Physical review. B, Condensed matter

Raman heterodyne interference: Symmetry analysis

Emily S. Kintzer, Masaharu Mitsunaga, Richard G. Brewer

Published Jun 1, 1985• 22 citations

Abstract

The Raman heterodyne interference phenomenon observed recently in the impurity-ion crystals ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$ and ${\mathrm{Pr}}^{3+}$:${\mathrm{LaF}}_{3}$ is examined from the viewpoint of symmetry analysis of the nonlinear susceptibility tensor. General Raman heterodyne signals are derived for all crystal symmetries and for all optical-frequency and radiofrequency polarizations. An example of the utility of this approach resolves a controversy over the crystal symmetry of ${\mathrm{LaF}}_{3}$, establishing that it is trigonal rather than hexagonal.

DOI: 10.1103/physrevb.31.6958

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Raman heterodyne interference: Observations and analytic theory

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Physical review. B, Condensed matterJun 1, 198549 citations

Spin Hamiltonian characterization and refinement for Pr 3 + :YAlO 3 and Pr 3 + :Y 2 SiO 5

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Symmetry analysis of Raman heterodyne interference

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Interference of scattering pathways in Raman heterodyne spectroscopy of multilevel atoms

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Physical review. B, Condensed matter

Raman heterodyne interference: Symmetry analysis

Emily S. Kintzer, Masaharu Mitsunaga, Richard G. Brewer

Published Jun 1, 1985• 22 citations

Publisher

Abstract

The Raman heterodyne interference phenomenon observed recently in the impurity-ion crystals

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

{\mathrm{YAlO}}_{3}

and

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

{\mathrm{LaF}}_{3}

is examined from the viewpoint of symmetry analysis of the nonlinear susceptibility tensor. General Raman heterodyne signals are derived for all crystal symmetries and for all optical-frequency and radiofrequency polarizations. An example of the utility of this approach resolves a controversy over the crystal symmetry of

{\mathrm{LaF}}_{3}

, establishing that it is trigonal rather than hexagonal.

DOI: 10.1103/physrevb.31.6958

Related papers

Raman heterodyne interference: Observations and analytic theory

Masaharu Mitsunaga, Emily S. Kintzer, Richard G. Brewer

The recently developed technique of Raman heterodyne detection has unveiled a new interference effect in the Zeeman spectrum of hyperfine transitions of impurity-ion solids. An earlier theory had been developed to explain the basic Raman heterodyne process which involves the resonant interaction of a three-level quantum system with coherent optical-frequency and radiofrequency fields. However, it was not realized that impurity-ion crystals can generate more than one type of Raman heterodyne signal and that these signals can interfere. This article describes two examples of interference where one originates from two or more inequivalent nuclear sites and the other from a single site that exhibits interference among Zeeman transitions. An analytical theory covering these two cases is presented and compared to observations for the impurity-ion crystals ${\mathrm{Pr}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ and ${\mathrm{Pr}}^{3+}$ : ${\mathrm{LaF}}_{3}$ , the interference behavior in the two being dramatically different.The recently developed technique of Raman heterodyne detection has unveiled a new interference effect in the Zeeman spectrum of hyperfine transitions of impurity-ion solids. An earlier theory had been developed to explain the basic Raman heterodyne process which involves the resonant interaction of a three-level quantum system with coherent optical-frequency and radiofrequency fields. However, it was not realized that impurity-ion crystals can generate more than one type of Raman heterodyne signal and that these signals can interfere. This article describes two examples of interference where one originates from two or more inequivalent nuclear sites and the other from a single site that exhibits interference among Zeeman transitions. An analytical theory covering these two cases is presented and compared to observations for the impurity-ion crystals ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$ and ${\mathrm{Pr}}^{3+}$:${\mathrm{LaF}}_{3}$, the interference behavior in the two being dramatically different.

