Towards quantum-dot arrays of entangled photon emitters

To make photonic quantum information a reality1,2, a number of extraordinary challenges need to be overcome. One challenge is to achieve large arrays of reproducible ‘entangled’ photon generators, while maintaining compatibility for integration with optical devices and detectors3–5. Semiconductor quantum dots are potentially ideal for this as they allow photons to be generated on demand6,7 without relying on probabilistic processes8,9. Nevertheless, most quantum-dot systems are limited by their intrinsic lack of symmetry, which allows only a small number (typically 1 out of 100, or worse) of good dots to be achieved per chip. The recent retraction of Mohan et al.10 seemed to question the very possibility of simultaneously achieving site control and high symmetry. Here, we show that with a new family of (111)-grown pyramidal sitecontrolled InGaAs1–dNd quantum dots it is possible to overcome previous hurdles and obtain areas with up to 15% of polarization-entangled photon emitters, with fidelities as high as 0.721+0.043. The idea underlining the principle of entangled photon emission with quantum dots relies on fundamental quantum physics: particle indistinguishability generates a superposition state when two energetically nearly degenerate quantum levels are populated at the same time. In quantum dots, the entanglement resides in the polarization of two photons emitted during cascaded biexciton–exciton recombination11. This leads to one difficulty: when the two excitonic levels are not perfectly degenerate (that is, there is a fine structure splitting, FSS), entanglement in the emission persists, but a phase term is introduced between the two (linearly) polarized photons that is proportional to both energy and time. This results in a relative rotation of the two photon polarizations (not constant in time), making entanglement virtually impossible to detect in a simple manner12. All currently reported quantum dot systems allowing entangled photon emission tend to have large FSS, fundamentally allowing only a few (post-growth selected) quantum dots on a semiconductor wafer to be good sources. Furthermore, to date, no entangled photon emission has been demonstrated in any system where accurate quantum dot position control is possible. It is clear from textbook physics that, to observe level degeneracy, one needs symmetric confinement. As discussed in a number of publications, growth along the [111]B crystallographic direction ideally shows C3V symmetry13–15, which should allow the realization of large arrays of position-controlled entangled photon emitters. In practice, however, a relatively broad range of FSS can be found on existing (111) systems, as for example in our pyramidal quantum dots. An efficient way to overcome asymmetry-related issues comprised exposing a quantum-dot layer to unsymmetrical dimethylhydrazine (U-DMHy, a standard source of nitrogen during metal–organic vapour phase epitaxy, MOVPE) during the quantum-dot formation process16,17. It was consistently observed that the presence of U-DMHy, within a certain range of growth conditions, helped to improve the symmetry of the quantum dots, enabling reproducible fabrication of nanostructures with FSS consistently below our detection limit of 4 meV. The investigated In0.25Ga0.75As1–dNd quantum dots were grown by MOVPE in 7.5-mm-pitch tetrahedral recesses etched in (111)Boriented GaAs. An atomic force microscopy (AFM) image (Fig. 1a) of a cleaved sample in side view shows the epitaxial layer structure (see Methods), with a quantum dot located at the central axis of the recess, within GaAs barriers. Photoluminescence extraction enhancement was achieved by selectively removing (back-etching) the substrate (Fig. 1b). The typical Lorentzian linewidth of the exciton transition was found to be 80+15 meV in our first samples. As we discuss in Supplementary section ‘Linewidth’, this broadening is not a fundamental limitation. Figure 1c presents a typical photoluminescence spectrum of the single quantum dots investigated in this work. The characteristic feature is a biexciton transition (XX) at higher energy (antibinding biexciton) in entangled photon emitters, always accompanied by the presence of a charged exciton (X*) at higher energy. The significance of the spectrum must be stressed, as it acts as a very precise and quick indicator for preselecting quantum dots that emit polarization-entangled photons (see Supplementary section ‘Significance of the excitonic pattern’, for more details). Figure 1e shows an isotropic linear polarization distribution proving quantum dots to be sources of unpolarized light. The dependence of photoluminescence intensity on excitation power is presented in Fig. 1d. This acts as a preliminary indicator of the excitonic transitions. Despite the deviation from the ideal linear and quadratic power dependence, the type of transition was unambiguously confirmed by photon correlation measurements. Average lifetime values are also consistent with the attributed transition types: 1.8+0.6 ns and 0.9+0.15 ns for exciton and biexciton, respectively. Figure 1f illustrates exciton (X) and biexciton (XX) transitions measured/filtered at perpendicular linear polarization angles. No difference can be identified visually between the spectra. In the presence of low symmetry (that is, with FSS), both peaks should be composed of two energetically distinguishable linearly polarized components (typically referred to as H and V). Here, no particular crystallographic direction can be consistently associated with H and V components, as the origins of FSS are related to random effects, and not to a shape elongation along certain directions as in self-assembled quantum dots. In our work, H and V only indicate 0 and 908 angles with respect to the linear polarizer. To obtain the exact value of FSS we apply a well-known FSS measuring procedure that involves taking a set of polarized spectra at smaller polarization angle steps (Fig. 1g)18. If the intermediate exciton level is degenerate, during the recombination cascade the emitted pair has a polarization