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Applied Optics

Dynamic Orientation of Spin 1 Nuclei I

K.L. Bhatia, M. L. Narchal

Published Feb 1, 1965• 8 citations
Publisher

Abstract

The Overhauser effect in an electron-nuclear coupled spin system (S = ½, 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 achieving stimulated emission are examined in detail. Several significant features hitherto unknown are brought out.

DOI
10.1364/ao.4.000175

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arXiv:0801.1723•Physical Review B•Mar 4, 2008•6 citations
The Overhauser effect in an electron-nuclear coupled spin system (S = ½, 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 achieving stimulated emission are examined in detail. Several significant features hitherto unknown are brought out.
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.
We analyze nuclear-spin dynamics in quantum dots and defect centers with a bound electron under electron-mediated coupling between nuclear spins due to the hyperfine interaction (``JJJ coupling'' in NMR). Our analysis shows that the Overhauser field generated by the nuclei at the position of the electron has short-time dynamics quadratic in time for an initial nuclear-spin state without transverse coherence. The quadratic short-time behavior allows for an extension of the Overhauser-field lifetime through a sequence of projective measurements (quantum Zeno effect). We analyze the requirements on the repetition rate of measurements and the measurement accuracy to achieve such an effect. Further, we calculate the long-time behavior of the Overhauser field for effective electron Zeeman splittings larger than the hyperfine coupling strength and find, both in a Dyson-series expansion and a generalized master-equation approach, that for a nuclear-spin system with a sufficiently smooth polarization the electron-mediated interaction alone leads only to a partial decay of the Overhauser field by an amount of the order of the inverse number of nuclear spins interacting with the electron.
Optically pumped nuclear spin polarization in single InAlAs quantum dots was investigated in detail with regards to the dependences on the excitation power and electron spin polarization. By increasing (or decreasing) the excitation power at a particular excitation polarization, an abrupt rise (or drop) and a clear hysteretic behavior were observed in the Overhauser shift of the photoluminescence under an external magnetic field of 5T5\phantom{\rule{0.3em}{0ex}}\mathrm{T}5T. Those features appear equivalently for the exciton and exciton complexes of the same quantum dot since the created nuclear field is equally effective. However, the degree of circular polarization shows different behaviors between a positively charged exciton and a neutral exciton or biexciton; further, only the positively charged exciton exhibits the precisely synchronized change and hysteretic behavior. It is suggested that the electron spin distribution is affected by the flip-flop of electron-nuclear spins. Further, the hysteresis is observed as a function of the degree of circular polarization of the excitation light, and its dependence on the excitation power is studied. The saturation of the Overhauser shift indicates the almost complete cancellation of the external magnetic field by the nuclear field.
We systematically investigate the universal spin decoherence dynamics of a localized electron in an arbitrary nuclear spin bath, which can even be far away from equilibrium due to the weak nuclear-lattice interaction. We show that the electron spin relaxation dynamics (as well as spin pure dephasing and Hahn echo decay) can always have a universal behavior as long as the initial state is composed of a sufficiently large amount of spin eigenstates. For a given system, the pattern of the universal dynamics depends on the complicated initial condition only via a single parameter, which measures the amount of phase coherence between different spin eigenstates in the initial state. Our results apply even when the number of the involved nuclei is not large and, therefore, provide a solid foundation in the comparison of the theoretical/numerical results to the experimental measurement. As an example, we also show the numerical results for systems of noninteracting spin bath in a zero magnetic field regime and discuss the features of universal decoherent dynamics.
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.