Highly pure single photon emission from spectrally uniform surface-curvature directed mesa top single quantum dot ordered array

Realizing spatially ordered single photon sources that can be readily integrated with light manipulating elements (LMEs) in a scalable architecture has been a major goal towards realizing on-chip integrated quantum optical circuits^1–3 (QOCs) for applications in quantum communication and quantum information processing (QIP). A significant step towards this goal was recently taken with the demonstration of a 5 × 8 array of a new class of semiconductor single quantum dots that form on the top of laterally confined mesas with an unprecedented control on the shape and size.^4–6 These mesa-top single quantum dots (MTSQDs) are formed by site-selective size-reducing epitaxial growth on nanomesas fabricated with specifically chosen edge orientations that induce directed-migration of atoms symmetrically from the sidewalls to the mesa top [Fig. 1(a)] during growth, thus ensuring spatially selective growth on the mesa top^4–6 [Fig. 1(b)]. The approach is thus dubbed substrate-encoded size-reducing epitaxy (SESRE).^7–9 The synthesized GaAs(001)/In_0.5Ga_0.5As/GaAs MTSQDs [Fig. 1(b)] being reported here were shown to be efficient single photon emitters at 10 K with g⁽²⁾(0) ∼ 0.15 and maintain reasonable single photon emission [g⁽²⁾(0) ∼ 0.3] up to liquid nitrogen temperature.^5,6 The emission wavelength from every MTSQD in the 5 × 8 array is shown in Fig. 1(c). These MTSQDs are formed with considerable control on the size and shape and thus, as-grown, exhibit highly uniform photoluminescence (PL) emission with a standard deviation of ∼8 nm, much better than the commonly studied lattice mismatch strain-driven spontaneously formed 3D island quantum dots dubbed self-assembled quantum dots (SAQDs).^5,6 The above noted PL and the encouraging g⁽²⁾(τ) behavior were, however, limited by the instrument resolution of ∼300 μeV. The true nature and the potential of this new class of epitaxial single QDs (SQDs) were thus not revealed.⁵ Strikingly, these studies revealed the presence of pairs of as-grown MTSQDs [marked by like-color circles in Fig. 1(c)] with emission within ∼300 μeV, a feature that makes this class of SQD arrays a particularly attractive and prime candidate for exploring interference and entanglement between photons originating from different but known MTSQDs through on-chip integration with light manipulating elements (cavity, waveguide, etc.).^5,10,11 The aim of this letter thus is to report on the true nature of these MTSQDs as revealed by PL, polarization-resolved PL, and g⁽²⁾(τ) studies carried out with a high spectral resolution of ∼15 μeV.

The high resolution studies reported here reveal ∼99% purity of single photon emission with a measured g⁽²⁾(0) of <0.02. These MTSQDs are found to have neutral exciton emission with linewidths of ∼10 μeV. Polarization-resolved PL studies reveal the symmetry of the QD confining potential to be <C_2v. A fine structure splitting (FSS) <10 μeV is found to accompany the loss of symmetry. The highly pure single photon emission and low FSS highlight the suitability of such QDs as on-chip single photon source arrays that are readily integrable with light manipulating elements (LMEs) (cavity, waveguide, etc.) to realize scalable on-chip quantum optical networks aimed at QIP.

