Solid-state ensemble of highly entangled photon sources at rubidium atomic transitions

Abstract

Semiconductor InAs/GaAs quantum dots grown by the Stranski-Krastanov method are among the leading candidates for the deterministic generation of polarization-entangled photon pairs. Despite remarkable progress in the past 20 years, many challenges still remain for this material, such as the extremely low yield, the low degree of entanglement and the large wavelength distribution. Here, we show that with an emerging family of GaAs/AlGaAs quantum dots grown by droplet etching and nanohole infilling, it is possible to obtain a large ensemble of polarization-entangled photon emitters on a wafer without any post-growth tuning. Under pulsed resonant two-photon excitation, all measured quantum dots emit single pairs of entangled photons with ultra-high purity, high degree of entanglement and ultra-narrow wavelength distribution at rubidium transitions. Therefore, this material system is an attractive candidate for the realization of a solid-state quantum repeater-among many other key enabling quantum photonic elements.

Figure 1. Growth and properties of highly homogeneous GaAs/AlGaAs quantum dots.

(a) Processing steps during the growth of GaAs/AlGaAs quantum dots (QDs): Al is deposited under low arsenic pressure, forming droplets on the surface of AlGaAs grown on a GaAs (001) substrate. The concurring dissolution of As through the droplets and diffusion of Al towards the substrate (illustrated by arrows) induces the formation of nanoholes with high symmetry. In a following annealing step the structures crystallize under a re-established As atmosphere. Then, the nanoholes are filled with GaAs and subsequently overgrown by AlGaAs to obtain isolated QDs with three-dimensional carrier confinement. (b) Exciton emission wavelength distribution for two different samples with GaAs infilling amounts of 2 nm (blue) and 2.75 nm (green) for more than 50 dots measured on each sample. Red markers indicate the rubidium D1 and D2 transition lines at 794.9 and 780.2 nm, respectively. Inset: sketch of envisioned interface between entangled photons from a QD and an atomic quantum memory based on the Raman scheme. (c) Occurrence of the exciton fine structure splitting, comparing the GaAs/AlGaAs QDs (blue) with InAs/GaAs QDs (grey). Inset: scheme of the biexciton (XX) decay indicating the spin-related fine structure splitting S between the intermediate exciton states (X).

Figure 2. Resonant excitation of the biexciton state in GaAs/AlGaAs quantum dots.

(a) Quantum dot (QD) emission spectrum for pulsed above-band excitation. The dominant exciton (X) and the biexciton (XX) transition are observed, which are spectrally close to other excitonic species. (b) Resonant excitation of the XX state using a two-photon excitation scheme. This efficient and coherent pumping mechanism results in a pure spectrum featuring primarily the XX–X cascade. The centric residual laser signal is strongly suppressed by using notch filters. (c) Intensity-autocorrelation measurement of the XX and X transition showing the coincidences plotted over the delay time τ. Very pure single-photon emission is confirmed by and . (d) Measurement of the fluorescence lifetime T₁ for the XX and X state. The respective fit functions (solid lines) denote the convolution between an exponential decay and the detector response function. Short radiative lifetimes of T_1,XX=112 ps and T_1,X=134 ps are determined. (e) Fluorescence intensities of the XX and X emissions as a function of the pulse area θ, obtained by excitation laser power-dependent measurements. Rabi oscillations up to 7π are observed for both transitions. An offset is added to the XX values for better visibility, with the dotted lines indicating zero intensity.

Figure 3. Degree of entanglement from a quantum dot with finite fine structure splitting.

(a) Cross-correlation measurements between the biexciton and exciton emission for co- and cross-polarized photons in the rectilinear (H, horizontal; V, vertical), diagonal (D, diagonal; A, antidiagonal) and circular (R, right-handed; L, left-handed) polarization bases. For better visibility an offset in the delay time τ is added in the cross-polarized case. From these measurements on a quantum dot (QD) with a finite fine structure splitting of S=2.3 μeV a fidelity F=0.88±0.03 to the state is deduced. (b,c) Real (b) and imaginary (c) part of the two-photon density matrix as reconstructed from 16 correlation measurements of the same QD by employing the maximum likelihood technique. The fidelity and concurrence extracted from this matrix are F=0.91 and C=0.90, respectively.

Figure 4. Entanglement fidelity of quantum dots with different fine structure splittings.

The data points and traces illustrate the entanglement fidelity (left axis) and the grey histogram bars the occurrence of quantum dots (right axis), both plotted over the fine structure splitting S. All measured GaAs/AlGaAs quantum dots (QDs) from the sample (black circles) emit entangled photons with a fidelity above the classical limit of F=0.5 (dashed line) even for the largest values of S=9.8 μeV (F=0.59). The highest fidelity is measured to be F=0.91 at a nonvanishing S=2.3 μeV. For comparison, fidelity values of InAs/GaAs QDs taken from ref. are plotted in orange, together with a Lorentzian fit. The fidelity uncertainties are obtained using error propagation and Poisson statistics for the coincidence counts. The uncertainties for S are determined by least square regression of polarization-dependent fluorescence measurements. Using a theoretical model, the fidelity F(T₁, S) is plotted for two radiative lifetimes T₁=120 ps (red) and T₁=220 ps (blue), representing the range of all measured values for T₁ in the sample. The applied model implies that both cross-dephasing and spin scattering processes are significantly suppressed in this material system. Together with the fine structure splitting distribution (grey histogram), the fidelity measurements strongly indicate that close to 100% of the QDs in the sample are polarization-entangled photon emitters.