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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Nuclear superradiance of the spin system

Dmitry S. Bulyanitsa, Andrey V. Druzhin, Evgeni D. Trifonov

Published Jan 14, 2000• 0 citations

Abstract

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.

DOI: 10.1117/12.375333

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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 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.

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.

We discuss the coherent behavior of a polarized, nuclear or electron, spin system for which the magnetic dipole radiation emitted in the radio-frequency region, has approximately quadratic dependence on the number of spins. An effective method of describing these phenomena is provided by computer simulation of a microscopic model of the spin system. Important aspects of this numeric simulation are described, together with a comparison with the theoretical predictions. The behavior of the transverse component of the magnetic moment,

{M}^{+}(t)

, in super-radiant conditions is studied. In addition, the role of dipole-dipole interactions in super-radiation phenomena is investigated in detail. It is shown that some important features of super-radiation cannot be described with the Bloch equations.

Radio wave amplification by stimulated emission of radiation (NMR laser) was observed in

{\mathrm{Al}}_{2}

{\mathrm{O}}_{3}

:

{\mathrm{Cr}}^{3+}

(ruby) with the

^{27}\mathrm{Al}

spin system pumped to an inverted Zeeman state by means of dynamic nuclear polarization (DNP) and with an LC circuit tuned to the NMR transitions. A theory is developed which combines standard Bloch equations with the dynamic equations of a heat-reservoir model for the spin dynamics. Experimental data concerning the relaxation and polarization mechanisms in the nonradiant state are presented, and the parameters of the reservoir model are determined. In accord with these results, dynamic NMR laser equations for different modes of operation (continuous or pulsed) are derived from which the threshold of the NMR laser, its critical behavior near threshold, and its transient response after

Q

-switch tuning can be calculated. The agreement between theory and experiments in the superradiant state reflects unambiguously the interplay between nuclear-spin relaxation, DNP, spin fluctuations, and the self-induced ordering of the

^{27}\mathrm{Al}

spins perpendicular to the applied field. In particular, the results highlight the decisive role of the electronic dipole-dipole system in the spin and NMR laser dynamics of ruby. Special emphasis is placed on the close relationship between the NMR laser, as a system far from thermal equilibrium which shows the phenomenon of cooperative self-organization, and a system at thermal equilibrium which undergoes a second-order phase transition. Thus, the rotating nuclear-spin magnetization is treated as an order parameter.