Hyperentanglement of Photons Emitted by a Quantum Dot

A hyperentangled state of light represents a valuable tool capable of reducing the experimental requirements and resource overheads, and it can improve the success rate of quantum information protocols. Here, we report on demonstration of polarization and time-bin hyperentangled photon pairs emitted from a single quantum dot. We achieved this result by applying resonant and coherent excitation on a quantum dot system with marginal fine structure splitting. Our results yield fidelities to the maximally entangled state of 0.81(6) and 0.87(4) in polarization and time bin, respectively.

Figure 1

(a) Energy scheme of the quantum dot. A laser coherently couples the ground $|g⟩$ to the biexciton state $|b⟩$ through two-photon resonant excitation. The excitation process is carried out via a virtual state (dashed line). The quantum dot system decays to the ground state via exciton state $|e⟩$ emitting the biexciton-exciton cascade. Because of vanishing fine structure splitting, the two orthogonally polarized decay paths are indistinguishable and the emitted photons are entangled in polarization. (b) Every excitation sequence consists of two phase-related excitation pulses that are required to generate entanglement in the time bin. The phase between the pulses ${\varphi }_p$ is imposed by an unbalanced Michelson interferometer. The emission probability for each pulse is kept low to minimize the double excitations. (c) The polarization analysis elements ($\lambda /4$ and $\lambda /2$ wave plates and polarizers) were placed before the time-bin analysis. (d) Both the generation and the analysis of the time-bin entanglement require unbalanced Michelson interferometers. The delay of the interferometer should be longer than any coherence in the quantum dot system, in our case 3 ns, which is 7 (14) times longer than the lifetime of the exciton (biexciton) photon. The entanglement is measured in the coincidence signal between a detector detecting biexciton photon ${XX}_{1,2}$ and a detector detecting an exciton one $X_{1,2}$.

Figure 2

(a) Projective measurements in the polarization basis. Here H, V, D and R denote horizontal, vertical, diagonal and right circular polarization, respectively. Each excitation pulse generates photons that after time-bin analysis interferometers can have three arrival times. The overall number of coincidence clicks in each projection we obtain by summing over all three arrival times. The ${\tau }_{xx}$ arrival is determined with respect to the excitation laser. (b) Projections in the time-energy basis. This type of projection gives more complex result consisting of five peaks. If entanglement is present, the middle peak will change its height as a function of the relative phase between the analysis interferometers. The number of coincidence clicks is here determined by summing over the central peak (marked in orange and delimited by the vertical dashed lines). Also here, the ${\tau }_{xx}$ arrival is determined with respect to the excitation laser.

Figure 3

(a) Real and imaginary parts of the reconstructed density matrix for the polarization and time-bin hyperentangled state. The insets upper left and lower right show, respectively, the real and the imaginary parts of the density matrix for the theoretically predicted state. (b) Real and imaginary parts of the reconstructed density matrices for entanglement in polarization (left) and time bin (right). Here $H$ and $V$ stand for the basis states in the polarization entanglement measurement while $E$ and $L$ are the basis states of the time-bin measurement. The theoretically expected states in these measurements were $(1/\sqrt{2})(|H{⟩}_{XX}|H{⟩}_X+|V{⟩}_{XX}|V{⟩}_X$ and $(1/\sqrt{2})(|\text{early}{⟩}_{XX}|\text{early}{⟩}_X+|\text{late}{⟩}_{XX}|\text{late}{⟩}_X$ for polarization and time-bin entanglement, respectively.