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Journal of Physics B Atomic Molecular and Optical Physics

Observation of dynamic Stark effect in Zeeman-split absorption lines and determination of dipole moment

Koichi Nittoh, T. Yoshida, Jun Watanabe, Toshio Watanabe, Itaru Yoguchi

Published Apr 28, 1998• 1 citation
Publisher

Abstract

A simple and straightforward method is presented for determining the electric-dipole moments of phototransitions between degenerate levels in atoms. In the present method, the dynamic Stark effect (DSE) is induced by a high-fluence laser light in the presence of a strong external magnetic field. The energy splitting caused by the DSE is measured by sweeping the frequency of the probe laser. As the separation width of the DSE peak is essentially given by a product of the dipole moment , the relevant Wigner 3- j symbol and the square root of the laser intensity, we are able to determine the value of in a direct way. As the DSE is induced between a pair of non-degenerate Zeeman sublevels, which is singled out by the external magnetic field, the result is free from any ambiguities brought about by the degeneracy such as the smoothing out of DSE peaks caused by the overlapping of the sublevel contributions. The method was tested against the transition between the 17 362 and levels in atomic uranium, giving the electric dipole moment .

DOI
10.1088/0953-4075/31/8/030

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Physical Review A•Jun 27, 2003•2 citations
A simple and straightforward method is presented for determining the electric-dipole moments of phototransitions between degenerate levels in atoms. In the present method, the dynamic Stark effect (DSE) is induced by a high-fluence laser light in the presence of a strong external magnetic field. The energy splitting caused by the DSE is measured by sweeping the frequency of the probe laser. As the separation width of the DSE peak is essentially given by a product of the dipole moment , the relevant Wigner 3- j symbol and the square root of the laser intensity, we are able to determine the value of in a direct way. As the DSE is induced between a pair of non-degenerate Zeeman sublevels, which is singled out by the external magnetic field, the result is free from any ambiguities brought about by the degeneracy such as the smoothing out of DSE peaks caused by the overlapping of the sublevel contributions. The method was tested against the transition between the 17 362 and levels in atomic uranium, giving the electric dipole moment .
Obtaining an accurate value of the electric dipole moment μ is essential in the fields of laser application technologies. A direct way of measuring the electric dipole moment μ is to observe the Rabi-oscillation which manifests itself in the coherent photo-excitation behavior of atoms. In the case of the elements which have large angular momenta, identifying the Rabi-oscillation in their excitation behavior becomes rather difficult. We proposed an accurate and straightforward method of determining the electric-dipole moment μ between multifold degenerate levels. The point is to remove the degeneracy by applying an external magnetic field with the aid of the Zeeman effect and, then, to realize a degeneration free coherent excitation. As a result, we can observe the Rabi-oscillations explicitly in the excitation vs. laser-fluence curves. The present method provides a reliable basis of experimental determination of μ. As an example, we applied the present method to a transition to 0–17,362 cm−1 level in uranium and obtained the value μ=0.86±0.06 (Debye).
Most conventional methods of determining the dipole moment μ are unsatisfactory when applied to transitions between degenerate levels; this is because the overlapping of transitions among magnetic sub‐levels modifies the photo‐excitation behavior in a complex way. To overcome this difficulty, two novel methods of determination are presented. One makes use of differently polarized laser light, and yields a set of excitation curves specific to each polarization. By treating μ as a parameter and fitting the curves through calculations, one can obtain the value of μ. In the other method, a magnetic field is applied to the atom under study in order to raise its degeneracy. As a result, simple Rabi oscillations manifest themselves and one can derive μ directly from their frequencies. These two methods of determining μ are tested on absorption lines in uranium, demonstrating that they work quite well and improve the accuracy of measured dipole moments.
