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Physical review. B, Condensed matter

Anticrossings in solid-state laser spectroscopy

Alexander J. Wokaun, Stephen Colby Rand, Ralph G. DeVoe, Richard G. Brewer

Published Jun 1, 1981• 18 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.23.5733

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We report the first observation of anticrossings in solid-state laser spectroscopy. Measurements are performed on the 6105-\AA{} zero-phonon transition 3H4(\ensuremathΓ1)\ensuremath↔1D2(\ensuremathΓ1)^{3}H_{4}({\ensuremath{\Gamma}}_{1})\ensuremath{\leftrightarrow}^{1}D_{2}({\ensuremath{\Gamma}}_{1})3H4​(\ensuremathΓ1​)\ensuremath↔1D2​(\ensuremathΓ1​) of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in a YAlO3{\mathrm{O}}_{3}O3​ 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 VVV between two neighboring levels (1 and 2) while a laser field resonantly excites the inhomogeneously broadened 2\ensuremath↔32\ensuremath{\leftrightarrow}32\ensuremath↔3 transition. Ground- and excited-state gyromagnetic ratios \ensuremathγi(i=X,Y,Z){\ensuremath{\gamma}}_{i}(i=X,Y,Z)\ensuremathγi​(i=X,Y,Z) and the interactions VVV are obtained by fitting the observed anticrossings to a diagonalized hyperfine-spin Hamiltonian for 141Pr3+^{141}\mathrm{Pr}^{3+}141Pr3+ 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.
Raman-heterodyne-detected paramagnetic resonance has been used to study the level anticrossing in the 3^{3}3A state of the N-V defect in diamond. The electron-paramagnetic-resonance (EPR) frequencies are well accounted for by a triplet-spin Hamiltonian. Comparison of the EPR spectra with the calculated transition dipole strengths indicates that optical pumping determines, to a large extent, the Raman-heterodyne-signal intensity. Spin alignment in the 3^{3}3A ground state under optical pumping leads to the collapse of the EPR signal at the level anticrossing, where the population is equalized due to the mixing of the spin states. This is substantiated by transient nutation and spin-echo measurements, from which the dipole moment and dephasing time are examined. Laser detuning within the 638-nm zero-phonon line shows that the Raman signal is only detectable when the laser frequency is tuned to the low-energy part of the optical line.
The sizable ground-state nuclear polarization which accompanies the optical pumping of the $^{3}H_{4}\ensuremath{-}^{1}D_{2}$ (16 872-${\mathrm{cm}}^{\ensuremath{-}1}$) $\ensuremath{\sigma}$ transition of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in LaF3{\mathrm{F}}_{3}F3​ was utilized to observe enhanced and saturated absorptions within the inhomogeneously broadened spectral line. The observed hyperfine splittings of the lowest 1D2^{1}D_{2}1D2​ state are 3.7 and 4.7 MHz at 2.0\ifmmode^\circ\else\textdegree\fi{}K. These splittings were fitted by a spin Hamiltonian $\mathcal{H}=D[{I}_{z}^{2}\ensuremath{-}\frac{I(I+1)}{3}]+(\frac{E}{2})({I}_{+}^{2}+{I}_{\ensuremath{-}}^{2})$, where $D=\ensuremath{-}1.10\ifmmode\pm\else\textpm\fi{}0.05$ and $E=\ensuremath{-}0.48\ifmmode\pm\else\textpm\fi{}0.05$ MHz. The observed linewidths (including the exciting laser linewidth) were 0.8 MHz. The deconvoluted optical transition linewidths (full widths at half-maximum) are 0.20\ifmmode\pm\else\textpm\fi{}0.05 MHz.
A novel phase-modulation technique which permits subkilohertz-laser stability and new levels of precision in laser spectroscopy was reported recently. For spectroscopy, the basic arrangement consists of a combination of an optical pump and a probe field which is phase modulated. The pump prepares the atomic sample by burning a narrow hole within the atom's inhomogeneous line shape, and the probe beam samples the prepared hole when its modulation sidebands are swept into resonance. Off resonance, the probe is balanced as pairs of sidebands produce heterodyne beat signals of opposite phase which just cancel. On resonance, the balance is upset and yields a nonvanishing beat signal with a Lorentzian absorption or dispersion line shape and with residual noise approaching the shot noise limit. Here we investigate the theory of phase-modulation spectroscopy. We treat the nonlinear response of an atomic two-level quantum system subject to an intense pump and a weak copropagating or counterpropagating phase-modulated probe beam. The density-matrix equations of motion are solved by a Laplace-transform method and by the novel use of a translation operator which allows the infinite hierarchy of coupled equations to close. A solution equivalent to the rate-equation result is developed and coherence corrections are found which predict new resonances that have just been detected in this laboratory. The delayed pump-probe technique encountered in solid-state laser spectroscopy is analyzed in this context for two- and three-level quantum systems. The response of a Fabry-Perot cavity to a phase-modulated light wave is examined also and reveals an unexpected absorption feature.
