arXiv subjects

Renuka Rajapakse

Publications and source records attributed to Renuka Rajapakse.

3 recordsLinked to original sources

arXiv2026

Modeling Quantum Billiards with the Finite Element Method: Searching for Quantum Scarring Candidates

An electron in quantum confinement takes on a discrete energy spectrum which is defined based on the solution to the Schrodinger Equation for a given potential. Well defined closed-form energy spectra are known for the particle in a box, circular potential, quarter circle potential, and an equilateral triangle. A closed-form solution for more complex shapes may not be known, but numerical methods can be used to find an approximate solution. In this research, an application of the Finite Element Method (FEM) in Wolfram Mathematica is presented and applied to Quantum Billiards with a variety of geometries. To assess the accuracy of the method, the computed energy states are analyzed in the limit of a polygon with an increasing number of sides, the numerical results are validated against analytical solutions for geometries with known exact forms, and a standard convergence test is conducted. The FEM results closely match analytical solutions for known potentials, demonstrating its high accuracy. For high energy index n, quantum scarring may emerge for certain geometries. The nature of quantum scarring and its presence in the computed models is also investigated qualitatively.

quant-ph↗

arXiv2019

Light propagation in systems involving two-dimensional atomic lattices

We study the optical response of a 2D square lattice of atoms using classical electrodynamics. Due to dipole-dipole interactions, the lattice atoms polarize as if the lattice were an atom with up to three resonance frequencies, with cooperatively shifted resonances and altered transition linewidths. We show that when the distance between two 2D lattices is large enough and Bragg reflections are absent, the lattices interact among themselves as if they radiated a plane wave whose amplitude is in accordance with the radiation from a dipole moment continuously distributed in the lattice plane. We employ these results to study light propagation in stacks of 2D lattices, drawing on simple qualitative pictures of the response of a 2D lattice and light propagation in 1D waveguides. We show that a stack of 2D lattices may emulate regularly spaced atoms in a lossless 1D waveguide, and argue that in a suitable geometry the resonance shifts characteristic of 1D and 2D lattice structures may completely cancel to eliminate density dependent resonance shifts of atoms bound to a 3D lattice. A generalization to the case of anisotropic polarizability, such as in the presence of a magnetic field, reveals light frequencies induced by the magnetic field for which the lattice is either completely transparent, or completely opaque.

physics.atom-ph↗

arXiv2013

Enhanced index of refraction in four-wave mixing media

Refractive index enhancement accompanied by vanishing absorption in a four-level atomic system interacting with two control and two probe fields in a regime of four-wave mixing (FWM) has been predicted and studied in the present work. We analyzed the maximal index enhancement in the four-level FWM system and gave index estimates for a real atomic gas of $^{40}$K, taking into account its multilevel structure and collisional and Doppler broadenings at large atomic densities. We also discussed how vanishing absorption with no nearby amplification can be realized in a two species system, consisting of a four-level FWM and a two-level system, where the latter provides additional absorption for one of the probe fields. We numerically estimated the index change in a system composed of $^{40}$K and $^{39}$K gases.

quant-ph↗