Ultimate photon entanglement in biexciton cascade

TL;DR

The paper addresses the intrinsic limitation on polarization-entangled photon generation in semiconductor quantum dots caused by nuclear spin fluctuations. It develops a theory for symmetric colloidal nanocrystals where a triplet exciton mediates the biexciton cascade, deriving analytical expressions for the two-photon concurrence as a function of the hyperfine strength via the dimensionless product $δτ$. A key result shows that, by tuning shape anisotropy and exchange interactions, the detrimental hyperfine effect can be suppressed, achieving near-unity entanglement, with the ideal point $Δ=2η$ yielding $C=1$ independent of $δτ$ in the model. The study provides quantitative estimates showing ultimate limits around $C \approx 0.9999$ for electrons (and about $0.9$ for heavy-hole excitons) and discusses practical routes (core-shell engineering, microcavities) to realize high-fidelity, deterministic entangled photon sources. This work thus promises three orders of magnitude improvement in entangled-photon fidelity for QD-based sources and outlines a route to the ultimate limits in semiconductor systems.

Abstract

The polarization entanglement of photons emitted by semiconductor quantum dots is unavoidably limited by the spin fluctuations of the host lattice nuclei. To overcome this limitation, we develop a theory of entangled photon pair generation by a symmetric colloidal quantum dot mediated by a triplet exciton. We derive general analytical expressions for the concurrence as a function of the hyperfine interaction strength and show that it is intrinsically higher than that in conventional doublet-exciton systems such as self-assembled quantum dots. The concurrence sensitively depends on the shape anisotropy and the strain applied to a nanocrystal. In particular, we uncover a possibility of completely suppressing the detrimental effect of the hyperfine interaction due to the interplay between nanocrystal anisotropy and electron-hole exchange interaction. We argue that this represents the ultimate limit for the generation of entangled photon pairs by semiconductor quantum dots.

Figures (3)

• Figure 1: Spherical colloidal nanocrystal of cubic semiconductor emits two entangled $\sigma^\pm$ photons in biexciton radiative cascade. The bright exciton state is threefold degenerate with respect to the total angular momentum projection $F_z=0,\pm1$. The dark exciton states have the angular momentum $F=2$ and are fivefold degenerate.
• Figure 2: The concurrence of the two photons emitted by a biexciton cascade in a nanocrystal as a function of the product of hyperfine interaction strength $\delta$ and exciton lifetime $\tau$. Black solid line is calculated for a spherical nanocrystal after Eq. \ref{['eq:C_spherical']}, black dotted line shows its asymptotic for small $\delta\tau$, Eq. \ref{['eq:C_small']}. Red dashed line is the concurrence for an oblate nanocrystal with $\Delta=2\eta$ calculated after Eq. \ref{['eq:C_oblate']}, which is exactly unity. Blue dotted line corresponds to the photon entanglement mediated by the lower exciton state in the case of a large splitting of light and heavy hole states, $\Delta\gg\eta$ in Eq. \ref{['eq:C_oblate']}.
• Figure 3: (a) Fine structure of bright exciton states in a slightly oblate nanocrystal with the optical transitions from the biexciton state and to the ground state. (b) Concurrence of a photon pair emitted in the biexciton cascade mediated by the upper and lower pairs of exciton states as a function of the nanocrystal anisotropy calculated after Eq. \ref{['eq:C_oblate']} for $\delta\tau_0=0.5$.