Time-bin entangled photons from a quantum dot

Abstract

Long-distance quantum communication is one of the prime goals in the field of quantum information science. With information encoded in the quantum state of photons, existing telecommunication fibre networks can be effectively used as a transport medium. To achieve this goal, a source of robust entangled single-photon pairs is required. Here we report the realization of a source of time-bin entangled photon pairs utilizing the biexciton-exciton cascade in a III/V self-assembled quantum dot. We analyse the generated photon pairs by an inherently phase-stable interferometry technique, facilitating uninterrupted long integration times. We confirm the entanglement by performing quantum state tomography of the emitted photons, which yields a fidelity of 0.69(3) and a concurrence of 0.41(6) for our realization of time-energy entanglement from a single quantum emitter.

FIG. 1. Schematic of time-bin entanglement generation and analysis

(a) Energy level scheme for resonant two-photon excitation of a biexciton (|b〉) from the ground state (|g〉). H-polarized pump laser populates the biexciton state resonantly through a virtual level (dashed grey line). Following the excitation, a V-polarized biexciton (XX_V) exciton (X_V) photon cascade is generated through the intermediate exciton state (|x_V〉). Exciton and biexciton photons are detuned from the excitation laser due to the biexciton binding energy E_b. (b) Quantum dot emission spectrum. (c) Scheme to generate and analyse time-bin entangled photons. Outputs of analysing interferometers, X₁, X₂, XX₁, and XX₂ are fibre coupled to avalanche photon diodes (APD). Here, ϕ_P, ϕ_X, and ϕ_XX are the phases in the pump and analysing interferometers, respectively, and Δt is the time difference between the early and late time bins.

FIG. 2. One bulk interferometer hosts both the pump and analysing interferometers

The interferometer is built with a 50:50 beam splitter cube and two retro-reflectors. The pump laser and the single photon pairs are in separate spatial modes. In and out-coupling of photons in the interferometer is made via single mode fibres. The phase of the biexciton and exciton analysing interferometers are controlled with phase plates, PP_XX and PP_X.

FIG. 3. Time-bin qubit and Bloch sphere representation

(a) Arrival time of the exciton photons recorded with respected to the pump pulse. The grey shaded regions are the 1.28 ns windows taken for extracting the triple coincidences (laser-biexciton-exciton). The side peaks are the projections onto the time basis states |0〉 and peak jection |1〉. The middle peak is the projection onto the energy bases |±X〉 and |±Y〉 for the phase settings ϕ_X = 0, π/2, respectively. Here, subscript A stands for the analysing and P for the pump interferometer. (b) The time-bin qubit states are represented on a Bloch sphere.

FIG. 4. Coincidences between biexciton and exciton outputs of the analysing interferometers

The coincidences are triggered on the laser-pulse arrival. The coincidences were recorded for phase settings: (a) ϕ_XX + ϕ_X = 0 and (b) ϕ_XX + ϕ_X = π. The arrival time is represented as the sum t_XX + t_X, where t_XX(X) is the arrival time of the biexciton (exciton) recombination photon with respect to the laser trigger.

FIG. 5. Reconstructed density matrix plotted as a bar chart

(a) Real part. (b) Imaginary part. The reduced value of 0.44 for the 00 (early-early) and 11 (late-late) populations is a consequence of the double excitations that appear as 01 (early-late) and 10 (late-early) populations. The reduced value of the off-diagonal elements (coherences) of about 0.24, comes from the lack finite coherence of the excitation and emission processes in the quantum dot.