Super-resolved snapshot hyperspectral imaging of solid-state quantum emitters for high-throughput integrated quantum technologies

The concept of snapshot quantum HSI is presented in Fig. 1. Spatial randomly distributed and spectral inhomogeneously broadened solid-state quantum emitters are placed in a 1D nanophotonic planar cavity, as shown in Fig. 1(a). Different from localized micro-cavities in which the lights are highly confined in three dimensions, the nanophotonic planar cavity only provides light confinement in the Z-direction while the photons can freely propagate in the XY plane. The extended mode profile in the XY plane enables couplings between the cavity mode and multiple quantum emitters while the light confinement along the Z direction determines the dispersive feature of the cavity mode. Despite the Purcell factor provided by the planar cavity is very limited due to the rather large mode volume, such a cavity can significantly modify the radiation patterns of the embedded quantum emitters. Due to the dispersive couplings to the cavity modes, the emissions from solid-state quantum emitters (1-5) can only escape from the cavity at specific angles, determined by their emission wavelengths, thus exhibit characteristic far-field radiation patterns in the Fourier plane and unique profiles in the image plane, as presented in Fig. 1(b). Based on the emission characteristics of single quantum emitters modified by the planar cavity mode, it is therefore possible to simultaneously extract the spatial positions ($\rm{x_{n}},\rm{y_{n}}$) and emission wavelengths ($\rm{\lambda_{n}}$) of an ensemble of single quantum emitters by analyzing a snapshot PL image. With the extracted QD parameters, we could consequently realize a much stronger cavity QED effect by removing the original planar cavity and deterministically coupling QDs to 3D confined cavities with significantly reduced mode volumes and pre-designed cavity resonances, as shown in Fig. 1(c).

We now implement the concept of snapshot HSI to an III-V semiconductor system in which InAs QDs are embedded in a GaAs/AlGaAs planar cavityramon2006emission ; flagg2009resonantly ; proux2015measuring ; cogan2023deterministic . Such coupled systems have been recognized as superior platforms for fabricating high-performance quantum light sources somaschi2016near ; ding2016demand ; bennett2016cavity ; unsleber2016highly ; he2017deterministic ; liu2021dual ; wei2022tailoring ; gines2022high ; coste2023high and integrated quantum photonic circuitsdusanowski2023chip . As presented in Fig. 2(a), an ensemble of InAs QDs grown by molecule beam epitaxy is embedded in a $\lambda$ GaAs layer sandwiched between a bottom and a top distributed Bragg reflector (DBR) consisting of 30 and 20 pairs of 1/4 $\lambda$ GaAs/$\rm Al_{0.9}Ga_{0.1}As$ layer, respectively. The resonant mode of the planar cavity is spectrally located in the middle of the DBR reflection band, as revealed from the reflection spectrum measured along the Z direction in Fig. 2(b). To map the cavity resonance as a function of the in-plane k-vector (radiation direction), we perform angle-resolved spectroscopy zhang2021momentum on an ensemble of QDs under a high excitation power at which the QD ensemble serves as a broadband light source for probing the cavity mode dispersion, see the setups in Fig. E1 of extended data. The radiation direction of the cavity mode is highly correlated to the cavity resonant wavelength and such a dispersion relation can be quantitatively reproduced by the 1D transfer-matrix method (TMM) (see methods), as shown in Fig. 2(c). For comparison, the QDs in bulk material present no dispersion feature in both far-field patterns and image profiles, see Fig. E2 of extended data.