In a double resonance experiment with a strong pump beam and a weak probe beam multiplet structures due to the AC Stark effect can be observed. The authors report the first observation of such a multiplet in a three-level experiment. The linearly polarised beams from a CW dye laser and a I 2 stabilised He-Ne laser were counter-propagating in the neon discharge cell and the saturating laser frequency was tuned across the resonances. The quadruplet structure was observed both for zero and for non-zero detuning delta 2 of the probe beam. The corresponding calculations for the three-level system with degenerate levels have been performed using the density matrix formalism with a tensorial expansion of the matrix elements. The theory includes the coupling of the various Zeeman sublevels by spontaneous emission and by the interaction with the two beams, and takes into account the finite value of the Doppler width.
A technique involving the laser-induced narrowing of a fluorescence line is used to obtain high-resolution spectra of Pr3+:LaCl3. The second-order effects caused by Zeeman and nuclear interactions are systematically investigated in the 3H4E2 to or from 1D2A1 transition. A non-zero perpendicular Zeeman splitting of the ground level, proportional to the square of the magnetic field, is measured and interpreted as being caused by the perturbation by the four upper Stark levels belonging to the 3H4 multiplet. The variation of the number and of the relative intensities of the hyperfine lines is demonstrated to be closely related to the angle between the external magnetic field direction and the crystal axis. It is unambiguously attributed to an angular dependence, with regard to the magnetic field direction, of the hyperfine states of the excited level. The importance of the effect, caused by a very distant perturbing level, is shown to be a result of the quasidegeneracy of the mu =0 excited level.
The Stark splitting of the second excited level of atomic hydrogen (with principal quantum number n=3n=3n=3) has been measured by pulsed laser spectroscopy in order to determine small electric fields by optical means. Doppler-free excitation with two counterpropagating laser beams at 205nm205\phantom{\rule{0.3em}{0ex}}\mathrm{nm}205nm allows us to measure the n=3n=3n=3 Stark spectra either by an optogalvanic signal after ionization by a third laser photon or by detection of the Balmer-$\ensuremath{\alpha}$ fluorescence photons emitted by the excited atoms. Three different cases of laser polarization have been investigated in order to evaluate the possibilities and limitations of this one-step laser excitation method for electric field determination, especially at field strengths below 200V∕cm200\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm}200V∕cm. The method provides the best field sensitivity achieved with lower excited levels that can be reached directly by two-photon absorption from the ground state (in contrast to the more sensitive Rydberg levels). For this purpose, an advanced tunable pulsed uv laser with narrow bandwidth almost at the Fourier limit has been used. The high spectral resolution allowed us to deduce electric field strengths as small as 50V∕cm50\phantom{\rule{0.3em}{0ex}}\mathrm{V}∕\mathrm{cm}50V∕cm from the frequency shift between two selected isolated Stark components. As a main advantage, this simple analysis of the measured spectra does not rely on knowledge of the line intensities which may be strongly affected by the measuring conditions.
In a magnetic field, the wave number of a pump laser light polarized along the field was fixed to the isolated ${\mathrm{Cs}}_{2}D{}^{1}{\ensuremath{\Sigma}}_{u}^{+}(v=46,J=54)\ensuremath{\leftarrow}X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}(v=0,J=55)$ line, and the excitation spectrum of the dissociated Cs(6p2P3/2)\mathrm{Cs}(6p{}^{2}{P}_{3/2})Cs(6p2P3/2​) atoms was measured by scanning the wave number of a probe laser light polarized perpendicular to the field. The population of each sublevel 6p2P3/2,mj6p{}^{2}{P}_{{3/2,m}_{j}}6p2P3/2,mj​​ of the dissociated atoms was determined from the line intensities in the mj{m}_{j}mj​-resolved excitation spectrum. The unequal population between the 6p2P3/2,+∣mj∣6p{}^{2}{P}_{3/2,+|{m}_{j}|}6p2P3/2,+∣mj​∣​ and $6p{}^{2}{P}_{3/2,\ensuremath{-}|{m}_{j}|}$ levels (atomic orientation) was observed and it was enhanced as the magnetic-field strength was increased. The atomic orientation is shown to be induced by the interference between the indirect predissociation, which occurs by a combination of the spin-orbit coupling of the $D{}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ state with the ${(2)}^{3}{\ensuremath{\Pi}}_{0u}$ state and the L-uncoupling and Zeeman interactions between the ${(2)}^{3}{\ensuremath{\Pi}}_{0u}$ and dissociative ${(2)}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ states, and the dissociation following a direct excitation to the ${(2)}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ state, which is allowed by spin-orbit coupling of the ${(2)}^{3}{\ensuremath{\Sigma}}_{u}^{+}$ state with the $B{}^{1}{\ensuremath{\Pi}}_{u}$ state. It is demonstrated that the atomic orientation is produced by the photodissociation in the presence of an external magnetic field even when all degenerated molecular $M=J,\dots{},0,\dots{},\ensuremath{-}J$ sublevels are excited by a light polarized linearly along the field.