Quantum Dot Biexciton Cascade — Entangled Photon Source

Cascade Source

Fine Structure & Timing

Fine-structure splitting δ 2.0 μeV

Exciton lifetime τ_X 300 ps

Post-selection gate window Δt 1000 ps

Measurement Basis (photon 1 & 2)

Live Statistics

Pairs fired

Gate-accepted

Measured correlation

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Theory (gated)

1.000

How it works

A quantum dot pumped to its biexciton state |XX⟩ decays in two steps: XX→X emits photon 1, then X→0 emits photon 2. Without electron–hole exchange interaction the intermediate exciton is doubly degenerate and the pair leaves the dot in the polarization-entangled state |ψ⟩ = (|H⟩₁|H⟩₂ + |V⟩₁|V⟩₂)/√2.

Real dots have a small fine-structure splitting δ between the H- and V-polarized bright exciton eigenstates. While the system waits in |X⟩ for a time t (exponentially distributed with mean τ_X), the state precesses:

|ψ(t)⟩ = (|H⟩₁|H⟩₂ + e^(iδt/ħ)|V⟩₁|V⟩₂) / √2
ω = δ / ħ            (precession angular frequency)
⟨cos ωt⟩ over Exp(τ_X) = 1 / (1 + (δτ_X/ħ)²)   (ungated visibility)

Measured in the H/V (energy) basis the two photons stay perfectly correlated for any δ — that's exactly the "which-path" information δ imprints (photon 1's energy already reveals which branch was taken). Measured in the D/A (diagonal) basis, which is only sensitive to the coherence between the two branches, the correlation visibility decays with δ and with how long the dot lingered in |X⟩ before decaying.

Post-selection gate window Δt keeps only pairs whose exciton dwell time was shorter than Δt, before enough phase has accumulated to wash out the coherence — exactly the trick real single-photon-source experiments use (fast timing electronics) to recover high-fidelity entangled pairs even from dots with nonzero δ.

Real-world relevance: this XX–X radiative cascade in an InAs/GaAs quantum dot is a leading solid-state source of both on-demand single photons and polarization-entangled photon pairs for quantum key distribution and photonic quantum computing.

Basis: H / V

Photon 1 (XX→X) Photon 2 (X→0), matched Rejected (gate/mismatch)

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