Mesoscopic Electronics and Optics

Yale University, New Haven CT

Investigators

Abstract

0084501 Stone This grant supports theoretical research topics related to the behavior of electrons and photons in confined geometries for which the spatial confinement scale is large compared to the wavelength but small enough (in many cases) that quantum or wave effects are important. A unifying theme of this research is that the confining potential is either disordered or complex enough to generate chaotic classical motion, so that one must employ techniques from quantum transport theory and/or semiclassical methods for classically chaotic systems ("quantum chaos theory"). Most of the specific proposals relate to two categories of systems: dielectric micro-cavity resonators and micro-lasers, and semiconductor quantum dots. For optical resonators, the theory of asymmetric resonant cavities (ACR's) will be further developed. ACR's are cylindrical or spherical dielectric resonators smoothly deformed from rotational symmetry. The resonances of such systems are non-perturbatively related to those of the symmetric system. In such a case semiclassical methods are very powerful since photons are non-interacting (in the linear regime) and these methods will be developed further. Within this theory, we will attempt to describe such effects as chaos-assisted tunneling and dynamical localization of photons. In addition, we expect to make substantial progress on the basic resonator theory of ARC's, developing a full quantitative theory of the output directionality and Q-value in various different parameter regimes, and understanding the conditions of single and multi-mode lasing. Finally, we will for the first time address the non-linear and quantum-optical properties of these resonators and micro-lasers. For the case of semiconductor quantum dots the problem is more difficult because treatment of the strong electron-electron interactions is essential. Here the focus will be on the role of disorder and/or chaos in causing interaction fluctuations which are not captured by mean-field theory. Specifically we intend to explore our recent discovery that interaction fluctuations play a major role in suppressing spontaneous magnetization in a model for a disordered quantum dot, i.e., the interaction fluctuations generically oppose the Stoner instability of itinerant electron systems. These effects appear to increase as the conductance decreases, so that they may also play an important role near the metal-insulator or superconductor-insulator transitions. In the regime where mean-field theory does work, we will study the evolution of the self-consistent spectrum using semiclassical methods applied to the self-consistent potential. %%% This grant supports theoretical research on the nanoscience of electrons (electrical charge) and photons (light). The topics are related to the behavior of electrons and photons in confined geometries for which the spatial confinement scale is large compared to the wavelength but small enough (in many cases) that quantum or wave effects are important. A unifying theme of this research is that the confining potential is either disordered or complex enough to generate chaotic classical motion, so that one must employ techniques from quantum transport theory and/or semiclassical methods for classically chaotic systems ("quantum chaos theory"). Most of the specific proposals relate to two categories of systems: dielectric micro-cavity resonators and micro-lasers, and semiconductor quantum dots. The topics are both of deep intellectual interest and of great potential application. ***