Erbium-doped solids are a promising platform for quantum technology due to the Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ 1.5-\textmu{}m optical transition in the telecom C band that can offer long coherence times. To characterize the intrinsic C2{\mathrm{C}}_{2}C2​ site of Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ in Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ for quantum information and photonic signal-processing applications, absorption and site-selective fluorescence spectroscopy were used to assign the Er3+4I15/2\mathrm{E}{\mathrm{r}}^{3+}\phantom{\rule{4pt}{0ex}}^{4}I_{15/2}Er3+4I15/2​$\ensuremath{\leftrightarrow}$4I13/2^{4}I_{13/2}4I13/2​ transitions. The lowest-to-lowest transition occurs at 1535.608 nm and laser absorption determined an inhomogeneous linewidth of 780 MHz in a 0.005%-doped crystal at 3.4 K. Time-resolved fluorescence established an upper limit for the excited-state lifetime of 8.5 ms. Angular-dependent Zeeman absorption was used to determine ground- and excited-state ggg tensors. The C2{\mathrm{C}}_{2}C2​-site ggg tensor components for the ground state are gx=1.60{g}_{x}=1.60gx​=1.60, gy=4.71{g}_{y}=4.71gy​=4.71, and gz=11.93{g}_{z}=11.93gz​=11.93 with a tipping angle of \ensuremath{\alpha} = $2.{06}^{\ensuremath{\circ}}$, whereas for the excited state the components are gx=1.08{g}_{x}=1.08gx​=1.08, gy=4.36{g}_{y}=4.36gy​=4.36, and gz=10.07{g}_{z}=10.07gz​=10.07 with a tipping angle of \ensuremath{\alpha} = $\ensuremath{-}11.{7}^{\ensuremath{\circ}}$. Optical decoherence can be suppressed by the application of a magnetic field parallel to $\ensuremath{\langle}111\ensuremath{\rangle}$ crystal axes where all C2{\mathrm{C}}_{2}C2​ sites become nearly magnetically equivalent with large ggg values so that spin flips of neighboring Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+ ions can be simultaneously suppressed. Using this magnetic field direction, two-pulse photon echoes gave a homogeneous linewidth of 5 kHz for an applied magnetic field of 0.5 T, narrowing and saturating at 2.5 kHz at 3.5 T. Decoherence over intermediate magnetic fields was described by spectral diffusion due to $\mathrm{E}{\mathrm{r}}^{3+}\text{\ensuremath{-}}\mathrm{E}{\mathrm{r}}^{3+}$ magnetic dipole interactions driven by the direct phonon process. With Er3+\mathrm{E}{\mathrm{r}}^{3+}Er3+:Y2O3{\mathrm{Y}}_{2}{\mathrm{O}}_{3}Y2​O3​ absorption at a convenient telecom laser wavelength and the ability to fabricate waveguides, our study suggests that this is a promising material system for quantum information and spectral hole-burning signal-processing applications.
We have observed kilohertz and sub-kilohertz resonance structures in RF-optical double resonance experiments of rare-earth-doped solids, when the frequency of the RF field is scanned across the hyperfine transitions while monitoring the resonant optical absorption of a CW laser. The effect is observed only when the laser spectral width is broad compared to the hyperfine structure. The observed line widths are apparently free of the inhomogeneous widths of hyperfine levels and the line shape has peculiar double peak structure. The effect is modelled with a resonance involving three atomic levels interacting with three electromagnetic fields, two optical and one RF, in a triangular or “delta’ configuration. While the ordinary optical-RF two-field resonance is limited by spin inhomogeneous width, the simultaneous excitation of three coupled transitions leads to narrow and highly nonlinear resonance structures that are not averaged by the inhomogeneous distribution of hyperfine transition.
In this series of papers we report on the generation and application of multiple pulse phase coherent sequences in optical spectroscopy.In this paper the effects of intense pulse trains on systems with only two resonant energy levels are analyzed, with particular attention to the effects of extreme inhomogeneous broadening and population depletion to nonresonant levels.It is shown that these effects, which are present in virtually all optical systems, make the simple gyroscopic model of optical coherent transients invalid.Exact calculations show, e.g., that a two-pulse photon echo is not maximized by a 1:2 length ratio for the pulses; that the maximum excited state population is not created by a 180" pulse; and that three equal pulses are almost as effective as a 1:2:1 ratio for producing three pulse echoes.The role of pulse phase is extensively analyzed.Pulse sequences are proposed and experimentally demonstrated which permit optical phase sensitive detection and measurement of ground state relaxation parameters.The experimental results are based on an extension of the acousto-optic modulation and fluoresence detection techniques of Zewail and Orlowski [Zewail et al., Chem.Phys.Lett.48, 256 (1977); Orlowski et al., ibid.54, 197 (1978)).The relative merits offluorescence and transverse polarization detection are discussed, and fluorescence detection is shown to be more generally useful for these new sequences.Finally, composite pulse trains are shown to be capable of substantially increasing the signal available from highly inhomogenously broadened transitions.In paper II we extend the treatment to multilevel systems with some emphasis on solid state applications.