The high resolution PL and polarization-resolved PL data were collected using a μ-PL system that employs a high-resolution (15 μeV) spectrometer (Horiba 1250M) with a 1200 gr/mm grating and a cryogen-free cryostat (Janis CCS-XG-M-204N). A pulsed excitation beam (640 nm 80 MHz diode laser) is focused on a single MTSQD of the array with an excitation spot of a diameter of 1.25 μm by a 40× NA 0.65 objective. The emitted photons are collected by the same objective, coupled to a single mode optical fiber, spectrally filtered by the spectrometer and detected by a silicon APD (Excelitas SPCM-NIR). Figure 2(a) shows the time- and polarization-integrated PL data from a typical MTSQD's exciton emission collected with a spectral resolution of 15 μeV with a pulsed excitation power of 30 nW (2.44 W/cm², 50% of saturation power for peak P₁) at 9.4 K. The constant background in Fig. 2(a) is contributed by the APD dark counts. The two peaks P₁ (919.108 nm) and P₂ (918.891 nm) of unequal intensity separated by 320 μeV are part of the neutral exciton decay manifold as supported by the observed near linear dependence of the emission intensity (I) on the excitation power (P) for both peaks, I ∼ P^1.14 for peak P₁ and I ∼ P^0.8 for peak P₂. This finding is consistent with the systematic study (albeit at the coarser resolution of ∼300 μeV) of the MTSQD neutral exciton emission reported previously in Ref. 5. The linewidths (Full width at half maximum, FWHM) of peaks P₁ and P₂ obtained through fitting the Lorentzian shape [red lines in Fig. 2(a)] are found to be ∼21 μeV and ∼34 μeV, respectively. To reveal the intrinsic linewidths of the peaks, we deconvoluted the PL spectrum following a convex optimization method with the least squares fitting.¹² A Lorentzian with a FWHM of 15 μeV is used to represent the independently calibrated instrument response function. The deconvoluted PL data reveal a linewidth of 10 μeV for peak P₁ and 24 μeV for peak P₂. Given their separation of ∼300 μeV and a measurement temperature of 9.4 K, the emission at peak P₂ is enabled by the presence of holes in the first excited hole state.

To shed light on the nature of peaks P₁ and P₂, we recall that a tetrahedrally bonded III–V semiconductor QD with a truncated pyramidal shape [same as the MTSQD shown in Fig. 1(b)] and correspondingly with a confinement potential symmetry of C_2v or higher is traditionally analyzed^13,14 in terms of ground level excitons constructed from J = 3/2, J_z = ±3/2 hole states and an electron state with S = 1/2, S_z = ±1/2, dubbed heavy hole (HH) excitons. The four excitons thus formed contain one pair with angular momentum projection |M| = |J_z − S_z| = 1 that can couple to the light field and are thus dubbed bright excitons and one pair with |M| = 2 that cannot couple to the light field and are dubbed dark excitons. The four excitons formed involving the J = 3/2, J_z = ±1/2 hole states [dubbed light hole (LH) excitons] constitute, in this description, a separate manifold. This clean separation is however not necessarily always a good approximation. Reference 15 demonstrates this through an atomic pseudopotential based analysis of the relative role of various contributions (pure confinement effect, local interface, QD shape, lattice strain, piezoelectric field, and alloy disorder) that lower the QD confinement potential symmetry and control the true wavefunctions of the hole states by projecting them onto the above recalled basis set of the traditional heavy and light hole description. The findings demonstrate the severe breakdown of the description in terms of HH and LH manifolds depending upon the nature of the confinement potential symmetries. Given the presence of lattice strain, piezoelectric fields, and alloy disorder, the MTSQDs are likely defined by a confinement potential of symmetry <C_2V for which the hole states cannot be described as purely HH or LH but at best as states with the mixed HH and LH character.^13–15 As discussed next, polarization-resolved PL studies confirm the confinement potential symmetry to be <C_2v.

Figure 2(b) shows the polarization-resolved PL peak intensity data (after APD background count subtraction) from peak P₁ as a function of the polarizer angle ϕ (defined with respect to the crystallographic [−1 1 0] direction) in the x-y plane perpendicular to the growth direction [001]. The QD is excited using the same conditions as for the PL data in Fig. 2(a) at 9.4 K. A set of PL spectra were recorded using a linear polarizer with an extinction ratio of 10⁴:1 inserted into the microscope whose angle is adjusted in steps of 10°. Aligning ϕ = 0° to the crystallographic [−1 1 0] orientation (with the aid of markers created on the sample) enables direct linkage of the PL to the QD shape as shown in Fig. 2(c). The measured polarization dependent PL data were corrected against the polarization dependent throughput of the spectrometer calibrated using an unpolarized thermal lamp. The measured polar pattern¹⁶ is seen to be elliptical with an ellipticity of ∼1.65 and the major axis along ϕ ∼100°, i.e. 10° with respect to the crystallographic [110] direction, the direction along the shorter diagonal of the QD rhombus base [Fig. 2(c)]. The observed ellipticity is a clear indication that the QD has confinement potential symmetry <C_2v^14,15 consistent with the QD shape that is a truncated pyramid with a rhombus base with edges along ⟨1 −3 0⟩ directions [Fig. 2(c)] and the presence of disorder owing to the fluctuating indium concentration in the GaAs/In_0.5Ga_0.5As/GaAs QD region.

