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Physical Review A

Level crossing and polarization rotation in doubly resonant third-harmonic generation in I2

Chen-Yu Tai, Ann Tarn

Published Jun 1, 1983• 8 citations
Publisher

Abstract

The gyromagnetic ratio of several states in ${\mathrm{I}}_{2}$ is studied with the technique of polarization rotation and level crossing in doubly resonant third-harmonic generation. The level-crossing curve has a linewidth of approximately the Doppler linewidth of the corresponding non-coherent process divided by the angular momentum quantum number. In the polarization-rotation work, a rotated angle 80\ifmmode^\circ\else\textdegree\fi{} is observed with little depolarization. The ratio of the angle rotated to the magnetic field of some 20 resonances can be divided into two groups: large ($\frac{\ensuremath{\Delta}\ensuremath{\theta}}{\ensuremath{\Delta}H}\ensuremath{\sim}10$\ifmmode^\circ\else\textdegree\fi{}/kG) and small ($\frac{\ensuremath{\Delta}\ensuremath{\theta}}{\ensuremath{\Delta}H}<2$\ifmmode^\circ\else\textdegree\fi{}/kG). A theory based on the interference between the different molecules is presented to explain the experimental data. The observed differences in $\frac{\ensuremath{\Delta}\ensuremath{\theta}}{\ensuremath{\Delta}H}$ is interpreted in terms of the difference in the transition branch in the one- and two-quantum transition. The gyromagnetic ratio of the ground state as determined by this technique is approximately -6 and that of the two-quantum excited state is approximately -20.

