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Journal of Experimental and Theoretical Physics

Superradiation of a system of nuclear spins

Dmitry S. Bulyanitsa, Andrey V. Druzhin, Evgenii Dmitrievich Trifonov

Published Aug 1, 2000• 1 citation
Publisher

Abstract

The superradiation of a system of nuclear spins is investigated taking into account the broadening of the NMR spectrum due to the stochasticity of the local magnetic field. The effect of the local field generated by nuclear spins randomly distributed in space is investigated. In this case it is possible to achieve better agreement with the experimentally observed characteristics of this phenomenon. Specifically, the possibility of a monopulse regime with a high initial inversion of the spin polarization is explained.

DOI
10.1134/1.1311982

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The superradiation of a system of nuclear spins is investigated taking into account the broadening of the NMR spectrum due to the stochasticity of the local magnetic field. The effect of the local field generated by nuclear spins randomly distributed in space is investigated. In this case it is possible to achieve better agreement with the experimentally observed characteristics of this phenomenon. Specifically, the possibility of a monopulse regime with a high initial inversion of the spin polarization is explained.
ABSTRACT It is shown that the magnetic field local inhomogeneous, caused by the stochastic spin distribution over the volume,effects significantly on the nuclear superradiation process. Keywords: Dicke superradiance, nuclear spin system 1. INTRODUCTION The possibility of the Dicke superradiance' in the nuclear spin system, placed in the magnetic field, was explained byBlombergen and Paund in 1954.2 Experimental researches of this effect related to more later time.3'4 The theoretical explanation of this experiment, based on the solution of the Maxwell - Bloch equations system was proposed (seealso7) in works.5'6 Further development of the nuclear spin superradiance theory is contained in works.8'4 A semi-classical approach,5'6 reproducing main features of the observed effect, contained a number of artificial assumptions. In particular, observation of the single pulses regime with high values of the initial spin polarizations couldn't beexplained with taking in account of Larmor frequency scanning, that took place in the experiment. To obtain thecorrespondence with the experimental data we had to artificially select the transverse relaxation time value.In the present paper we throw out these assumptions and show that the role of additional relaxation mechanismcan play line width, caused by the local magnetic field. Here we are not pretend to give the exact description of thementioned experiment,4 but only point to the sufficiently features of the phenomenon considered.
The main part of this review is devoted to the comprehensive description of coherent radiation by nuclear spins. The theory of nuclear spin superradiance is developed and the experimental observations of this phenomenon are considered. The intriguing problem of how coherence develops from initially incoherent quantum fluctuations is analysed. All main types of coherent radiation by nuclear spins are discussed, which are: free nuclear induction, collective induction, maser generation, pure superradiance, triggered superradiance, pulsing superradiance, punctuated superradiance, and induced emission. The influence of electron-nuclear hyperfine interactions and the role of magnetic anisotropy are studied. Conditions for realizing spin superradiance by magnetic molecules are investigated. The possibility of nuclear matter lasing, accompanied by pion or dibaryon radiation, is briefly touched.
A theory is proposed to account for the superradiance emitted by a system of nuclear spins interacting with a resonant circuit. A study is reported of the dependences of the parameters of the superradiance pulses on the main parameters of the medium. A comparison is made of these dependences with the corresponding expressions in the optical superradiance case. The transition from superradiance to maser operation is investigated. It is shown that the calculations are in full agreement with the experimental curves.
An orderly account is given of the processes of coherent propagation, amplification, and generation of pulses in polyatomic resonant media. The characteristic features of the propagation of solitons in resonant media of finite length are considered. Comparisons are made of the exponential and lethargic amplification of pulses in resonant media. It is shown that an allowance for the reflection of the field from the boundaries of an active medium gives rise to a qualitatively different dependence of the parameters of the pulses on the reflection coefficients under superradiance and lasing conditions, which makes it possible to introduce a criterion to distinguish lasing from superradiance. An analysis is made of the characteristics of collective superradiance, which is a new case of coherent generation of pulses. Experimental and theoretical investigations of rf superradiance emitted by systems of nuclear spins are reviewed.
The extension of double resonance methods in nuclear magnetic resonance is presented. The origin of the problem and its reduction to an abstract problem are discussed. The theorem that allows the calculation of the ensemble average of the linear response of a system with a strong time-dependent stochastic perturbation is given and applied to one-spin and two-spin systems with scalar coupling. The question of convergence is discussed and a relation between level shift and line broadening is stated. The nuclear magnetic resonance spectra are described in relation to the shape of the power spectrum of the stochastic perturbation. The example shows that the functional expansion of the density operator is useful to calculate the effects of strong stochastic perturbations on a quantum mechanical system. (M.C.G.)
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.