Raman heterodyne detection of nuclear magnetic resonance

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 ${}_{}{}^3{}_{}{}^{}H_4^{}{}_{}{}^{}\left({\Gamma }_1\right)\to {}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}\left({\Gamma }_1\right)$. The laser field of frequency ${\omega }_E$ and the rf field (${\omega }_H$) induce a light wave at the sum ${\omega }_E+{\omega }_H$ (anti-Stokes) and difference ${\omega }_E-{\omega }_H$ (Stokes) frequencies, generating an absorptive or dispersive heterodyne beat signal (${\omega }_H$) 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.