Student Projects

SURE+ (Summer Undergraduate Research Experience) Project 2024.

Title: Entanglement of the energy eigenstates of harmonic oscillator systems.

Students: Yousef Salah, Osama Al Mukbel, Amanuel Kiros, Osama Hussein, and Robel Worku.

Summary: We address the problem of understanding the entanglement of the (non-gaussian) energy eigenstates of (disordered) harmonic oscillators system. The PI et al made recently a breakthrough on the problem of analyzing the entanglement of the eigenstates of the oscillators system that correspond to a single excitation. We build on that to investigate eigenstates with higher excitation. In principle, we invoke the explicit formulas of the eigenstates of the oscillators system to study their $\epsilon$-Renyi entanglement entropy $\epsilon\in(0,1)$. Our main goal is to prove an area law for the entanglement of the eigenstates that correspond to two excitations.

Proposal: Here (pdf).

Output: Paper is in preparation.

Thesis Proposed Title: Transport of quantum walks in electric fields 

MSc. Student: Yousef Salah (2025-  )

Abstract: Quantum walks represent a basic subroutine in many quantum algorithms. They play an important role in studying physical phenomenas, and they form important blocks in many quantum technologies. We propose to work on disorder-free quantum walks with localization-like behavior. The emphasis will be on studying the transport of quantum walks in the presence of periodic/quasi-periodic quantum walks. This is a subject of an increasing interest with both experimental and analytical approaches.