Analyzing Quantum Exceptional Point Invisibility for Experimentally Realizable Triple-Gaussian Potentials

For general quantum systems, certain energies correspond to exceptional points (EPs) where unique, non-Hermitian dynamics occur. For example, within quantum scattering, they correspond to points of invisibility where particles can pass through any barrier unimpeded. We seek to identify experimentally realizable EPs for a quantum particle interacting with various potential barriers to further elucidate the complex theory involved and verify results. We primarily analyze the triple-Gaussian potential, a setup that can be experimentally realized via lasers, and compare it to the triple-rectangular potential that can be analytically solved with the Transfer Matrix Method (TMM). A key finding is that increasing the central Gaussian barrier merges EPs, acting as a quantum filter by selectively permitting certain energies to pass. Additionally, we discover EPs for the triple-delta potential, a theoretical setup consisting of three infinitesimally thin barriers. This project serves as a foundation for further EP analyses, including experimental verification of invisibility effects for ultracold atom experiments. Understanding these EPs has broad applications, including the development of highly sensitive quantum sensors for early earthquake detection, enhanced navigation systems for autonomous vehicles, noninvasive biosensing through “invisible” nanoparticles, and improved quantum error correction crucial for advancing quantum computing technologies.