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Measurement of atomic oscillator strengths in ytterbium by observation of coherent Rabi oscillations of excited-state populations

C. Haynam, B. Comaskey, Earl F. Worden, Jeffrey A. Paisner

Published Jan 1, 1987• 1 citation
OpenAlex

Abstract

Two methods have been used to measure the oscillator strength of the transition between the ground and 17,992 cm level in XUYb. The first technique involves exciting the transition with a laser pulse that is nearly time-bandwidth limited, of uniform intensity, and has a reproducible shape from shot to shot. The population left in the excited state after the pulse varies sinusoidally with a period that depends on the integral over time of the electric field amplitude and the transition oscillator strength. These are the Rabi oscillations that are predicted by application of the Schrodinger equation to the two-level atom. The second method involves observation of the polarization rotation of a set of degenerate sublevels brought about by a light-shift laser. One sublevel (m/sub j/ = 0) of the J = 1 level at 17,992 cm is populated by a linearly polarized laser. A second copropagating light-shift laser, which is linearly polarized at an angle to the first laser, is tuned between 7.5 and 30 GHz off-resonance with the transition. The light-shift laser causes population to be promoted into the m/sub j/ = +-1 levels through the virtual J = 0, m/sub j/ = 0 level. Two linearly polarized photoionizing lasers photoionize the population only from the m/sub j/ = +-1 levels. The photoion signal oscillates cosinusoidally with a period that depends only on the integrated pulse intensity, the laser detuning, and the transition oscillator strength. Finally, polarization selectivity has been shown experimentally to allow selective photoionization of the odd isotopes of ytterbium using broadband lasers.

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We have used two methods to measure the oscillator strength of the transition between the ground and 17992 cm-1 level in 174Yb. The first technique involves exciting the transition with a laser pulse that is nearly time-bandwidth limited, of uniform intensity, and has a reproducible shape from shot to shot. The population left in the excited state after the pulse varies sinusoidally with a period that depends on the integral over time of the electric field amplitude and the transition oscillator strength. These are the Rabi oscillations that are predicted by application of the Schrodinger equation to the two-level atom. The excited-state population is probed using a two-step photoionization to the continuum. The electric field amplitude is determined from the temporal profile and the intensity of the laser pulse. The second method involves observation of the polarization rotation of a set of degenerate sublevels brought about by a time-bandwidth limited light-shift laser. One sublevel (mj = 0) of the J = 1 level at 17992 cm-1 is populated by a linearly polarized laser. A second copropagating light-shift laser, which is linearly polarized at an angle to the first laser, is tuned between 7.5 and 30 GHz off-resonance with the transition. The light-shift laser causes population to be promoted into the mi = ±1 levels by a virtual transition through the ground J = 0, = 0 level. Two linearly polarized photoionizing lasers photoionize the population only from the mi = ±1 levels. The photoion signal oscillates sinusoidally with a period that depends only on the integrated pulse intensity, the laser detuning, and the transition oscillator strength.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 22, 1988•2 citations

