A theory is presented of radiation trapping effects in time-resolved, stepwise-excited, electron-photon coincidence signals. The theory is based on a detailed analysis of laser-induced optical pumping effects in the stepwise excitation process combined with a multipole treatment of the radiation trapping processes. New data from a stepwise excitation experiment on the inelastic excitation of the 6 ${\mathrm{}}^{1}$ ${\mathit{P}}_{1}$ state in ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$-Hg collisions and previously reported data are compared with the predictions of the theory. Good agreement is found between experiment and theory, including confirmation that under some experimental conditions, the ${\mathit{P}}_{10}$ Stokes parameter of the coincidentally detected stepwise excited fluorescence increases in magnitude with increasing target gas density. \textcopyright{} 1996 The American Physical Society.A theory is presented of radiation trapping effects in time-resolved, stepwise-excited, electron-photon coincidence signals. The theory is based on a detailed analysis of laser-induced optical pumping effects in the stepwise excitation process combined with a multipole treatment of the radiation trapping processes. New data from a stepwise excitation experiment on the inelastic excitation of the 6${\mathrm{}}^{1}$${\mathit{P}}_{1}$ state in ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$-Hg collisions and previously reported data are compared with the predictions of the theory. Good agreement is found between experiment and theory, including confirmation that under some experimental conditions, the ${\mathit{P}}_{10}$ Stokes parameter of the coincidentally detected stepwise excited fluorescence increases in magnitude with increasing target gas density. \textcopyright{} 1996 The American Physical Society.

Physical Review AJun 1, 19968 citations

Level-crossing experiments by two-photon excitation

G. Hermann, G. Lasnitschka, Jan Richter +1 more

Zeitschrift für Physik D Atoms Molecules and ClustersMar 1, 19912 citations

Time-delayed detection in level anticrossing spectroscopy

J. B. Marques, Luis Lorenzo Sánchez-Soto, Eusebio Bernabéu

Il Nuovo Cimento DMar 1, 19910 citations

Anticrossings in solid-state laser spectroscopy

Alexander J. Wokaun, Stephen Colby Rand, Ralph G. DeVoe +1 more

We report the first observation of anticrossings in solid-state laser spectroscopy. Measurements are performed on the 6105-\AA{} zero-phonon transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\leftrightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$ of ${\mathrm{Pr}}^{3+}$ in a YAl ${\mathrm{O}}_{3}$ crystal at 2\ifmmode^\circ\else\textdegree\fi{} K where both ground- and excited-state anticrossings appear. A perturbation theory of the anticrossing signal is derived from the wave equations of motion for a three-level quantum system subject to a static interaction $V$ between two neighboring levels (1 and 2) while a laser field resonantly excites the inhomogeneously broadened $2\ensuremath{\leftrightarrow}3$ transition. Ground- and excited-state gyromagnetic ratios ${\ensuremath{\gamma}}_{i}(i=X,Y,Z)$ and the interactions $V$ are obtained by fitting the observed anticrossings to a diagonalized hyperfine-spin Hamiltonian for $^{141}\mathrm{Pr}^{3+}$ which includes second-order ligand field corrections in terms containing the electron orbital angular momentum. Under certain conditions, one anticrossing signal develops into a strongly modulated oscillation with a period of \ensuremath{\sim} 20 G, an unexpected feature which appears to be a nonlinear optical coherence effect. The influence of anticrossing state mixing on optical free-induction-decay observations is also discussed.We report the first observation of anticrossings in solid-state laser spectroscopy. Measurements are performed on the 6105-\AA{} zero-phonon transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\leftrightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$ of ${\mathrm{Pr}}^{3+}$ in a YAl${\mathrm{O}}_{3}$ crystal at 2\ifmmode^\circ\else\textdegree\fi{} K where both ground- and excited-state anticrossings appear. A perturbation theory of the anticrossing signal is derived from the wave equations of motion for a three-level quantum system subject to a static interaction $V$ between two neighboring levels (1 and 2) while a laser field resonantly excites the inhomogeneously broadened $2\ensuremath{\leftrightarrow}3$ transition. Ground- and excited-state gyromagnetic ratios ${\ensuremath{\gamma}}_{i}(i=X,Y,Z)$ and the interactions $V$ are obtained by fitting the observed anticrossings to a diagonalized hyperfine-spin Hamiltonian for $^{141}\mathrm{Pr}^{3+}$ which includes second-order ligand field corrections in terms containing the electron orbital angular momentum. Under certain conditions, one anticrossing signal develops into a strongly modulated oscillation with a period of \ensuremath{\sim} 20 G, an unexpected feature which appears to be a nonlinear optical coherence effect. The influence of anticrossing state mixing on optical free-induction-decay observations is also discussed.

