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Applied Optics

Dynamic Orientation of Spin I Nuclei II

K.L. Bhatia, M. L. Narchal

Published Jun 1, 1966• 6 citations
Publisher

Abstract

The Jeffries-Abragam effect in an electron-nuclear coupled spin system (S = (1/2), I = 1) is studied in detail. From a population-distribution analysis of the system, the nuclear orientation parameters are computed and their temperature dependence discussed. Conditions for obtaining stimulated emission are examined in detail. The results are compared with those of an earlier paper.

DOI
10.1364/ao.5.001075

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arXiv:0801.1723•Physical Review B•Mar 4, 2008•6 citations
The Jeffries-Abragam effect in an electron-nuclear coupled spin system (S = (1/2), I = 1) is studied in detail. From a population-distribution analysis of the system, the nuclear orientation parameters are computed and their temperature dependence discussed. Conditions for obtaining stimulated emission are examined in detail. The results are compared with those of an earlier paper.
The method of partial distributions is used to compute the normalized population distribution in an electron-nuclear coupled spin system in which I = S = 1/2. The expressions obtained are more general than those reported previously in that they include the effects of competitive relaxation and competitive radiative induced transition probabilities. It is clear that positive and negative enhancement may be obtained either by the Overhauser or the Jeffries-Abragam effect irrespective of the relative magnitudes of the nuclear Zeeman and hyperfine interaction energies. A small enhancement is not necessarily due to incomplete saturation, but may well be the result of compensating emission and absorption.
The time-dependent Schrodinger equation of a many particle spin system consisting of an electron in a quantum dot interacting with the spins of the nuclei (N) in the dot due to hyperfine interaction is solved exactly for a given arbitrary initial state. The electron spin dynamics is then expressed in terms of the reduced density matrix of the composite system by computing the marginal density matrix of the electron. This is accomplished by classifying states of the system by the total spin of the coupled electron and nuclear system that commutes with the system Hamiltonian. These states are used in enumerating and finding the exact solution of the time-dependent Schrodinger equation. In each sector of the total spin, the problem reduces to solving a linear simultaneous set of equations that are solved by matrix inversion. Such solutions enable one to make a reliable approximate scheme for purposes of numerical estimation of the various physical quantities. A methematical and physical discussion of this procedure with the density matrix approach to this problem is given here. To elucidate the procedure and its advantages, special cases of N=3,4 are given in some detail in an Appendix.
We have investigated the quantum dynamics of the electron-nuclei coupled system in a double quantum dot and discovered a couple of new phenomena related to the quantum nature of nuclear spin system. Especially, the bunching of results of the electron spin measurements and the revival in the conditional probabilities are salient features of quantum dynamics. The underlying mechanism is the squeezing of the nuclear spin state through the electron spin measurements. This squeezing is expected to lead to the elongation of the electron spin coherence time. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
We investigate quantum dynamics in the electron-nuclei coupled spin system in quantum dots and clarify the fundamental features of quantum correlation induced via successive electron-spin measurements. This quantum correlation leads to interesting phenomena such as the bunching of outcomes in the electron-spin measurements and the revival of an arbitrary initial electron-spin state. The nuclear spin system is also affected by the quantum correlation and is, in fact, squeezed via conditional measurements or postselection. This squeezing is confirmed by calculating the increase in the purity of the nuclear spin system. Thus, the successive electron-spin measurements provide a probabilistic method to squeeze the nuclear spin system. These new features are predicted not only for the case of double quantum dots occupied by a pair of electrons but also for the case of a single quantum dot occupied by a single electron or a pair of electrons.