Physical review. B, Condensed matterJun 1, 198549 citations

Spin Hamiltonian characterization and refinement for Pr 3 + :YAlO 3 and Pr 3 + :Y 2 SiO 5

Marko Lovrić, Philipp Glasenapp, Dieter Suter

Rare-earth ions in dielectric crystals play an important role in high-resolution laser spectroscopy and are interesting candidates for storing quantum states of photons. We characterize the praseodymium hyperfine interaction of the ground-state ( ${}^{3}$ H ${}_{4}$ ) and one excited-state ( ${}^{1}$ D ${}_{2}$ ) for two important compounds: praseodymium doped in yttrium aluminum perovskite and praseodymium doped in yttrium orthosilicate. The spin Hamiltonian parameters are determined by numerical analysis of Raman-heterodyne spectra, which were collected for a range of static external magnetic field strengths and orientations. For Pr ${}^{3+}$ :YAlO ${}_{3}$ , we present a full analysis without restrictions for the Zeeman and quadrupole tensors, and our new characterization for Pr ${}^{3+}$ :Y ${}_{2}$ SiO ${}_{5}$ resolves a controversy in the literature.Rare-earth ions in dielectric crystals play an important role in high-resolution laser spectroscopy and are interesting candidates for storing quantum states of photons. We characterize the praseodymium hyperfine interaction of the ground-state (${}^{3}$H${}_{4}$) and one excited-state (${}^{1}$D${}_{2}$) for two important compounds: praseodymium doped in yttrium aluminum perovskite and praseodymium doped in yttrium orthosilicate. The spin Hamiltonian parameters are determined by numerical analysis of Raman-heterodyne spectra, which were collected for a range of static external magnetic field strengths and orientations. For Pr${}^{3+}$:YAlO${}_{3}$, we present a full analysis without restrictions for the Zeeman and quadrupole tensors, and our new characterization for Pr${}^{3+}$:Y${}_{2}$SiO${}_{5}$ resolves a controversy in the literature.

