Computational Investigation of Generation of Entangled Photon Pair from Biexcitonic-to-Exciton Cascade Decay in Semiconductor Nanoparticles

This computational work aims to investigate the generation of entangled photon pairs in quantum dots. Entangled photon pairs (EPP) are important in quantum optics and are essential for quantum information, quantum teleportation, quantum key distribution, and controlled logic operations. Semiconductor nanoparticles such as quantum dot (QD) are especially well suited for EPP generation and have been proven to have high-entanglement fidelity, extraction efficiency, and photon indistinguishability.<br/>Accurate description of biexcitonic and exciton states are crucial for accurate prediction of generation of EPPs. In this work, we have used the frequency-dependent geminal-screened electron-hole interaction kernel method (FD-GSIK) for treating the excitonic and biexcitonic states. The FD-GSIK is a first-principles, explicitly-correlated, real-space method that avoids using unoccupied orbitals to construct the electron-hole interaction kernel by performing a complete infinite-order diagrammatic summation of particle-hole excitations and deriving a renormalized R12 real-space electron-hole correlator operator. The FD-GSIK method also bypasses the computationally expensive AO-to-MO integral transformation step by computing all integrals directly in the real-space numerically using Monte Carlo integration. The frequency-dependent component of the FD-GSIK method implements the necessary quasiparticle screening needed for describing biexcitonic states.<br/>In this work, the combination of dressed-atom approach and FD-GISK method was applied to investigate exciton binding energies and biexciton binding energies for large quantum dots (Pb₁₄₀S₁₄₀, Pb₁₄₀Se₁₄₀, Cd₁₄₄Se₁₄₄). Chemical insights from biexciton binding energies, exciton binding energies, fine-structure splitting, oscillator strengths, degree of entanglement, and time-dependent electron-hole recombination probability for these quantum dots will be presented. The results from these calculations demonstrate the efficacy of the FD-GSIK method for capturing electron-hole correlation and treating 2-electron 2-hole excitation in large clusters and nanoparticles. Future and ongoing work in this direction including enhancing photon-entanglement characteristics by optimizing surface ligands and adding core/shell heterojunctions will be discussed.