Evolution of Entanglement Between Distinguishable Light States

We investigate the evolution of quantum correlations over the lifetime of a multiphoton state. Measurements reveal time-dependent oscillations of the entanglement fidelity for photon pairs created by a single semiconductor quantum dot. The oscillations are attributed to the phase acquired in the intermediate, nondegenerate, exciton-photon state and are consistent with simulations. We conclude that emission of photon pairs by a typical quantum dot with finite polarization splitting is in fact entangled in a time-evolving state, and not classically correlated as previously regarded.

Figure 1

Schematics of entangled photon pair generation in quantum dots. (a) Energy of a quantum dot as a function of time following excitation to the initial biexciton ($XX$) state. The state $\Psi$ is marked for times corresponding to emission of the first and second photons. (b) Biphoton intensity and the phase of the photon pair superposition for dots with exponential radiative decay and zero and finite fine structure splitting $S$ as indicated.

Figure 2

Recovery of entanglement by time discrimination. (a) Schematic of the time-dependent gate(s) applied to postselect photon pairs based on the time interval $\tau$. Fidelity and photon pair intensity are plotted on left and right axes. The first gate begins at time ${\tau }_g$ and has width $w$. (b) Fidelity $f^{+}$ and fraction of photon pairs retained after postselection in time within a gate of width $w$, beginning at $\tau ={\tau }_g=0$. Bands denote measurement errors dominated by Poissonian counting noise. Dashed horizontal line represents the limit for classical behavior. (c) Calculated behavior corresponding to (b). Solid curves and dashed curves represent simple (time-independent) and extended (time-dependent) treatment of the uncorrelated light contribution, respectively. (d) Measured natural linewidth of photon pairs postselected with a 1 and 0.39 ns single gate.

Figure 3

Experimental and calculated fidelity $f^{+}$ with the entangled state ${\Psi }^{+}$ as a function of the time between photons. When $f^{+}$ is minimum, high fidelity with other entangled states is expected. (a) Measured fidelity for a single quantum dot with different fine structure splitting $S$ as indicated. Bands denote measurement errors dominated by Poissonian counting noise. (b) Calculated fidelity corresponding to experimental conditions in (a). Solid lines and dashed lines represent simple (time-independent) and extended (time-dependent) treatment of the uncorrelated light contribution, respectively.