Polarization entanglement and qubit error rate dependence on the exciton-phonon coupling in self-assembled quantum dots

TL;DR

The paper addresses polarization-entangled photon generation from quantum dots embedded in micropillar cavities and the decoherence effects stemming from exciton-phonon coupling and fine-structure splitting. It develops a polaron master-equation framework to nonperturbatively include phonon interactions and computes the two-photon density matrix and concurrence for the biexciton–exciton cascade, enabling analysis of QBER in BBM92-type QKD. A key finding is that phonon-induced one-photon incoherent processes dominate entanglement degradation, with cavity-mediated effects being suppressed at higher phonon-bath temperatures due to renormalization of the coupling and Rabi frequency. The work provides a theoretical toolkit for designing QD-based polarization-entangled photon sources and offers guidance on operating conditions and temporal filtering to mitigate decoherence in quantum communication protocols.

Abstract

Polarization-entangled photons are key resources for a wide range of protocols in quantum computation and quantum key distribution. Achieving a near-unity degree of polarization entanglement is essential for minimizing qubit error rates in secure key distribution. In this work, we theoretically investigate polarization-entangled photon pairs generated via a quantum-dot radiative cascade embedded in a micropillar cavity. To account for the unavoidable exciton-phonon interactions in the quantum dot-cavity system, we develop a polaron master-equation framework and examine its impact on the degree of entanglement and the resulting qubit error rate. We derive analytical expressions for phonon-induced incoherent scattering rates and show that one-photon incoherent processes dominate, leading to a substantial reduction of entanglement. We further demonstrate that at elevated phonon-bath temperatures, cavity-mediated effects, such as cross-coupling between exciton states, ac Stark shifts, and multiphoton emission, are significantly suppressed due to phonon-induced renormalization of the cavity coupling strength and the Rabi frequency. Finally, we analyze a BBM92 quantum key distribution protocol and study the evolution of the qubit error rate as a function of the phonon-bath temperature.

Figures (8)

• Figure 1: (color online) Schematic diagram of various phonon-mediated incoherent excitation and de-excitation. (a) and (b) phonon-induced one-photon incoherent excitation of H-polarized exciton and biexciton states, (c) and (d) phonon-induced one-photon de-excitation of $H$ polarized exciton and biexciton states, (e) phonon-assisted two-photon incoherent excitation of the biexciton state, and (f) phonon-induced cross-coupling between the $H$ and $V$ polarized exciton states.
• Figure 2: (color online) Phonon-mediated scattering rates with $\delta$ = 20 $\mu$eV and $g$ = 70 $\mu eV$, (a) $\Gamma^{+}$ and $\Gamma^{-}$ at $T = 4 \, \mathrm{K}$ and $T = 20 \, \mathrm{K}$.(b) $\langle \Gamma^{+}_{\Omega} \rangle$ and $\langle \Gamma^{-}_{\Omega} \rangle$ at $T = 4 \, \mathrm{K}$ and $T = 20 \, \mathrm{K}$. $\langle \Gamma^{\pm}_\Omega \rangle$ are the time averaged decay rates over one pulse width, given as, $\langle \Gamma^{\pm}_\Omega \rangle$$=$$\int_{-\infty}^{\infty} \Gamma^{\pm}_\Omega$$dt /2t_p$.
• Figure 3: (color online) Different Phonon-mediated two-photon scattering rates with $\delta$ = 20 $\mu$eV and $g$ = 70 $\mu eV$, (a) $\Gamma^{TP}$ at $T = 4 \, \mathrm{K}$ and $T = 20 \, \mathrm{K}$.(b) $\langle \Gamma^{TP}_{\Omega} \rangle$ at $T = 4 \, \mathrm{K}$ and $T = 20 \, \mathrm{K}$. $\langle \Gamma^{TP}_\Omega \rangle$ is the time-averaged decay rate over one pulse width, given as, $\langle \Gamma^{TP}_\Omega \rangle$$=$$\int_{-\infty}^{\infty} \Gamma^{TP}_\Omega$$dt /2t_p$.
• Figure 4: (color online) Concurrence as a function of $g$ for different temperatures with (a) ${T_p}^{\prime} = 200$ ps and $\delta = 0$ (b) ${T_p}^{\prime} = 50$ ps and $\delta = 0$, (c) ${T_p}^{\prime}= 200$ ps, for $\delta =$ 0, 20 $\mu$eV (d) ${T_p}^{\prime} = 50$ ps, for $\delta =$ 0, 20 $\mu$eV.
• Figure 5: (color online) Two-photon density matrix of polarization-entangled state at $g$ = 70 $\mu$eV for (a) $T = 4 \, \mathrm{K}$, (b) $T = 8 \, \mathrm{K}$ (c) $T = 16 \, \mathrm{K}$ and (d) $T = 20 \, \mathrm{K}$. As the temperature rises, a dip in the off-diagonal elements is visible due to reduced coherence between the states.