Coherence of an Entangled Exciton-Photon State

We study the effect of the exciton fine-structure splitting on the polarization entanglement of photon pairs produced by the biexciton cascade in a quantum dot. Entanglement persists despite separations between the intermediate energy levels of up to $4\mu \mathrm{eV}$. Measurements show that entanglement of the photon pair is robust to the dephasing of the intermediate exciton state responsible for the first-order coherence time of either single photon. We present a theoretical framework incorporating the effects of spin scattering, background light, and dephasing. We distinguish between the first-order coherence time, and a parameter which we measure for the first time and define as the cross-coherence time.

Figure 1

Decay paths in a degenerate (a) and nondegenerate (b) quantum dot. Wave function evolution (c) of the superimposed intermediate states showing 3 dephasing events. The first 2 are single-photon decoherence events and do not affect the relative phase relationship. The 3rd event is a cross-coherence dephasing event which randomizes the relative phase.

Figure 2

(a) Predicted fidelity as a function of FSS for a dot. Ideal behavior is shown in black, and effects of only spin scattering, cross dephasing, or background light are shown by red, orange, and blue. (b) Phase of $z$for different first-order cross coherence as indicated.

Figure 3

Fidelity of the output state as a function of fine-structure splitting, measured for two typical dots $A$ (red discs) and $B$ (blue squares). Solid lines are Lorentzian fits to the data points. Inset: individual correlations for dot $A$ in the rectilinear, diagonal, and circular bases.

Figure 4

(a) Exponential decay of exciton photoluminescence intensity with time for dot $A$. Red line indicates fit used to determine lifetimes. Inset shows exciton lifetime with varying field. (b) Visibility of single-photon interference fringes for dot $A$, used to determine first order coherence time.