A typical wide-field PL image of the QD ensemble in the planar cavity is collected by a customized microscope and presented in Fig. 3(a). Each individual QD presents itself as a bright spot at a particular position with a specific spot size in the wide-field PL image. The spatial positions of QDs respective to the pre-fabricated alignment marks can be extracted with an accuracy down to 20 nm (see Fig. E3 in the extended data) by using the single molecule super-localization technique which is now widely employed for achieving spatial overlap between the QDs and the optical modes supported by the nanophotonic structures liu2019solid ; liu2021dual ; wei2022tailoring . Here, we focus on the relations between the emission wavelengths, far-field radiation patterns, and image profiles of different QDs. Fig. 3(b) presents confocal $\mu$PL spectra of 15 individual QDs in the field-of-view, showing sharp exciton emission lines associated with single QDs. The QD spectra are displayed from bottom to top by the order of their emission wavelengths. The measured far-field radiation patterns and image profiles together with the calculations for 5 representative QDs (1-5) with different wavelengths are presented in Fig. 3(c-f), respectively. The single QD emission lines exhibit ring-like far-field patterns due to the couplings to the planar cavity. As the QD emission wavelength moves towards the cavity resonance measured in the Z direction (dashed vertical line), the QD radiation angle (k-vector) decreases and forms an emission ring with a smaller diameter in the far-field, as presented in Fig. 3(c,e). Such a behavior faithfully follows the dispersion characteristics of the planar cavity mode as shown in Fig. 2(c). In contrast, the image profile of single QDs is in the form of an Airy beam consisting of a central bright spot surrounded by concentric rings with decreased intensities in Fig. 3(d,f). Notably, those QDs with short emission wavelengths feature image sizes appreciably smaller than the standard diffraction limit set by the QD emission wavelength and the numerical aperture (NA) of the objetive yang2013minimized (see Fig. E4 in the extended data), which provides a nanophotonic alternative of single-molecule super-resolution microscopy to the well-established technologies based on stimulated emission depletion (STED)vicidomini2018sted ; liu2017amplified ; jin2018nanoparticles ; pu2022super , structured illumination microscopy (SIM)heintzmann2009subdiffraction and single-molecule localization microscopy (SMLM)lelek2021single ; chi2020descriptor ; pertsinidis2010subnanometre . Due to the Fourier-transform relation between the far-field pattern and the image profile, the QD with a larger emission angle exhibits a smaller image size, which consequently correlates the emission wavelength to the image profile.

The crosscuts of the PL image profiles in Fig. 3(d, f) are presented in Fig. 4(a) consisting of bright central peaks and weak side lobes. The FWHM of the central peak, w, and the radius of the first ring, r, (the distance between the central peak and the first side lobe) are closely correlated to the QD emission wavelength. We plot the emission wavelength as a function of w and compare the experimental results to the calculations in Fig. 4(b). The red line is the calculation without any free parameter, which matches well with the trend of the experimental data but exhibits a slight offset. By performing a background subtraction in the model (yellow line), we achieve a perfect agreement between the experimental data and the calculation. The necessity of adding a correction in the model is probably due to the weak unwanted emission from other exciton states of QDs which leads to the over-estimation of w. The deviation ($\Delta_{1}=w_{\rm{exp}}-w_{\rm{cal}}$) of the measured w from the calculated values for QDs with different wavelengths are further presented in Fig. 4(c), in which all the experimental data fall within the 1 nm range of the calculation with a mean value of 0.13 nm and a standard deviation of 0.43 nm when implementing the background subtraction. To avoid any post-correction in the modeling, we investigate the characteristic of the radius of the first ring, r, which is less sensitive to the unwanted background emission in the sample. Without any free parameter and background subtraction, we achieve an excellent agreement between the experiment and the calculation, as shown in Fig. 4(d). The experimental data are well within the 1 nm range of the calculation, showing a deviation ($\Delta_{2}=r_{\rm{exp}}-r_{\rm{cal}}$) (Fig. 3(e)) with a mean value of 0.1 nm and a standard deviation of 0.44 nm. Based on the relations obtained and verified in Fig. 4(b, d), QD emission wavelengths with an accuracy down to 0.1 nm can be reliably extracted from their image profiles. Therefore, we could simultaneously extract the emission wavelengths and spatial positions of a large number of QDs from a snapshot wide-field PL image. With the employment of snapshot HSI of QDs in a planar cavity (see Fig. 4(f)), we could fabricate a large array of high-performance quantum light sources e.g., single-photon sourcessomaschi2016near ; ding2016demand ; bennett2016cavity ; unsleber2016highly ; he2017deterministic ; liu2021dual ; wei2022tailoring , entangled photon pair sourcesgines2022high and multi-photon entangled sourcescoste2023high , via etching micropillar structures at the QD locations and targeting the cavity resonances to the QD emission wavelengths by controlling the sizes and geometries of the etched micropillars, as schematically shown in Fig. 4(g) and experimentally verified in Fig. E5. In addition, integrated quantum photonic circuits based on DBR waveguides, as shown in Fig. 4(h), can be realized for pursuing on-chip Hong-Ou-Mandel interference between two QDsdusanowski2023chip . Here we emphasize that the spectrometer is only used in Fig. 3(b) to verify our method, it is not needed in the practical implementation of the HIS process.