Physical Review BJan 24, 201224 citations

Symmetry analysis of Raman heterodyne interference

D. R. Taylor

Optics CommunicationsDec 1, 198412 citations

Raman heterodyne detection of nuclear magnetic resonance

N. C. Wong, Emily S. Kintzer, J. Mlynek +2 more

A novel coherent Raman effect induced by a laser and a radio-frequency (rf) field is used to detect cw and pulsed nuclear magnetic resonance (NMR) in ground and excited electronic states. The effect is illustrated in the impurity-ion solid ${\mathrm{Pr}}^{3+}$ : La ${\mathrm{F}}_{3}$ at 1.6 K utilizing the ${\mathrm{Pr}}^{3+}$ optical transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\rightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$. The laser field of frequency ${\ensuremath{\omega}}_{E}$ and the rf field (${\ensuremath{\omega}}_{H}$) induce a light wave at the sum ${\ensuremath{\omega}}_{E}+{\ensuremath{\omega}}_{H}$ (anti-Stokes) and difference ${\ensuremath{\omega}}_{E}\ensuremath{-}{\ensuremath{\omega}}_{H}$ (Stokes) frequencies, generating an absorptive or dispersive heterodyne beat signal (${\ensuremath{\omega}}_{H}$) with the laser field at a photodetector. The theory of this effect is characterized in a new three-level perturbation calculation which requires, unlike the usual stimulated Raman effect, that all three transitions be electric- or magnetic-dipole allowed. Detailed predictions are confirmed by cw measurements of the ${\mathrm{Pr}}^{3+}$ : La ${\mathrm{F}}_{3}$ hyperfine splittings where the optical heterodyne signals are shot-noise limited. The ${\mathrm{Pr}}^{3+}$ nuclear quadrupole parameters are obtained for the $^{3}H_{4}$ and $^{1}D_{2}$ states where the line centers are determined with kilohertz precision. The corresponding wave functions show significant hyperfine-state mixing, as required for all three transitions to be dipole allowed. The cw line shapes are narrow (30-160 kHz), inhomogeneously broadened by nuclear magnetic interactions, and reveal either a Gaussian or an anomalous second-derivative---like line shape. The spin-echo measurements for the $^{3}H_{4}$ and $^{1}D_{2}$ hyperfine transitions yield homogeneous line shapes which are Lorentzian, and rather surprisingly, linewidths in the narrow range 10-20 kHz, a result which tests current line-broadening theories.A novel coherent Raman effect induced by a laser and a radio-frequency (rf) field is used to detect cw and pulsed nuclear magnetic resonance (NMR) in ground and excited electronic states. The effect is illustrated in the impurity-ion solid ${\mathrm{Pr}}^{3+}$: La${\mathrm{F}}_{3}$ at 1.6 K utilizing the ${\mathrm{Pr}}^{3+}$ optical transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\rightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$. The laser field of frequency ${\ensuremath{\omega}}_{E}$ and the rf field (${\ensuremath{\omega}}_{H}$) induce a light wave at the sum ${\ensuremath{\omega}}_{E}+{\ensuremath{\omega}}_{H}$ (anti-Stokes) and difference ${\ensuremath{\omega}}_{E}\ensuremath{-}{\ensuremath{\omega}}_{H}$ (Stokes) frequencies, generating an absorptive or dispersive heterodyne beat signal (${\ensuremath{\omega}}_{H}$) with the laser field at a photodetector. The theory of this effect is characterized in a new three-level perturbation calculation which requires, unlike the usual stimulated Raman effect, that all three transitions be electric- or magnetic-dipole allowed. Detailed predictions are confirmed by cw measurements of the ${\mathrm{Pr}}^{3+}$: La${\mathrm{F}}_{3}$ hyperfine splittings where the optical heterodyne signals are shot-noise limited. The ${\mathrm{Pr}}^{3+}$ nuclear quadrupole parameters are obtained for the $^{3}H_{4}$ and $^{1}D_{2}$ states where the line centers are determined with kilohertz precision. The corresponding wave functions show significant hyperfine-state mixing, as required for all three transitions to be dipole allowed. The cw line shapes are narrow (30-160 kHz), inhomogeneously broadened by nuclear magnetic interactions, and reveal either a Gaussian or an anomalous second-derivative---like line shape. The spin-echo measurements for the $^{3}H_{4}$ and $^{1}D_{2}$ hyperfine transitions yield homogeneous line shapes which are Lorentzian, and rather surprisingly, linewidths in the narrow range 10-20 kHz, a result which tests current line-broadening theories.

Physical review. B, Condensed matterNov 1, 1983110 citations

Symmetry considerations regarding light propagation and light polarization for coherent interactions with ions in crystals

