Entanglement robustness to excitonic spin precession in a quantum dot

A semiconductor quantum dot (QD) is an attractive resource to generate polarization-entangled photon pairs. We study the excitonic spin precession (flip-flop) in a family of QDs with different excitonic fine-structure splitting (FSS) and its impact on the entanglement of photons generated from the excitonic-biexcitonic radiative cascade. Our results reveal that coherent processes leave the time postselected entanglement of QDs with finite FSS unaffected while changing the eigenstates of the system. The flip-flop's precession is observed via quantum tomography through anomalous oscillations of the coincidences in the rectilinear basis. A theoretical model is constructed with the inclusion of an excitonic flip-flop rate and is compared with a two-photon quantum tomography measurement on a QD exhibiting the spin flip-flop mechanism. A generalization of the theoretical model allows estimating the degree of entanglement as a function of the FSS and the spin precession rate. For a finite temporal resolution, the negativity is found to be oscillating with respect to both the FSS and the spin precession rate. This oscillatory behavior disappears for perfect temporal resolution and maximal entanglement is retrieved despite the flip-flop process.

Figure 1

Typical $\mu \mathrm{PL}$ emission spectra of the studied quantum dots (a) QD1 with a FSS of ${\delta }_{\text{FSS}}=(12.7\pm 0.2)\mu \mathrm{eV}$ and (b) QD2 with a FSS of ${\delta }_{\text{FSS}}=(47.6\pm 0.6)\mu \mathrm{eV}$. Polarization-resolved measurements of the FSS are displayed in the inset of each graph. Polarization-resolved cross-correlation measurement of (c) QD1 and (d) QD2 in the $HH$ basis (red) and in the $HV$ basis (blue) obtained with SPCMs with 550 ps temporal resolution. The inset shows the same measurement using SNSPDs with a temporal resolution of 100 ps for comparison.

Figure 2

Measured correlation values $g_{HV}$ for several QDs as a function of their FSS. The two QDs discussed in the text are indicated as QD1 (${\delta }_{\text{FSS}}=12.7\pm 0.2\mu \mathrm{eV}$) and QD2 (${\delta }_{\text{FSS}}=47.6\pm 0.6\mu \mathrm{eV}$). The colored curves are extracted from the theoretical model for different spin precession rates.

Figure 3

(a) Sixteen polarization-resolved measurements representing the full tomography of QD1. The red curves result from the fitting model taking the spin precession processes in the QD into account and convoluted to the setup resolution. This fitting is used to calibrate the model and to extrapolate it for the other QDs studied here. (b) Extrapolated negativity as a function of the delay for a perfect temporal resolution (blue) and a 100 ps resolution (red).

Figure 4

Negativity as a function of the spin precession rate and the FSS for a resolution of (a) 50 ps and of (b) 100 ps.