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NMRによる固体中の多光子吸収過程 II (実験)

Yoshinori Manmoto, Satoh, Mitsuo, Norio Akiyama

Published Mar 20, 1991• 0 citations
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Abstract

The theory of multiphoton processes in solids by a rotary-saturation method in NMR have been proposed by us. In this paper, we apply the theoretical ideas to fluorine nuclei in a CaF_2 single crystal and analyse the experimental results by the theory. We found evidence that (1) the experimental results of multiphoton processes can be explained fundamentally by the theory but cannot be fully ; (2) one type of single spin-n photon transitions is taking place, but another type of two spin-n photon transitions is not confirmed yet in this crystal ; (3) the linewidths of the multiphoton absorptions are extremely narrow at the magic angle but do not completely vanish because of the presence of a perturbing field ; (4) the effects of the energy level mixing through the dipole-dipole interactions on the multiphoton transitions are negligible over a wide range around the magic angle ; (5) the inhomogeneity of the rf field used to quantize the spin system in the rotating frame affects considerably the results of the rotary-saturation experiments.

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T. Yabuzaki, S. Nakayama, Y. Murakami +1 more

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Physical Review A•Dec 1, 1974•52 citations
The theory of multiphoton processes in solids by a rotary-saturation method in NMR have been proposed by us. In this paper, we apply the theoretical ideas to fluorine nuclei in a CaF_2 single crystal and analyse the experimental results by the theory. We found evidence that (1) the experimental results of multiphoton processes can be explained fundamentally by the theory but cannot be fully ; (2) one type of single spin-n photon transitions is taking place, but another type of two spin-n photon transitions is not confirmed yet in this crystal ; (3) the linewidths of the multiphoton absorptions are extremely narrow at the magic angle but do not completely vanish because of the presence of a perturbing field ; (4) the effects of the energy level mixing through the dipole-dipole interactions on the multiphoton transitions are negligible over a wide range around the magic angle ; (5) the inhomogeneity of the rf field used to quantize the spin system in the rotating frame affects considerably the results of the rotary-saturation experiments.
Theoretical investigation of multiphoton processes in solids by rotary-saturation method in NMR is presented. In order to analize the results obtained by this method, it is necessary to introduce the conception of doubly rotating reference frame. The second quantization of a perturbing field, the calculation of the nth order time-dependent perturbation, dipole-dipole interaction and the motion of magnetization are all treated in this frame. Multiphoton transitions in solids have strong dependences on the time during perturbation, the strength of perturbing field and the angle between the direction of quantization and that of perturbing field. Rotary-saturation method produces easily magic angle at which the width of multiphoton absorption lines extremely narrow, so that even higher-order transitions can be observed separately each other.
The optical analog of the nuclear magnetic resonance rotary saturation effect is demonstrated and analyzed. A 9.6-\ensuremath{\mu}m CO2{\mathrm{O}}_{2}O2​ laser resonance excitation of vibrational transitions in gaseous CH3{\mathrm{H}}_{3}H3​F creates an effective splitting in the interaction representation of the optical two-level system. A radio-frequency standing-wave Stark electric field is tuned in rotary saturation resonance with the splitting. The change in transmitted laser beam intensity, because of rotary resonance, is measured in terms of transient optical signals obtained by the Stark switching method of Brewer and Shoemaker. The measured single and multiphoton rotary saturation resonance signals are compared with perturbation and computer solutions of nonlinear Bloch-Maxwell macroscopic equations. Doppler-free rotary saturation spectra are obtained in the presence of inhomogeneous Doppler broadening by a special scheme of Fourier analysis. A discussion is presented of the coupling of energy between two traveling waves that are in double resonance with the optical two-level system. The concept of spin temperature is discussed in relation to a coherently excited optical level system with a long fluorescence lifetime. The possibility of a cross-relaxation double resonance experiment between an optical system and a spin system is outlined.
The use of four pulsed rf fields for the excitation of multiphoton resonances in a two-level system is investigated. A general theoretical description of the experiment is provided based on the Floquet formalism and application of basic conservation laws to the overall transition process. The predictions of the theory are compared with computer simulations of the time evolution of the magnetization according to the exact time-dependent Hamiltonian. It is shown that N-photon resonances occur when the fields are applied at frequencies \ifmmode\pm\else\textpm\fi{}k\ensuremath{\omega} and \ifmmode\pm\else\textpm\fi{}l\ensuremath{\omega} from the Larmor frequency, where k and l are positive integers having no common factors and where 0\ensuremath{\le}k<l, k+l=N. For any resonance k photons are taken from the outer field pair and l are taken from the inner field pair. A total of 2[(l+k)!]/(k!l!) mutually interfering transition pathways exist for the overall process and the resultant magnitude of the effective N-photon field is very sensitive to the relative initial phases of the rf fields. The spiral motion observed for multiphoton resonances induced by double-frequency irradiation is absent here when the field intensities are symmetrical. In addition, the fraction of total applied rf intensity available for multiphoton pumping is considerably greater than for two fields. Phase cycling to enhance detection of multiphoton effects and multiphoton spin locking are considered.
The first observation of optical rotary saturation is reported. Bloch-like equations of motion for rotary saturation are solved by a perturbation calculation and also numerically on a computer. In addition to the rotary-saturation resonance, multiphoton transitions are predicted and observed. A "Debye resonance in the rotating frame" naturally emerges from the equations. The case of two traveling waves interacting with a two-level system is shown to be mathematically equivalent to the rotary-saturation equations.
Two-quantum rotary echoes predicted by Bloch like equations for two-quantum transition have been observed in a multi-level NMR system of 27 Al nuclei in Al 2 O 3 . An rf field exactly at resonance to the two-quantum transition ( Δ m =2) was turned on at t =0 and its phase was shifted by 90° at t =τ. The echo at t =2τ was observed by using the technique of transfer of coherence reported previously. Characteristic dependence of the echo width upon inhomogeneity of rf field amplitude was confirmed experimentally.
Energies of the coupled system of a spin-1/2 atom in a static magnetic field and an oscillating rf field are analyzed with the resolvent formalism and numerically calculated by quantizing the rf field, for the general case that the strong rf field is oriented in an arbitrary direction to the static magnetic field. It is shown that, if the component of the static field along the direction of the rf field has particular values, level crossings take place and multiphoton transitions by even or odd numbers of rf photons become forbidden, even when the polarization of the rf field satisfies the parity condition for the multiphoton transitions. Particular attention is given to the direction and amount of the shifts of the level crossings by the rf field, together with the shifts of the anticrossings or of the multiphoton transitions. Theoretical results are verified by the optical-pumping experiments with cesium vapor.