Yiwen Sun, G. M. Wang, R. L. Cone +2 more

Spectroscopic studies and the efficiency of optical coherent transient devices can be adversely affected by interference arising from several distinct Rabi frequencies associated with crystallographically equivalent but orientationally inequivalent crystal sites. General symmetry principles have been used to find light field directions that guarantee both optimum single-Rabi-frequency interaction and the most efficient coherent transient generation in arbitrary crystals. This theoretical analysis has been applied experimentally to a wide range of rare earth crystals, many of which are important for technological applications. Site interference in optical nutation provides a simple illustration of this effect. Optimum single-Rabi-frequency nutation signal was obtained for the ${}^{3}{H}_{6}(1)$ to ${}^{3}{H}_{4}(1)$ transition of 0.1% ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ when the light $\stackrel{\ensuremath{\rightarrow}}{E}$ vector is along special crystal directions $〈111〉$ or $〈001〉.$ Quantitative comparison of nutation frequencies for light polarized along different directions allowed the determination of the optical transition dipole moment to be along $〈110〉$ for this transition. The transition dipole moment derived from the nutation signal agrees within 15% with that obtained from absorption experiments. Other applications of nutation measurements are discussed, including a procedure for determining site occupancy in crystals with crystallographically inequivalent sites.Spectroscopic studies and the efficiency of optical coherent transient devices can be adversely affected by interference arising from several distinct Rabi frequencies associated with crystallographically equivalent but orientationally inequivalent crystal sites. General symmetry principles have been used to find light field directions that guarantee both optimum single-Rabi-frequency interaction and the most efficient coherent transient generation in arbitrary crystals. This theoretical analysis has been applied experimentally to a wide range of rare earth crystals, many of which are important for technological applications. Site interference in optical nutation provides a simple illustration of this effect. Optimum single-Rabi-frequency nutation signal was obtained for the ${}^{3}{H}_{6}(1)$ to ${}^{3}{H}_{4}(1)$ transition of 0.1% ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ when the light $\stackrel{\ensuremath{\rightarrow}}{E}$ vector is along special crystal directions $〈111〉$ or $〈001〉.$ Quantitative comparison of nutation frequencies for light polarized along different directions allowed the determination of the optical transition dipole moment to be along $〈110〉$ for this transition. The transition dipole moment derived from the nutation signal agrees within 15% with that obtained from absorption experiments. Other applications of nutation measurements are discussed, including a procedure for determining site occupancy in crystals with crystallographically inequivalent sites.

Physical review. B, Condensed matterDec 15, 200071 citations

Interference of scattering pathways in Raman heterodyne spectroscopy of multilevel atoms

Tilo Blasberg, Dieter Suter

Raman heterodyne detection of nuclear magnetic resonance is a sensitive technique for optical detection of an NMR transition, which is driven by a resonant radio-frequency field. The observed signal is linear in the transition matrix elements of the magnetic resonance transition and two optical transitions. This linearity is the reason that signal contributions from different sites or different rf transitions can interfere, in many cases destructively. In this article, we discuss such an interference effect, which appears to have been overlooked in the past. It occurs between signal contributions that originate from the same magnetic resonance transition of atoms with different positions within the inhomogeneously broadened optical resonance line. These atoms contribute to the coherent Raman scattering through different scattering paths, which involve optical transitions to different nuclear spin states of the same electronic state. We show that the interference between all possible scattering paths leads to complete signal cancellation, if the atoms that are involved in the different scattering paths are equally polarized. To study the effect and to eliminate the interference, we used a pump-and-probe technique with two laser beams. With two independent laser frequencies, it becomes possible to separate the individual scattering paths. We calculate the dependence of the signal on the frequency of both laser beams as well as on the radio frequency and compare the results to experimental data from ${\mathrm{Pr}}^{3+}$ : ${\mathrm{YAlO}}_{3}$ . Our results show that the interference reduces the signal amplitude of the conventional Raman heterodyne experiment but can be eliminated in the new experiment.Raman heterodyne detection of nuclear magnetic resonance is a sensitive technique for optical detection of an NMR transition, which is driven by a resonant radio-frequency field. The observed signal is linear in the transition matrix elements of the magnetic resonance transition and two optical transitions. This linearity is the reason that signal contributions from different sites or different rf transitions can interfere, in many cases destructively. In this article, we discuss such an interference effect, which appears to have been overlooked in the past. It occurs between signal contributions that originate from the same magnetic resonance transition of atoms with different positions within the inhomogeneously broadened optical resonance line. These atoms contribute to the coherent Raman scattering through different scattering paths, which involve optical transitions to different nuclear spin states of the same electronic state. We show that the interference between all possible scattering paths leads to complete signal cancellation, if the atoms that are involved in the different scattering paths are equally polarized. To study the effect and to eliminate the interference, we used a pump-and-probe technique with two laser beams. With two independent laser frequencies, it becomes possible to separate the individual scattering paths. We calculate the dependence of the signal on the frequency of both laser beams as well as on the radio frequency and compare the results to experimental data from ${\mathrm{Pr}}^{3+}$:${\mathrm{YAlO}}_{3}$. Our results show that the interference reduces the signal amplitude of the conventional Raman heterodyne experiment but can be eliminated in the new experiment.