Physical review. B, Condensed matterJun 1, 198118 citations

Optically Induced Magnetization in Ruby

Jan P. van der Ziel, N. Bloembergen

The magnetization of ruby in a magnetic field at 300\ifmmode^\circ\else\textdegree\fi{}K is changed when the ruby is optically pumped with linearly polarized radiation from a $Q$ -switched ruby laser. With a magnetic field parallel to the trigonal axis, laser light polarized parallel to this axis induces transitions from the spin \ifmmode\pm\else\textpm\fi{}\textonehalf{} levels of the $^{4}A_{2}$ ground state to the levels of the $\overline{E}(^{2}E)$ excited state. The change in ${M}_{z}$ is linearly proportional to $H$ except near the anticrossing points of the $^{4}A_{2}$ spin levels at 2.07 and 4.14 kG. At these field strengths, there is an enhancement of the magnetization caused by state mixing of the $^{4}A_{2}$ wave functions. When $H$ has a small component perpendicular to the $z$ axis, a magnetization is detected parallel to this component in the vicinity of 4.14 kG. The effect requires a long ground-state relaxation time. In a separate experiment, the relaxation of ${M}_{z}$ was found to vary from 0.13 \ensuremath{\mu}sec in zero magnetic field to a constant value of 0.57 \ensuremath{\mu}sec for fields above 60 G.The magnetization of ruby in a magnetic field at 300\ifmmode^\circ\else\textdegree\fi{}K is changed when the ruby is optically pumped with linearly polarized radiation from a $Q$-switched ruby laser. With a magnetic field parallel to the trigonal axis, laser light polarized parallel to this axis induces transitions from the spin \ifmmode\pm\else\textpm\fi{}\textonehalf{} levels of the $^{4}A_{2}$ ground state to the levels of the $\overline{E}(^{2}E)$ excited state. The change in ${M}_{z}$ is linearly proportional to $H$ except near the anticrossing points of the $^{4}A_{2}$ spin levels at 2.07 and 4.14 kG. At these field strengths, there is an enhancement of the magnetization caused by state mixing of the $^{4}A_{2}$ wave functions. When $H$ has a small component perpendicular to the $z$ axis, a magnetization is detected parallel to this component in the vicinity of 4.14 kG. The effect requires a long ground-state relaxation time. In a separate experiment, the relaxation of ${M}_{z}$ was found to vary from 0.13 \ensuremath{\mu}sec in zero magnetic field to a constant value of 0.57 \ensuremath{\mu}sec for fields above 60 G.

Physical ReviewMay 17, 196557 citations

{\mathrm{}}^{1}

{\mathit{P}}_{1}

state in ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$-Hg collisions and previously reported data are compared with the predictions of the theory. Good agreement is found between experiment and theory, including confirmation that under some experimental conditions, the

{\mathit{P}}_{10}

Stokes parameter of the coincidentally detected stepwise excited fluorescence increases in magnitude with increasing target gas density. \textcopyright{} 1996 The American Physical Society.

{\mathrm{Pr}}^{3+}

in a YAl

{\mathrm{O}}_{3}

crystal at 2\ifmmode^\circ\else\textdegree\fi{} K where both ground- and excited-state anticrossings appear. A perturbation theory of the anticrossing signal is derived from the wave equations of motion for a three-level quantum system subject to a static interaction

V

between two neighboring levels (1 and 2) while a laser field resonantly excites the inhomogeneously broadened $2\ensuremath{\leftrightarrow}3$ transition. Ground- and excited-state gyromagnetic ratios ${\ensuremath{\gamma}}_{i}(i=X,Y,Z)$ and the interactions

V

are obtained by fitting the observed anticrossings to a diagonalized hyperfine-spin Hamiltonian for

^{141}\mathrm{Pr}^{3+}

which includes second-order ligand field corrections in terms containing the electron orbital angular momentum. Under certain conditions, one anticrossing signal develops into a strongly modulated oscillation with a period of \ensuremath{\sim} 20 G, an unexpected feature which appears to be a nonlinear optical coherence effect. The influence of anticrossing state mixing on optical free-induction-decay observations is also discussed.

The magnetization of ruby in a magnetic field at 300\ifmmode^\circ\else\textdegree\fi{}K is changed when the ruby is optically pumped with linearly polarized radiation from a

Q

-switched ruby laser. With a magnetic field parallel to the trigonal axis, laser light polarized parallel to this axis induces transitions from the spin \ifmmode\pm\else\textpm\fi{}\textonehalf{} levels of the

^{4}A_{2}

ground state to the levels of the

\overline{E}(^{2}E)

excited state. The change in

{M}_{z}

is linearly proportional to

H

except near the anticrossing points of the

^{4}A_{2}

spin levels at 2.07 and 4.14 kG. At these field strengths, there is an enhancement of the magnetization caused by state mixing of the

^{4}A_{2}

wave functions. When

H

has a small component perpendicular to the

z

axis, a magnetization is detected parallel to this component in the vicinity of 4.14 kG. The effect requires a long ground-state relaxation time. In a separate experiment, the relaxation of

{M}_{z}

was found to vary from 0.13 \ensuremath{\mu}sec in zero magnetic field to a constant value of 0.57 \ensuremath{\mu}sec for fields above 60 G.