Theory of the inverse hook method for measuring oscillator strengths

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The theory of a new method to measure oscillator strengths is presented. The method exploits the ac Stark interaction of a laser pulse detuned from a transition between an initially populated state a and a second state b of an atom. We assume the density matrix \ensuremath{\rho} of state a initially has only diagonal elements given by 〈m\ensuremath{\Vert}\ensuremath{\rho}\ensuremath{\Vert}m〉=C+${\mathrm{Dm}}^{2}$ where C and D\ensuremath{\ne}0 are constants and m is the Zeeman sublevel quantum number. The laser pulse is linearly polarized along an axis different from the quantization axis and therefore rearranges the atoms among the various Zeeman sublevels. Changes of the relative Zeeman sublevel populations induced by the laser pulse can be readily detected by monitoring changes in the angular distribution or polarization of fluorescent light emitted when the atoms radiatively decay to some final state f. This paper considers the general problem where states a, b, and f have arbitrary angular momentum. We derive the functional dependence of the polarized fluorescent light fluence on the laser pulse fluence (pulse energy per unit area).For spatially uniform laser pulses, these signals are periodic functions of the laser fluence. When the laser is completely speckled, we show that the signal is well approximated by a Lorentzian curve. This latter case is of considerable experimental interest since most pulsed dye lasers have poor transverse mode structure which can readily be converted into a statistically well-defined speckle pattern. The oscillator strength of the transition between states a and b is found using (1) the fluence half-width of the ``depolarization curve,'' the Lorentzian-like dependence of the fluorescence polarization on the laser pulse fluence, (2) the detuning of the laser from the transition frequency ${\ensuremath{\omega}}_{\mathrm{ab}}$, and (3) some known constant factors which depend on the angular momenta of states a, b, and f. The physics of the situation is very similar to that of the conventional hook method with this difference: the roles of the atoms and the photons have been interchanged. We therefore call this new method the inverse hook method. The inverse hook method is relatively insensitive to the details of the atomic absorption line shape and also to the temporal and spatial profile of the laser pulse. It yields absolute oscillator strengths and it is especially suitable for measurements of transitions between excited atomic states, including autoionizing states.

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Selective photoionization of ytterbium isotope is studied numerically based on a three-step photoionization scheme, 4f146s2 1S0 (0 cm−1) → 4f146s6p 3P1 (17992.008 cm−1) → (4f136s26p) (7/2, 3/2)2 (35196.98 cm−1) → auto-ionization state (52353 cm−1) → Yb+, by the density matrix theory with the consideration of atomic hyperfine structures and magnetic sublevels. To examine the physical model, the numerical isotopic abundance of ytterbium is compared with that from mass spectroscopy experiment, showing that they are in good agreement with each other. The excitation process and ionization process of ytterbium, especially for odd isotopes, are discussed and analyzed in detail on this basis. The effects of frequency detuning, power densities, spectral bandwidths, polarization of two excitation lasers, and atomic Doppler broadening on the total ionization yield and isotopic abundance are investigated numerically and the optimal excitation conditions for 176Yb enrichment are identified semi-quantitatively.

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Selective photoionization of168Yb in a three-level atomic medium by the collinear propagation of laser pulses

