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NMRによる固体中の多光子吸収過程 I(理論)

Yoshinori Manmoto, Satoh, Mitsuo, Norio Akiyama

Published Mar 20, 1990• 0 citations
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Abstract

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.

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NMRによる固体中の多光子吸収過程 II (実験)

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4C1 - Nonlinear effects in an NMR experiment

J. Pommier, H. Benoit

We have studied multiple-photon transition in a low-field nuclear magnetic resonance (NMR) experiment. It is well known that a saturation of the NMR occurs when using a sufficiently high alternating magnetic field which induces multiple-photons transitions. We show theoretically that these multiphoton transitions are accompanied by an harmonic generation. For an-photon transition, this generation occurs mostly on thenth and (n \pm 1)th harmonic. For an irradiating field2H_{1} \cos \omegat of pulsation ω such thatn\omega= \gamma H_{0}=\omega_{0}where H0is the steady field and θ is the angle between H0and H1the amplitudesS\min{n}\max{n}andS\min{n}\max{n+1}of these components are given byS\min{n}\max{n} = f_{n}(\theta) (H_{1})^{n},S\min{n}\max{n+1} = \cos \theta f_{n}(\theta) (H_{1})^{n+1}. We have verified these equations in a low-field NMR experiment (H_{0} = 0.7Gs/s), polarizing first a flowing liquid in a high magnetic field. The liquid then flows in a modified Bloch spectrometer. The receiving coil is still perpendicular to the steady field but it is possible to adjust the angle θ between the axis of the emission coils (H1field) and the steady-field H0. Using a synchronous detection at the output of the receiving coil on the pulsation(n - 1) \omega, n\omega, or(n + 1) \omega, we have directly detected multiphoton transistions. The above equations have been verified forn = 2ton = 5. There are slight discrepancies at high excitation which may be explained taking into account a large saturation.

IEEE Journal of Quantum Electronics•Sep 1, 1966•3 citations
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 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.
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.
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.
A general theory has been developed to calculate the response, in NMR conditions, of a spin system irradiated by two nearly resonant waves having different frequencies and intense enough to produce an appreciable saturation. The absorption signal has been calculated employing the statistical operator technique, treating the electromagnetic field by the second quantization formalism. Two kinds of transitions are expected: The first one arises from processes in which n photons of one wave are emitted and n photons of the other wave are absorbed, the second one arises from processes involving the emission of n photons of one wave and the absorption of n ± 1 photons of the other. In the first case all the transitions coalesce in a single dispersionlike signal, which occurs when the frequencies of the two waves are nearly the same; in the second case a many-line spectrum occurs in which emission and absorption lines are present. The experimental results here reported strictly agree with theoretical previsions.
We have discussed the problems of non linear interaction between electromagnetic radiations with atoms from semi-classical point of view. Time dependent Schrödinger equation for single electron system is solved by using perturbative technique to obtain transition probability. Higher order perturbation is also discussed which is used in multiple processes, in which two or more quanta are emitted instead of a single photon. The theory is based on assumption that the perturbation is small. From this transition probability ionization rate and absorption cross-section of hydrogen atom is calculated. Its variation with photon energy and field strength is analyzed which agrees very well with experimental observations.The Himalayan PhysicsVol. 3, No. 32012Page : 40-43
We have studied multiple-photon transition in a low-field nuclear magnetic resonance (NMR) experiment. It is well known that a saturation of the NMR occurs when using a sufficiently high alternating magnetic field which induces multiple-photons transitions. We show theoretically that these multiphoton transitions are accompanied by an harmonic generation. For an-photon transition, this generation occurs mostly on thenth and (n \pm 1)th harmonic. For an irradiating field2H_{1} \cos \omegat of pulsation ω such thatn\omega= \gamma H_{0}=\omega_{0}where H0is the steady field and θ is the angle between H0and H1the amplitudesS\min{n}\max{n}andS\min{n}\max{n+1}of these components are given byS\min{n}\max{n} = f_{n}(\theta) (H_{1})^{n},S\min{n}\max{n+1} = \cos \theta f_{n}(\theta) (H_{1})^{n+1}. We have verified these equations in a low-field NMR experiment (H_{0} = 0.7Gs/s), polarizing first a flowing liquid in a high magnetic field. The liquid then flows in a modified Bloch spectrometer. The receiving coil is still perpendicular to the steady field but it is possible to adjust the angle θ between the axis of the emission coils (H1field) and the steady-field H0. Using a synchronous detection at the output of the receiving coil on the pulsation(n - 1) \omega, n\omega, or(n + 1) \omega, we have directly detected multiphoton transistions. The above equations have been verified forn = 2ton = 5. There are slight discrepancies at high excitation which may be explained taking into account a large saturation.