the appearance of additional lines in the two-photon absorption spectrum due to superradiance of the dye laser, the anomalous width of some of the two-photon resonances and the use of two-photon resonances for calibration purposes in investigation of autoionization resonances.