In the absence of a first principle based theoretical analysis of the nature of the hole states in the MTSQDs, we seek some insight into the degree of the conventional description of HH and LH mixing in the observed ground state exciton decay (peak P₁). As noted above, the ground hole state in the tetrahedrally bonded III–V semiconductor based quantum dots of confinement potential symmetry < C_2v has mixed J_z = ±3/2 (HH) and J_z = ±1/2 (LH) character.¹⁴ In such a case, the transition dipole moments of the two allowed transitions can be denoted as $⟨uE+−er→uH+⟩+⟨uE−−er→uH−⟩$ and $⟨uE+−er→uH+⟩−⟨uE−−er→uH−⟩$⁠, where $|uE±⟩$ and $|uH±⟩$ represent the Bloch parts of the wavefunction of the electron and the mixed hole states, respectively. The mixed HH and LH character of the QD hole states involved in the transitions with the electron states $|uE±⟩=|12,±12⟩$ is now represented as follows:¹⁴ $uH±⟩=1−β2−γ232,±32⟩+βe±2iθ32,∓12⟩±γe±2iφ32,±12⟩$⁠. Here, $|uH±>$ is described using the Luttinger-Kohn basis with β and γ representing the amplitude and θ and φ the phase of mixing of the $|32,±32⟩$ hole state with the $|32,±12⟩$ and $|32,∓12⟩$ hole states, respectively. One may further show that the photons from such two states approximated as point transition-dipoles with the above-mentioned dipole moments will produce polar patterns with ellipticity $e=1−23β2−γ2+2β1−β231−23β2−γ2−2β1−β23$ when the dielectric effect of the surrounding medium and the effect of the measurement geometry are neglected. The ellipticity greater than one observed in Fig. 2(b) thus qualitatively indicates that the MTSQD has a nonzero β and has a confinement potential of less than C_2v symmetry, unlike QDs with C_2v which have a circular polar pattern.¹⁴ To estimate the degree of intrinsic mixing of the HH and LH, we calculate the integrated photon flux from peak P₁ within the collection cone of the objective lens as a function of polarization. The calculation employs a finite element method and assumes that the two transitions emit as point dipoles (with transition dipole moments as discussed above) embedded in GaAs nanomesa of size and shape obtained from SEM images [not shown but similar to Fig. 1(a)]. The parameters β, γ, θ, and φ representing the mixing are used as fitting parameters to compare the calculated photon flux from the two transitions with the measured data shown in Fig. 2(b). We find that the measured data can be explained by the combined photon flux [the black curve in Fig. 2(b) of the two transitions] one polarized primarily along [110] (blue curve in Fig. 2(b) representing the dipole element $⟨uE+−er→uH+⟩+⟨uE−−er→uH−⟩$⁠) and the other primarily along [1–10] [red curve in Fig. 2(b) representing the dipole element $⟨uE+−er→uH+⟩−⟨uE−−er→uH−⟩$] directions but with different amplitudes due to the mixing of the HH-LH manifold represented by |β| = 0.25 ± 0.02. Limited by the measurement geometry in the x-y plane, the parameter γ cannot be obtained from the data and the fitting.

The polarization dependent PL coupled with the nearly linear power dependence of the integrated PL noted above, we thus conclude, indicates that peak P₁ with an intrinsic linewidth of ∼10 μeV is from the neutral exciton comprising two non-degenerate closely spaced states, their spacing dubbed fine structure splitting (FSS). We note that the change in the measured energy of peak P₁ as a function of the polarizer angle is within the error of spectrometer wavelength repeatability which prevents deducing the FSS beyond our resolution limit. Their linewidths and splitting (the FSS) are thus inferred to be less than 10 μeV. Such FSS is comparable to the best reported for other types of QDs such as the QDs in ordered recesses,¹⁷ the typical 3D island based SAQDs,^1–3,18 and the well explored nanowire QDs.^19,20 Such a low FSS in the MTSQDs in spatially regular arrays is a highly encouraging figure of merit for their use in QOCs. Thus, we next present the measurements of the two photon emission correlation function for photons emitted from peak P₁ to examine the intrinsic purity of the single photon emission from the MTSQD.

