Biexciton Cascade Phase-Ring — Polarization Precession Diagram

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 fine structure the intermediate exciton is doubly degenerate and the pair leaves the dot polarization-entangled: |ψ⟩ = (|H⟩₁|H⟩₂ + |V⟩₁|V⟩₂)/√2.

This 2D view drops the 3D flight animation entirely and instead plots the physics directly as three phase-space diagrams:

Polarization phase ring (top) — a live radius-1 vector sweeps through angle φ = δt/ħ while the dot waits in |X⟩; when photon 2 fires, that trial's final angle (mod 2π) is stamped permanently onto the ring as a dot, colour-coded by whether it matched photon 1. Over many trials the ring fills in and its angular spread is a direct, visual histogram of the accumulated dephasing.
Cascade timeline (middle) — each pump event scrolls right→left as a coloured bar spanning its exciton dwell time tX, ending in an accept (bright) or gate-reject (dim) tick.
Gated visibility curve V(δ) (bottom) — the exact analytic curve V(δ) = ⟨cos(δt/ħ)⟩ over t ~ Exp(τ_X) truncated at the gate window Δt, evaluated across the full δ range, with your current δ marked and the running measured correlation overlaid as a point.

ω = δ / ħ
V(δ,τ_X,Δt) = ∫₀^Δt e^(-t/τ_X) cos(ωt) dt  /  ∫₀^Δt e^(-t/τ_X) dt
V(δ,τ_X,∞)  = 1 / (1 + (δτ_X/ħ)²)

In the H/V (energy) basis the two photons stay perfectly correlated for any δ — the ring fills with only matched (green) dots on the diagonal-symmetric pattern. In the D/A (diagonal) basis, only sensitive to coherence between the two decay branches, the ring shows a genuine mix of matched/mismatched dots whose fraction traces V(δ) exactly. The gate window keeps only fast-decaying pairs, which is exactly how real single-photon-source experiments recover high-fidelity entanglement from a dot with nonzero δ.

Basis: H / V

Matched pair (accepted) Mismatched pair (accepted) Rejected (gate window)