DOI
10.1103/physreva.27.3078

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Oct 21, 1998•0 citations
The gyromagnetic ratio of several states in I2{\mathrm{I}}_{2}I2​ is studied with the technique of polarization rotation and level crossing in doubly resonant third-harmonic generation. The level-crossing curve has a linewidth of approximately the Doppler linewidth of the corresponding non-coherent process divided by the angular momentum quantum number. In the polarization-rotation work, a rotated angle 80\ifmmode^\circ\else\textdegree\fi{} is observed with little depolarization. The ratio of the angle rotated to the magnetic field of some 20 resonances can be divided into two groups: large (\ensuremathΔ\ensuremathθ\ensuremathΔH\ensuremath∼10\frac{\ensuremath{\Delta}\ensuremath{\theta}}{\ensuremath{\Delta}H}\ensuremath{\sim}10\ensuremathΔH\ensuremathΔ\ensuremathθ​\ensuremath∼10\ifmmode^\circ\else\textdegree\fi{}/kG) and small (\ensuremathΔ\ensuremathθ\ensuremathΔH<2\frac{\ensuremath{\Delta}\ensuremath{\theta}}{\ensuremath{\Delta}H}<2\ensuremathΔH\ensuremathΔ\ensuremathθ​<2\ifmmode^\circ\else\textdegree\fi{}/kG). A theory based on the interference between the different molecules is presented to explain the experimental data. The observed differences in \ensuremathΔ\ensuremathθ\ensuremathΔH\frac{\ensuremath{\Delta}\ensuremath{\theta}}{\ensuremath{\Delta}H}\ensuremathΔH\ensuremathΔ\ensuremathθ​ is interpreted in terms of the difference in the transition branch in the one- and two-quantum transition. The gyromagnetic ratio of the ground state as determined by this technique is approximately -6 and that of the two-quantum excited state is approximately -20.
The intensity of the resonant third-harmonic generation in I2{\mathrm{I}}_{2}I2​ vapor is found to decrease with increasing strength of an external magnetic field even when the exciting light is polarized parallel to the magnetic field. This effect is explained with a theory based on the interference between different molecules. The gyromagnetic ratio of the excited state is determined in this work. This technique may also be applied to study the mechanism of the various processes of saturation in resonant wave mixing.
Magnetic-field-induced resonant third-harmonic generation in I2{\mathrm{I}}_{2}I2​ with circularly polarized light is studied. With a magnetic field perpendicular to the propagating direction of the light, the axial symmetry is broken and the angular momentum is no longer conserved in such a system, and the third harmonic may be generated under such conditions. Quantum beats in photon-echo-like third-harmonic generation with nonsynchronous laser pulses are also studied. The intensity of the harmonic generated may be interpreted in terms of the interference between a molecule and itself as well as the interference between different molecules. The gyromagnetic ratio of the resonant states is measured.
The technique of harmonic generation with circularly polarized light is applied to study the Land\'e ggg factor of the two-quantum excited states of I2{\mathrm{I}}_{2}I2​ molecules. Systematic and abrupt changes in the ggg factor are observed. The large change in the ggg factor is interpreted in terms of perturbation by a level that has no bound state. Enhancement of harmonic generation in a high magnetic field with linearly polarized light is also observed in some resonances that have a small ggg factor in the two-quantum state. The enhancement is interpreted in terms of constructive interference of resonances originating from the ground state and the first thermally excited vibrational state.
We studied alignment-to-orientation conversion caused by excited-state level crossings in a nonzero magnetic field of both atomic rubidium isotopes. Experimental measurements were performed on the transitions of the D2{D}_{2}D2​ line of rubidium. These measured signals were described by a theoretical model that takes into account all neighboring hyperfine transitions, the mixing of magnetic sublevels in an external magnetic field, the coherence properties of the exciting laser radiation, and the Doppler effect. In the experiments, laser-induced fluorescence components were observed at linearly polarized excitation and their difference was taken afterwards. By observing the two oppositely circularly polarized components, we were able to see structures not visible in the difference graphs, which give deeper insight into the processes responsible for these signals. We studied how these signals are dependent on intensity and how they are affected when the exciting laser is tuned to different hyperfine transitions. The comparison between experiment and theory was carried out fulfilling the nonlinear absorption conditions. The theoretical curves described the experimental measurements satisfactorily, reproducing even small features in the shapes of the curves.
A technique of third-harmonic generation (THG) with nonsynchronous pulses is applied to study the dynamics of resonant wave mixing. A circularly polarized laser pulse is focused into a cell containing I2{\mathrm{I}}_{2}I2​ vapor to create the coherent dipole moments. An oppositely circularly polarized pulse is then focused into the same region to generate the third harmonic. Since no THG is produced by any individual pulse, correlated THG can be easily measured without using any fast detection scheme. A theory is presented to explain the measured coherent lifetime of approximately 1 ns. The technique of wave mixing with two linearly polarized pulse is applied to study saturation in resonant THG and to measure the homogeneous relaxation rate of the molecular states. This technique is also applied to study the photon echo generating process.
In recent years interest has significantly quickened in investigation of nonlinear optical and spectroscopic phenomena in such unique objects as Rydberg atoms (the atoms in the energy states near the ionization limit) and van der Waals complexes (dimers). These objects are characterized, in particular, by that their energy states are strongly degenerate due to a large value of angular (rotational) momentum. Here, the problem arises of adequate theoretical description of experimental results, especially when polarization peculiarities of nonlinear radiation processes are considered. The problem is caused by the existence of a huge number of quantum magnetic sublevels of energy states, which are, in the general case, coherently coupled to each other and take part in the radiation processes. Figure 1 gives a vivid presentation of the problem arising even in such a seemingly simple case when one need describe the radiation transitions caused by a strong monochromatic field between two energy levels with large values of the angular momentum J. If the field polarization is arbitrary, the whole set of the magnetic sublevels turn out to be coupled by radiative transitions. Formally, the problem becomes essentially multilevel. In this case not only the hope fades of solving it analytically using the traditional quantum-mechanical approach, but the problems of numerical solution grow abruptly with increasing quantum number J as well. On the other hand, as is often the case, every cloud has a silver lining. With large J we approach the situation when the rotational motion of particles can be described classically. It turns out that the transition from the quantum description of orientation states of the angular momentum to the classical one simplifies the problem radically: it reduces to the problem of radiation processes in the simplest model of nondegenerate states. In this case the rotational motion manifests itself in a dependence of the density matrix elements on orientation angles of the angular momentum as on a parameter.