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Physical Review Letters

Inverse Hook Method for Measuring Oscillator Strengths

William Arie van Wijngaarden, Keith Bonin, W. Happer, E. Miron, David S. Schreiber, Takashi Arisawa

Published May 12, 1986• 11 citations
Publisher

Abstract

We describe a new method for measuring oscillator strengths for transitions between excited atomic states. The oscillator strength is determined from changes in the angular distribution or polarization of fluorescent light induced by the ac Stark effect of a laser pulse. The method can be thought of as a variant of the hook method in which the roles of atoms and photons have been interchanged.

DOI
10.1103/physrevlett.56.2024

Related papers

Theory of the inverse hook method for measuring oscillator strengths

William Arie van Wijngaarden, Keith Bonin, W. Happer

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.

Physical Review A•Aug 1, 1987•3 citations

Inverse hook method for measuring oscillator strengths for transitions between excited atomic states [1]

William Arie van Wijngaarden, Keith Bonin, W. Happer

Hyperfine Interactions•Dec 1, 1987•5 citations

Measurement Of Atomic Oscillator Strengths Using Pulsed Single-Frequency Dye Lasers

C. Haynam, B. Comaskey, Michael Austin Johnson +2 more

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

Measuring atomic oscillator strengths by single atom spectroscopy

Jianwei Lee, Syed Abdullah Aljunid, Meng Khoon Tey +3 more

We propose a method for assessing the oscillator strengths of atomic transitions based on single atom spectroscopy. The method is based on a direct measurement of an AC Stark shift of atomic energy levels for the single atom trapped in an optical tweezer. The method is independent on a knowledge of the trapping field at the atom. The results can be applied to obtaining the previously unknown oscillator strengths for dipole transitions involving the first excited state of alkali metals.

Conference on Lasers and Electro-Optics•Jan 1, 2009•0 citations

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

C. Haynam, B. Comaskey, Earl F. Worden +1 more

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.

•Jan 1, 1987•1 citation

Oscillator strength determination in LaCl3:Pr3+ by photon upconversion

Jeffrey A. Sell, Francis K. Fong

In this paper, we outline a novel method for the determination of oscillator strengths in rare-earth crystals. This method involves the observation of fluorescence resulting from a sequential two-photon excitation process. The rate equations are analyzed and a simple linear relationship between the laser flux, the fluorescent intensity, and the oscillator strength is derived. The equations are applied to LaCl3:Pr3+ and the resulting oscillator strength measured for the 3H6→3P1 transition is found to be in good agreement with the value measured by conventional absorption techniques. One advantage of the present method is the elimination of the need to determine the dopant concentration.

The Journal of Chemical Physics•May 15, 1975•4 citations
We describe a new method for measuring oscillator strengths for transitions between excited atomic states. The oscillator strength is determined from changes in the angular distribution or polarization of fluorescent light induced by the ac Stark effect of a laser pulse. The method can be thought of as a variant of the hook method in which the roles of atoms and photons have been interchanged.
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.
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.
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.
In this paper, we outline a novel method for the determination of oscillator strengths in rare-earth crystals. This method involves the observation of fluorescence resulting from a sequential two-photon excitation process. The rate equations are analyzed and a simple linear relationship between the laser flux, the fluorescent intensity, and the oscillator strength is derived. The equations are applied to LaCl3:Pr3+ and the resulting oscillator strength measured for the 3H6→3P1 transition is found to be in good agreement with the value measured by conventional absorption techniques. One advantage of the present method is the elimination of the need to determine the dopant concentration.