A. S. Choe, Yongjoo Rhee, Jongmin Lee +2 more

The medium of the three-level Yb atom corresponding to the three-colour, three-step, three-photon scheme of 6 1 S 0 (0 cm -1 ) to 6 3 P 1 (17992008 cm -1 ) to (7/2, 3/2) 2 4f 13 6s 2 6p (35196.98 cm -1 ) to autoionization state (52353 cm -1 ) is chosen to examine the selective photoionization of 168 Yb. The Maxwell-Bloch equation is numerically solved, where the interacting laser pulses are supposed to be collinear and resonant with the transition lines of 168 Yb, and the effects of Doppler broadening and laser bandwidth are incorporated. Firstly, the thin medium dynamics are examined to determine the optimal energy of laser pulses for the selective photoionization of 168 Yb, and to determine Yb isotopes which have a large influence on the excitation of 168 Yb. Secondly, the thick medium dynamics are investigated, resulting in the fact that the laser pulse for the first transition is prominently deformed due to the near-resonant interaction with 171 Yb and 173 Yb, and the ion yield along the propagation of the laser beam is strongly dependent on the initial energy of pulse for the first transition and the time-delay between input pulses.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 14, 1995•15 citations
Two methods have been used to measure the oscillator strength of the transition between the ground and 17,992 cm level in XUYb. The first technique involves exciting the transition with a laser pulse that is nearly time-bandwidth limited, of uniform intensity, and has a reproducible shape from shot to shot. The population left in the excited state after the pulse varies sinusoidally with a period that depends on the integral over time of the electric field amplitude and the transition oscillator strength. These are the Rabi oscillations that are predicted by application of the Schrodinger equation to the two-level atom. The second method involves observation of the polarization rotation of a set of degenerate sublevels brought about by a light-shift laser. One sublevel (m/sub j/ = 0) of the J = 1 level at 17,992 cm is populated by a linearly polarized laser. A second copropagating light-shift laser, which is linearly polarized at an angle to the first laser, is tuned between 7.5 and 30 GHz off-resonance with the transition. The light-shift laser causes population to be promoted into the m/sub j/ = +-1 levels through the virtual J = 0, m/sub j/ = 0 level. Two linearly polarized photoionizing lasers photoionize the population only from the m/sub j/ = +-1 levels. The photoion signal oscillates cosinusoidally with a period that depends only on the integrated pulse intensity, the laser detuning, and the transition oscillator strength. Finally, polarization selectivity has been shown experimentally to allow selective photoionization of the odd isotopes of ytterbium using broadband lasers.
We have used two methods to measure the oscillator strength of the transition between the ground and 17992 cm-1 level in 174Yb. The first technique involves exciting the transition with a laser pulse that is nearly time-bandwidth limited, of uniform intensity, and has a reproducible shape from shot to shot. The population left in the excited state after the pulse varies sinusoidally with a period that depends on the integral over time of the electric field amplitude and the transition oscillator strength. These are the Rabi oscillations that are predicted by application of the Schrodinger equation to the two-level atom. The excited-state population is probed using a two-step photoionization to the continuum. The electric field amplitude is determined from the temporal profile and the intensity of the laser pulse. The second method involves observation of the polarization rotation of a set of degenerate sublevels brought about by a time-bandwidth limited light-shift laser. One sublevel (mj = 0) of the J = 1 level at 17992 cm-1 is populated by a linearly polarized laser. A second copropagating light-shift laser, which is linearly polarized at an angle to the first laser, is tuned between 7.5 and 30 GHz off-resonance with the transition. The light-shift laser causes population to be promoted into the mi = ±1 levels by a virtual transition through the ground J = 0, = 0 level. Two linearly polarized photoionizing lasers photoionize the population only from the mi = ±1 levels. The photoion signal oscillates sinusoidally with a period that depends only on the integrated pulse intensity, the laser detuning, and the transition oscillator strength.
The theory of a new method to measure oscillator strengths is presented. The method exploits the ac Stark interaction of a laser pulse detuned from a transition between an initially populated state a and a second state b of an atom. We assume the density matrix \ensuremath{\rho} of state a initially has only diagonal elements given by 〈m\ensuremath{\Vert}\ensuremath{\rho}\ensuremath{\Vert}m〉=C+Dm2{\mathrm{Dm}}^{2}Dm2 where C and D\ensuremath{\ne}0 are constants and m is the Zeeman sublevel quantum number. The laser pulse is linearly polarized along an axis different from the quantization axis and therefore rearranges the atoms among the various Zeeman sublevels. Changes of the relative Zeeman sublevel populations induced by the laser pulse can be readily detected by monitoring changes in the angular distribution or polarization of fluorescent light emitted when the atoms radiatively decay to some final state f. This