Entanglement transfer from electron spins to photons in spin light-emitting diodes containing quantum dots

We show that electron recombination using positively charged excitons in single quantum dots provides an efficient method to transfer entanglement from electron spins onto photon polarizations. We propose a scheme for the production of entangled four-photon states of GHZ type. From the GHZ state, two fully entangled photons can be obtained by a measurement of two photons in the linear polarization basis, even for quantum dots with observable fine structure splitting for neutral excitons and significant exciton spin decoherence. Because of the interplay of quantum mechanical selection rules and interference, maximally entangled electron pairs are converted into maximally entangled photon pairs with unity fidelity for a continuous set of observation directions. We describe the dynamics of the conversion process using a master-equation approach and show that the implementation of our scheme is feasible with current experimental techniques.

Figure 1

(Color online) Schematic setup for the transfer of entanglement between electrons and photons. An electron entangler (gray box) injects a pair of spin-entangled electrons into two current leads. The electrons recombine individually in one quantum dot located in the left (L) and one in the right (R) spin LED and give rise to the emission of two photons.

Figure 2

(Color online) (a) Schematic setup to obtain bipartite entanglement of photons 1 and 2 by measuring the photons 3 and 4 of the GHZ state in bases of linear polarizations $H,V$ and $H^{\prime },V^{\prime }$, respectively (see the text). In (b) and (c), we show the von Neumann entropy (b) $E=E_{\min }$ and (c) $E=E_{\max }$ as a function of the polar angles ${\theta }_1$ and ${\theta }_2$ for photon emission. $E$ oscillates between (b) and (c) as a function of ${\varphi }_1$ and ${\varphi }_2$, as explained in the text. The photon-polarization entanglement is maximal for ${\theta }_1={\theta }_2=0$, whereas for ${\theta }_i=\pi ∕2$ entanglement is absent. In (c), $E_{\max }=1$ for the continuous set of directions ${\theta }_1={\theta }_2∊[0,\pi ∕2)$.