Theory

Picoelectrodynamics

Light-matter interaction is central to probe several fundamental properties of condensed matter systems. Over the past decade, the study of how light interacts with nanometer scale artificial structures such as photonic crystals and metamaterials has led to the emergence of nanophotonics. My work has enabled to leap beyond nanophotonics and introduced the field of picoelectrodynamics. Picoelectrodynamics comprises of light-matter interaction in natural media at sub-nanometer (nm) length scales. We predict silicon as the first example of a picophotonic media which hosts ultrashort picoscale electromagnetic waves. These waves exist in a frequency regime where propagating waves are conventionally thought to be forbidden, and are highly oscillatory even within a single unit cell of silicon. Our findings demonstrate that natural media such as silicon exhibit a variety of yet to be discovered electromagnetic phases of matter and provides a pathway towards the discovery of atomic scale light-matter phenomena.

Non-asymptotic Quantum Scattering Theory

Accurate determination of carrier transport properties in quantum materials is critical for designing high-performance electronic devices and on-chip quantum information platforms.  We developed a scalable first-principles informed quantum transport theory to investigate the carrier transport properties of low-dimensional materials. While first-principles calculations effectively determine the atomistic potentials associated with defects and impurities, they are ineffective for direct modeling of carrier transport properties at length scales relevant for device applications. Traditionally, scattering properties are obtained by applying the asymptotic boundary conditions. However, these boundary conditions do not account for the decaying evanescent mode contributions, that are crucial while determining the transport properties of low-dimensional systems. We developed a novel non-asymptotic quantum scattering theory to obtain the transport properties in proximity to the scattering centers, for confined as well as open domain in one-, two- and three-dimensional systems. This theory is further extended to two- and three-dimensional materials by integrating with k.p perturbation theory, with inputs from ab-initio electronic structure calculations. Density functional theory (DFT) calculations are used to obtain the material parameters, thermal contributions, defect and interfacial potential distributions. Hence, we combine the best of three different numerical methods to obtain a versatile multiscale formalism. The fundamental advances in the theory of quantum transport accomplished here will guide us to develop cutting-edge nanodevices and quantum information platforms. This project was conducted in collaboration with Prof. Ashwin Ramasubramaniam at University of Massachusetts, Amherst. 

Tuning Spatial Entanglement for Deterministic Teleportation Protocols

Confined geometries such as semiconductor quantum dots (QDs) are promising candidates for fabricating quantum computing devices. When several quantum dots are in close proximity, spatial correlation between electrons in the system becomes significant, leading to spatial entanglement. The spatial entanglement properties are of great interest to realize all-electronic, solid-state quantum computing devices. To this end, there have been several proposals to define deterministic teleportation protocols for quantum information processing in semiconducting nanodevices. For all such applications, it is important to fabricate devices operating at the resonant spatial entanglement values.

We explored optimal setups to realize deterministic teleportation protocols, by computing the entanglement spectroscopy of few-electron semiconducting quantum dots. We have developed a finite-element based variational method, to compute the few-electron wavefunctions and the corresponding Von Neumann entropy. Resonances in the entanglement values are observed, as a consequence of avoided level crossings in the energy spectrum of the system, with an applied electric field. A phase transition from the unpaired to paired electronic state is also observed due to the electron cluster formation at excited states. Such phase transition can be detected via additional local maxima in the entanglement spectrum. The ability to tune the entanglement values with external parameters opens avenues for engineering quantum bits, and fabricate devices for quantum information processes.