A standard Hanbury Brown–Twiss (HBT) instrumentation is employed for measurements of two photon coincidence counts. The emitted photons from the MTSQD bright exciton [peak P₁, Fig. 2(a)], collected at 9.4 K under the same excitation as described before using an acceptance window of ∼70 μeV [indicated by the blue shade in Fig. 2(a)], are directed towards the HBT setup with its two detectors for measuring coincident counts. Figure 3 shows the measured histogram of the coincidence counts (black dots) as a function of τ, the time difference between the detection events at the two APD detectors. The background count contributed by the dark counts from the two Si APDs has been subtracted in the plot. The g⁽²⁾(0) is obtained from calculating the ratio of the τ = 0 peak area to the average of the other peaks. The g⁽²⁾(0) is found to be almost zero with a upper bound of 0.02, indicating that the single photon emission purity, $1−g20$⁠, of MTSQDs is around 99%. The ultra-low g⁽²⁾(0) is also confirmed from the fitting of the measured data shown as red lines in Fig. 3 with the near zero peak at τ = 0. The revealed highly pure (around 99%) single photon emission from MTSQDs is comparable to other SQD based best SPSs^17,19–25 reported in the literature, such as the QDs in recesses,^17,21 the SAQDs,²³ and the nanowire SQDs.^19,20,24,25 As reported previously,^5,6 these MTSDQ array SQDs can provide single photon emission even at 77 K with a single photon emission purity of ∼80% [g⁽²⁾(0) ∼ 0.3]. The intrinsic purity and the robustness of single photon emission at elevated temperature from such spatially ordered and as-grown highly spectrally uniform SQDs suggest that MTSQDs are highly promising candidates for single photon sources for on-chip integration with LMEs such as resonant cavity and waveguide for realizing on-chip QOCs.

In summary, we have demonstrated that the spectrally uniform InGaAs MTSQD array containing as-grown pairs of QDs emitting within 300 μeV synthesized using the SESRE approach has sharp exciton emission with an intrinsic linewidth of 10 μeV and FSS < 10 μeV, a figure of great importance for QD potential use in QOCs. The ordered uniform MTSQDs can emit highly pure single photons with purity around 99% as deduced from the measured g⁽²⁾(0) <0.02 at 9.4 K. The purity of single photon emission from this new class of ordered and spectrally uniform QDs is comparable to the best reported for other classes of SQDs not necessarily in ordered arrays in the literature.^1–3,22,23 This makes MTSQDs a promising candidate for single photon sources to be on-chip integrated with LMEs to realize optical circuits.

We close noting that with the overgrowth of a planarizing layer, similar to QDs in recesses,^26,27 the MTSQDs can be embedded in the GaAs layer with a flat top surface, enabling ready integration with lithographically carved light manipulating elements as discussed in Refs. 5 and 11. Many favorable properties of the MTSQDs provide strong incentive to further explore the paradigm of using these SQD arrays to construct on-chip QOCs by integrating them with the typically well explored 2D photonic crystal based light manipulating elements^23,28–30 or, alternatively, using the newer approach of exploiting a single Mie resonance of a co-designed network built of subwavelength sized dielectric building blocks (DBBs)^5,11 to provide the simultaneously needed light manipulating functions of enhancing photon emission rate, directing photon emission, guiding, beam splitting, and combining on-chip. Further studies of MTSQDs examining their coherence time and indistinguishability of the emitted photon and integrating these QDs with DBB based light manipulating elements are underway.

The authors thank Army Research Office (ARO) (W911NF-15-1-0298) and Air Force Office of Scientific Research (AFOSR) (FA9550-17-01-0353 and FA9550-10-01-0066) for their support.