Entangled Photon Pair Generator via Biexciton-Exciton Cascade in Semiconductor Quantum Dots and its Simulation

TL;DR

This work addresses on-demand generation of entangled photon pairs using the biexciton–exciton cascade in semiconductor quantum dots. It provides a physical description, a rigorous mathematical framework (including a four-level QD Hilbert space, a mode-resolved light Hilbert space, a total Hilbert space, and a Lindblad master equation), and a Python-based software simulation that yields a Kraus-channel description of the emitted photons. It analyzes the impact of fine-structure splitting $\Delta$ and biexciton binding $E_b$ across several excitation schemes (e.g., resonant two-photon excitation and detuned phonon-assisted excitation), revealing when high-fidelity entangled photons are achievable and how spectral-temporal-mode structure interacts with polarization entanglement. The results provide practical guidance for incorporating entangled-photon sources into larger quantum-optical experiments and highlight the trade-offs between mode structure and entanglement visibility.

Abstract

The generation of entangled photon pairs is highly useful for many types of quantum technologies. In this work an entangled photon pair generator that utilises the biexciton-exciton cascade in semiconductor quantum dots is described on a physical, mathematical, and software level. The system is implemented and simulated as a self-contained component in a framework for bigger quantum optical experiments. Thus, it is a description to further the holistic understanding of the system for interdisciplinary audiences in a hopefully simple yet sufficient manner. It is described from the condensed matter physics fundamentals, over the most important quantum optical properties, to a mathematical description of the used model, and finally a software description and simulation, making it an executable description of such a system.

Figures (6)

• Figure 1: Different spin configurations for excitonic quasi-particles in the s-shell: a) Excitons $\mathrm{X}$ b) Dark excitons $\mathrm{DX}$ c) Positive trions $\mathrm{X}^+$ d) Negative trions $\mathrm{X}^-$ e) Biexciton $\mathrm{XX}$ The arrows indicate spin direction, while an empty circle depicts a $\mathrm{h}^+$ and a filled circle an $\mathrm{e}^-$. Adapted from ThesisOpticalCharacterisationOfTelecommunication-WavelengthQDs.
• Figure 2: In the idealised biexciton-exciton cascade (left), exciton levels are degenerate, with uniform energy differences between the ground state $\ket{\mathrm{G}}$ and exciton states $\ket{\mathrm{X_{1}}}$ or $\ket{\mathrm{X_{2}}}$, as well as between the biexciton state $\ket{\mathrm{XX}}$ and the exciton states. In contrast, the non-idealised biexciton-exciton cascade (right) features distinct energy differences for each level transition, characterized by unique wavelengths. The degeneracy of the exciton levels is lifted by the Fine Structure Splitting (FSS) $\Delta$. The binding energy between two excitons is denoted $E_\text{b}$, the energy of the ground level is denoted $E_{\mathrm{G}}$, and the energy of the idealised exciton level is denoted $E_{\mathrm{X}}$.
• Figure 3: The mechanism of resonant of the biexciton. The excitation laser is marked in cyan.
• Figure 4: The mechanism of detuned phonon-assisted of the biexciton. The excitation laser is marked in cyan.
• Figure 5: Different excitation scenarios (from left to right: $\pi$-pulse, $5\pi$-pulse, $\pi$-pulse detuned by $\qty{3.18}{\giga\hertz}$, with a without , i.e.$\Delta = \qty{0}{\micro\electronvolt}$).