paper considers the general problem where states a, b, and f have arbitrary angular momentum. We derive the functional dependence of the polarized fluorescent light fluence on the laser pulse fluence (pulse energy per unit area).For spatially uniform laser pulses, these signals are periodic functions of the laser fluence. When the laser is completely speckled, we show that the signal is well approximated by a Lorentzian curve. This latter case is of considerable experimental interest since most pulsed dye lasers have poor transverse mode structure which can readily be converted into a statistically well-defined speckle pattern. The oscillator strength of the transition between states a and b is found using (1) the fluence half-width of the ``depolarization curve,'' the Lorentzian-like dependence of the fluorescence polarization on the laser pulse fluence, (2) the detuning of the laser from the transition frequency ${\ensuremath{\omega}}_{\mathrm{ab}}$, and (3) some known constant factors which depend on the angular momenta of states a, b, and f. The physics of the situation is very similar to that of the conventional hook method with this difference: the roles of the atoms and the photons have been interchanged. We therefore call this new method the inverse hook method. The inverse hook method is relatively insensitive to the details of the atomic absorption line shape and also to the temporal and spatial profile of the laser pulse. It yields absolute oscillator strengths and it is especially suitable for measurements of transitions between excited atomic states, including autoionizing states.
An established photoionization branching-ratio measurement method, in which an excited level of an atom is populated by a pulsed laser from the ground level and repopulation of the ground level is measured by a second laser or lasers, is extended to the case with a finite lower-level lifetime. Two pulsed dye lasers populate the upper and the lower levels of the transition of interest. A third pulsed dye laser probes the time evolution of the lower level by a photoionization process. This measurement, coupled with the upper- and the lower-level lifetimes, permits the determination of the branching ratio and transition probability. Cerium branching ratios obtained are compared with those that we determined from the emission spectrum of cerium. The method is tested for the difficult case in which the lifetimes of the transition levels are nearly equivalent. The effects of magnetic sublevels are investigated in ytterbium.
Highly selective photoionization of the ytterbium atom by coherent two-photon excitation was demonstrated experimentally. The Yb atom was excited by two single-mode lasers and ionized by a time-delayed broadband laser. The isotope ratio of the ions was analyzed by a time-of-flight mass spectrometer. The ion yield and the selectivity were recorded as a function of detuning of the first exciting laser. The maximum of ion yield was observed when the laser was detuned from resonance. The selectivity of 168Yb^{168}\mathrm{Yb}168Yb was increased higher than 20 000 when the laser was blue-detuned to the most efficient position. Also, numerical analysis was performed to explain the experimental results. \textcopyright{} 1996 The American Physical Society.
Selective photoionization of ytterbium isotope is studied numerically based on a three-step photoionization scheme, 4f146s2 1S0 (0 cm−1) → 4f146s6p 3P1 (17992.008 cm−1) → (4f136s26p) (7/2, 3/2)2 (35196.98 cm−1) → auto-ionization state (52353 cm−1) → Yb+, by the density matrix theory with the consideration of atomic hyperfine structures and magnetic sublevels. To examine the physical model, the numerical isotopic abundance of ytterbium is compared with that from mass spectroscopy experiment, showing that they are in good agreement with each other. The excitation process and ionization process of ytterbium, especially for odd isotopes, are discussed and analyzed in detail on this basis. The effects of frequency detuning, power densities, spectral bandwidths, polarization of two excitation lasers, and atomic Doppler broadening on the total ionization yield and isotopic abundance are investigated numerically and the optimal excitation conditions for 176Yb enrichment are identified semi-quantitatively.
The medium of the three-level Yb atom corresponding to the three-colour, three-step, three-photon scheme of 6 1 S 0 (0 cm -1 ) to 6 3 P 1 (17992008 cm -1 ) to (7/2, 3/2) 2 4f 13 6s 2 6p (35196.98 cm -1 ) to autoionization state (52353 cm -1 ) is chosen to examine the selective photoionization of 168 Yb. The Maxwell-Bloch equation is numerically solved, where the interacting laser pulses are supposed to be collinear and resonant with the transition lines of 168 Yb, and the effects of Doppler broadening and laser bandwidth are incorporated. Firstly, the thin medium dynamics are examined to determine the optimal energy of laser pulses for the selective photoionization of 168 Yb, and to determine Yb isotopes which have a large influence on the excitation of 168 Yb. Secondly, the thick medium dynamics are investigated, resulting in the fact that the laser pulse for the first transition is prominently deformed due to the near-resonant interaction with 171 Yb and 173 Yb, and the ion yield along the propagation of the laser beam is strongly dependent on the initial energy of pulse for the first transition and the time-delay between input pulses.