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Journal of Physics D Applied Physics

Experimental verification of the relation between the delay time and the tipping angle for a superradiant pulse

Jin-Hong Chen, Xi‐an Mao

Published Jan 1, 1999• 10 citations
Publisher

Abstract

According to Dicke's theory of superradiance, the relation between the delay time and the tipping angle for superradiant pulses can be expressed by , where is the radiation damping time constant. This relation is verified by nuclear magnetic resonance (NMR) experiments on a normal water sample. The radiation damping time and the delay time are independently measured, and the tipping angle is evaluated. The tipping angle can be as big as several degrees if the spin inversion is not perfect. It can also be as small as rad, when the residual coherence in the transverse plane is destroyed by a strong field gradient pulse.

DOI
10.1088/0022-3727/32/7/003

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According to Dicke's theory of superradiance, the relation between the delay time and the tipping angle for superradiant pulses can be expressed by , where is the radiation damping time constant. This relation is verified by nuclear magnetic resonance (NMR) experiments on a normal water sample. The radiation damping time and the delay time are independently measured, and the tipping angle is evaluated. The tipping angle can be as big as several degrees if the spin inversion is not perfect. It can also be as small as rad, when the residual coherence in the transverse plane is destroyed by a strong field gradient pulse.
In optical superradiance studies, data were reported supporting a relation between the delay time $({\ensuremath{\tau}}_{D})$ and the tipping angle $({\ensuremath{\delta}}_{0}),$ ${\ensuremath{\tau}}_{D}=({\ensuremath{\tau}}_{R}/4)[\mathrm{ln}({\ensuremath{\delta}}_{0}/2\ensuremath{\pi}){]}^{2},$ where ${\ensuremath{\tau}}_{R}$ is the radiation damping time constant. We found that the same data also satisfy another relation, ${\ensuremath{\tau}}_{D}={\ensuremath{\tau}}_{R}\mathrm{ln}[\mathrm{cot}({\ensuremath{\delta}}_{0}/2)].$ The derivation of the two relations is reexamined. It is found that the former relation does not have sound theoretical background, and could lead to considerable errors when it is used to interpret experimental results.
We report the first direct measurement of the effective initial tipping angle ${\ensuremath{\theta}}_{0}$ in superfluorescence. A coherent pulse of small area $\ensuremath{\theta}$, resonant on the superfluorescence transition, is injected into a completely inverted sample of cesium atoms and the delay of the out-put pulse is measured as a function of $\ensuremath{\theta}$. The value of ${\ensuremath{\theta}}_{0}$ obtained agrees in essence with 2(N)12\frac{2}{{(N)}^{\frac{1}{2}}}(N)21​2​. The latter value is predicted by recent theories which consider the quantum initiation of superfluorescence and which take propagation effects into account.
The authors report on an experimental study of intensity and delay fluctuations for a two-level system by analysing stochastic distribution of the polarisation of superradiant pulses emitted on the transition 6p 2 P 1 /2 to 6s 2 S 1/2 of rubidium atoms. They develop a theoretical interpretation of their results. Finally, use of these properties of polarisation fluctuations has permitted one to study the very beginning of the superradiant emission and to give a new estimate of the so-called 'tipping angle'.
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.
We introduce a straightforward quantum-electrodynamic approach to the problem of superradiant spontaneous emission from a system of two-level atoms, and also discuss two classical superradiant systems. The same physical concepts underlie our treatment of both the quantum and classical cases. Explicit expressions are found which describe the time evolution and directional character of the radiated power. Our approach applies to an arbitrary number of atoms which are confined to a region with linear dimensions which may be large compared with the mean wavelength of the emitted radiation. The radiative decay half-life of a large many-atom system is found to be much shorter than the natural lifetime of a single atom, but not as short as the half-life of a small atomic system with the same number of atoms. The far-field radiation pattern appropriate to the case of a circular cylinder of emitters which have been excited by a plane-wave pulse is considered in detail. Polar plots are presented of the radiation patterns produced when the atoms are excited by a plane-wave pulse. Exciting pulses traveling in directions both parallel and at an angle of 10\ifmmode^\circ\else\textdegree\fi{} to the axis of the cylinder are considered. A discussion and generalization of Dicke's "coherence-brightening" criterion is given.