Physical review. B, Condensed matterMay 1, 19955 citations

The Raman heterodyne interference phenomenon observed recently in the impurity-ion crystals

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

{\mathrm{YAlO}}_{3}

and

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

{\mathrm{LaF}}_{3}

{\mathrm{LaF}}_{3}

, establishing that it is trigonal rather than hexagonal.

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

{\mathrm{YAlO}}_{3}

and

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

{\mathrm{LaF}}_{3}

, the interference behavior in the two being dramatically different.

{}^{3}

{}_{4}

) and one excited-state (

{}^{1}

{}_{2}

) for two important compounds: praseodymium doped in yttrium aluminum perovskite and praseodymium doped in yttrium orthosilicate. The spin Hamiltonian parameters are determined by numerical analysis of Raman-heterodyne spectra, which were collected for a range of static external magnetic field strengths and orientations. For Pr

{}^{3+}

:YAlO

{}_{3}

, we present a full analysis without restrictions for the Zeeman and quadrupole tensors, and our new characterization for Pr

{}^{3+}

{}_{2}

SiO

{}_{5}

resolves a controversy in the literature.

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

: La

{\mathrm{F}}_{3}

at 1.6 K utilizing the

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

optical transition $^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\rightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})$. The laser field of frequency ${\ensuremath{\omega}}_{E}$ and the rf field (${\ensuremath{\omega}}_{H}$) induce a light wave at the sum ${\ensuremath{\omega}}_{E}+{\ensuremath{\omega}}_{H}$ (anti-Stokes) and difference ${\ensuremath{\omega}}_{E}\ensuremath{-}{\ensuremath{\omega}}_{H}$ (Stokes) frequencies, generating an absorptive or dispersive heterodyne beat signal (${\ensuremath{\omega}}_{H}$) with the laser field at a photodetector. The theory of this effect is characterized in a new three-level perturbation calculation which requires, unlike the usual stimulated Raman effect, that all three transitions be electric- or magnetic-dipole allowed. Detailed predictions are confirmed by cw measurements of the

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

: La

{\mathrm{F}}_{3}

hyperfine splittings where the optical heterodyne signals are shot-noise limited. The

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

nuclear quadrupole parameters are obtained for the

^{3}H_{4}

and

^{1}D_{2}

states where the line centers are determined with kilohertz precision. The corresponding wave functions show significant hyperfine-state mixing, as required for all three transitions to be dipole allowed. The cw line shapes are narrow (30-160 kHz), inhomogeneously broadened by nuclear magnetic interactions, and reveal either a Gaussian or an anomalous second-derivative---like line shape. The spin-echo measurements for the

^{3}H_{4}

and

^{1}D_{2}

hyperfine transitions yield homogeneous line shapes which are Lorentzian, and rather surprisingly, linewidths in the narrow range 10-20 kHz, a result which tests current line-broadening theories.

{}^{3}{H}_{6}(1)

{}^{3}{H}_{4}(1)

transition of 0.1%

{\mathrm{Tm}}^{3+}:{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}

when the light $\stackrel{\ensuremath{\rightarrow}}{E}$ vector is along special crystal directions

〈111〉

〈001〉.

Quantitative comparison of nutation frequencies for light polarized along different directions allowed the determination of the optical transition dipole moment to be along

〈110〉

for this transition. The transition dipole moment derived from the nutation signal agrees within 15% with that obtained from absorption experiments. Other applications of nutation measurements are discussed, including a procedure for determining site occupancy in crystals with crystallographically inequivalent sites.

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

{\mathrm{YAlO}}_{3}

. Our results show that the interference reduces the signal amplitude of the conventional Raman heterodyne experiment but can be eliminated in the new experiment.