We further show that a proper modification of the cavity configuration could be exploited for building deterministically coupled thin-film QD devices with expanded functionalities and reduced footprints. The proposed planar open cavity is schematically shown in Fig. 5(a). A 180 nm GaAs layer containing InAs QDs and a 450-nm-thick $\rm Al_{0.7}Ga_{0.3}As$ sacrificial layer are grown on a bottom DBR consisting of 20 pairs of 1/4 $\lambda$ GaAs/$\rm Al_{0.9}Ga_{0.1}As$ layer. A movable DBR mirror made of 20 pairs of 1/4 $\lambda$ GaAs/$\rm Al_{0.9}Ga_{0.1}As$ layer is placed on the top of the QD wafer with an air gap of 1000 nm, which could be precisely controlled by a piezo-nanopositionertomm2021bright . The normal reflection spectrum of the proposed planar open cavity is presented in Fig. 5(b), exhibiting two cavity resonances in the stop band. We intentionally designed the fundamental cavity resonance to the proximity of the InAs QD emission wavelength range (895 nm - 920 nm) for HSI. The dispersion diagram of the targeted cavity mode is shown in Fig. 5(c) in which the cavity resonance features a similar dispersion characteristic to that of the planar cavity in Fig. 2(c). By using a microscope objective with an NA of 0.60 (corresponding to a divergence angle of 36.8 degrees), there is a one-to-one correspondence between the emission angle (k-vector) and the emission wavelength. Such a dispersion relation can be further mapped to the relation between the PL image profile and the QD emission wavelength in Fig. 5(d) from which the QD emission wavelength can be directly extracted from the radius of the first ring in the PL image. With the spatial and spectral information of QDs obtained from the HSI, suspended membrane cavities with deterministically coupled QDs, such as circular Bragg resonators and high-Q photonic crystal cavities, can be fabricated for state-of-the-art quantum light sources and strong light-matter interactions (see Fig. E6 of extended data), as schematically shown in Fig. 5(e). To avoid the suspended membrane structures for large-scale integrations, more scalable devices such as microring quantum frequency convertors, phase shifters, interferometers and grating couplers, as shown in Fig. 5(f), can also be pursued by transferring the thin GaAs layer containing QDs on a low-index insulator substratecastro2022expanding (see Fig. E7 of extended data).

To conclude, we’ve extended the HSI concept from classical optics to advanced quantum technologies by simultaneously extracting both spatial and spectral information of multiple solid-state quantum emitters from a snapshot wide-field PL image. We experimentally perform HIS of QDs in a planar cavity towards the realization of an extensive array of deterministically coupled QD-micropillar quantum light sources and integrated quantum photonic circuits based on DBR waveguides. To build integrated quantum photonic circuits with reduced footprints and expanded functionalities, such as frequency converters, phase shifters, interferometers and grating couplers, we propose and numerically demonstrate the feasibility of snapshot HSI of QDs in a planar open cavity. Our HSI technique can be straightforwardly adapted to other types of solid-state quantum emittersaharonovich2016solid , e.g., NV centers, single molecules, and defects in GaN or 2D materials for high-throughput optical characterizations sutula2023large . More generally, it is also possible to implement snapshot HSI into biophysics where fast tracking and identification of single fluorescent particles are highly desirable yet technologically challenging. Our work provides an unprecedented tool to advance both classic optics and quantum photonics by enabling high-throughput deterministic light-matter interactions at the nanoscale.