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Bulletin of the American Physical Society

Quantum Mechanical Scattering in Nanoscale Systems

Anthony G. Gianfrancesco, Andrei Victor Ilyashenko, C.R. Boucher, L. R. Ram‐Mohan

Published Feb 29, 2012• 0 citations
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Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.
Using a scattered field interference mechanism, we theoretically demonstrate the quantum statistics control with a hybrid system comprised of a quantum emitter and a plasmonic multimode nanocavity. Enhanced through multimode interactions, destructive interference between scattered fields from the emitter and nanocavity is able to change the photon statistics from bunching to antibunching. This transition cannot be explained by treating the plasmonic nanocavity in the dipole approximation. In some specific regions, an effective single-mode model, which is equivalent to the multimode model, is derived by simply shifting the transition frequency and modifying decay rates of the nearby quantum emitter. Superior to the closed optical microcavity, this hybrid system can be used to control the photon statistics without the need for strong coupling, and may find applications in nanoscale refractive index sensing.
Robin (or mixed) boundary conditions in quantum mechanics have received considerable attention in the last two decades, in particular, for applications to nanoscale systems. However, their utility has remained obscure to the larger physics community; in fact, one may find extant claims in the literature about the supposed naturalness of the specific Dirichlet (or vanishing) boundary condition. Here we demonstrate that not only are Dirichlet boundary conditions unnatural, but that Robin boundary conditions have utility in the long-wavelength approximation of short-ranged potentials. For illustration, we consider a non-relativistic particle in one dimension under the influence of the multi-step and Morse potential. We derive the scattering and bound states for these potentials and determine the parameters that describe those states in an effective system, namely one in which there is a free particle with a boundary. This method appears to be generically applicable and also generalizable to many other real systems.