Entanglement Swapping with Photons Generated on Demand by a Quantum Dot

Photonic entanglement swapping, the procedure of entangling photons without any direct interaction, is a fundamental test of quantum mechanics and an essential resource to the realization of quantum networks. Probabilistic sources of nonclassical light were used for seminal demonstration of entanglement swapping, but applications in quantum technologies demand push-button operation requiring single quantum emitters. This, however, turned out to be an extraordinary challenge due to the stringent prerequisites on the efficiency and purity of the generation of entangled states. Here we show a proof-of-concept demonstration of all-photonic entanglement swapping with pairs of polarization-entangled photons generated on demand by a GaAs quantum dot without spectral and temporal filtering. Moreover, we develop a theoretical model that quantitatively reproduces the experimental data and provides insights on the critical figures of merit for the performance of the swapping operation. Our theoretical analysis also indicates how to improve state-of-the-art entangled-photon sources to meet the requirements needed for implementation of quantum dots in long-distance quantum communication protocols.

Figure 1

Schematic illustration of the setup used for the entanglement swapping experiment. $XX$ and $X$ photons are separated by volume Bragg gratings (VBG). $X$ photons are sent into an unbalanced Mach-Zehnder interferometer with an internal delay $\mathrm{\Delta }\tau$ matching the time distance between the early-($E$) and late-($L$) coming entangled pairs. The latter BS of the interferometer performs a partial Bell state measurement (BSM). $XX$ photons are sent to a non-polarizing beam splitter (BS) followed by two sets of wave plate (WP), linear polarizer (P) and single-photon counting avalanche photodiode (APD) at the two output ports. In the inset, a sketch representing the ideal entanglement swapping process is shown.

Figure 2

(a) Fourfold coincidences histograms as a function of the delays between the BSM and the $XX$ detection events on the two tomography channels, recorded for cross- (left) and co-polarized (right) linear polarization. Peaks along the main diagonal would correspond to $XX$ photons excited from the same laser pulse and are therefore absent due to the single photon purity of the QD. The two peaks at the center belong to events synchronized with a BSM and differ only on whether $X{X}_E$ or $X{X}_L$ is detected on channel $A$. Bunching for HV and antibunching for HH are observed, as expected for the $|{\mathrm{\Psi }}^{-}⟩$ state. (b) Cross-correlation histograms between $XX$ photons in linear, diagonal, and circular polarization bases. These data are reduced from the fourfold coincidences histograms as presented in panel (a) by binning over the time tags on channel $B$ in the time window included between -1 and 2.8 ns.

Figure 3

(a) Real and imaginary part of the two-photon density matrix reconstructed from measurement that probes the polarization state of the $XX$ photons selected in conjunction with a BSM on their entangled partners. The matrix refers to the QD with FSS equal to $0.6\mu \mathrm{eV}$ and HOM visibility of 0.63. (b) Contour plot showing the expected fidelity to the $|{\mathrm{\Psi }}^{-}⟩$ state as a function of HOM visibility and the ratio between FSS and radiative lifetime. The ellipses refer to the QDs considered in this work, are labeled with the experimental values of fidelity to $|{\mathrm{\Psi }}^{-}⟩$, and their semi-axes are given by the uncertainties on FSS and visibility. The star indicates the expected value of fidelity to $|{\mathrm{\Psi }}^{-}⟩$ for a QD combining broadband Purcell enhancement [13, 14] and strain tuning of the FSS [11].