High Purcell-enhancement in quantum-dot hybrid circular Bragg grating cavities for GHz-clockrate generation of indistinguishable photons

TL;DR

The paper presents a deterministic QD–hCBG platform that achieves strong Purcell enhancement with $F_ ext{P}>25$ and ultrashort $T_1<30$ ps, enabling GHz-clock-rate generation of photons with high indistinguishability. By precisely aligning QDs to the hCBG cavities using marker-based CL mapping, the authors achieve sub-40 nm spatial accuracy, enabling spectral overlap and robust Purcell control. They demonstrate both quasi-resonant and strictly resonant excitation, obtaining Hong–Ou–Mandel visibilities up to $V_ ext{HOM}^ ext{corr} o0.96$ and maintaining significant indistinguishability up to 30 K, with GHz operation demonstrated at 1.28 GHz. The results highlight the viability of high-Purcell solid-state emitters for quantum information technologies operating at GHz clock-rates, and point to future improvements via cavity design and active charge control to push performance further.

Abstract

We present Purcell-enhanced ($F_\mathrm{P}>25$) semiconductor InAs quantum dot decay times of $T_1<30\,$ps, enabled by deterministic hybrid circular Bragg gratings (hCBGs). We investigate the benefits of these short $T_1$ times on the two-photon indistinguishability for quasi-resonant and strictly resonant excitation, and observe visibilities $\geq96\%$ at 12.5$\,$ns time delay of consecutively emitted photons. The strongly Purcell-enhanced decay times enable a high degree of indistinguishability for elevated temperatures of up to 30$\,$K, and moreover, allow for excitation of up to 1.28$\,$GHz repetition rate. Our work highlights the prospects of high Purcell-enhanced solid-state quantum emitters for applications in quantum information and technologies operating at GHz clock-rates.

Figures (16)

• Figure 1: (a) Schematic depiction of a QD-hCBG cavity. $R+\delta{R}$ represent a variation in size of the CBG's central disc. (b) FEM-simulated spectral dependency of the Purcell factor $F_\mathrm{P}$ of an hCBG cavity with $\delta{R}$ variation. (c) Cathodoluminescence (CL-) map of a QD-containing hybrid flip-chip substrate with fabricated markers. Two QD emission patterns are indicated. (d) CL-map in (c) after the marker-aligned fabrication of hCBG cavities at the determined QD-positions. (e) Scanning Electron Microscopy (SEM) image of a fabricated QD-hCBG cavity. (f) Simulated $F_\mathrm{P}$ for one of the two orthogonal polarisations plotted as heatmap for up to $\pm$100 nm spatial mismatch of QD and hCBG cavity. The dashed ellipse corresponds to the estimated spatial integration accuracy $\sigma_\mathrm{spatial}\sim32$ nm.
• Figure 2: (a) QD-hCBG spectra obtained under white-light excitation, CL spectra before the integration and PL spectra in above-band and quasi-resonant excitation. (b) and (c) Experimental and theoretical cavity mode wavelength $\lambda_\mathrm{C}$ and experimental $Q$-factor at low and room temperature for deterministically integrated hCBGs and prior calibration process for fabricated $\delta{R}$ of the hCBG. (d) Time-resolved measurements in logarithmic scale and extracted $T_1$-times for several X$^+$ transitions in deterministic QD-hCBG cavities with varying spectral detuning, alongside the instrument response function (IRF). The extracted $T_1$-times by exponential fitting are indicated. (e) Experimental $F_\mathrm{P}$ values obtained from $T_1$-times with varying spectral detuning, as well as corrected for reduced Q-factors in the experiment for easier comparison to the simulations. For ideal emitter placement, the red solid line corresponds to the $F_\mathrm{P}$ of a cavity with $\delta{R}=30$ nm, while the red dashed line shows the $F_\mathrm{P}$ for $\delta{R}=0$ nm. The gray shaded curve indicates the theoretical $F_\mathrm{P}$ for $\delta{R}$-values in-between these two extrema for the investigated hCBGs. The black dashed line represents Purcell enhancement for an emitter that is spatially misaligned to the hCBG mode by 50 nm.
• Figure 3: (a) $\mu$PL-spectrum of a QD-hCBG cavity under quasi-resonant excitation and corresponding time-resolved measurement as inset. (b,c) Time-resolved second-order-auto-correlation measurements in a Hanbury-Brown and Twiss (HBT) configuration $\mathrm{g}^{(2)}(\tau)$ and two-photon-interference measurements in Hong-Ou-Mandel (HOM) configuration $g^{(2)}_\mathrm{HOM}(\tau)$ for emitter and conditions as in (a). (d) $\mu$PL-spectrum and time-resolved measurement (inset) for the same QD-hCBG cavity as in (a), but for strictly resonant (s-shell) excitation of the X$^+$ state with a $\pi$-pulse. (e,f) $\mathrm{g}^{(2)}(\tau)$ and $g^{(2)}_\mathrm{HOM}(\tau)$ for the same conditions as in (d).
• Figure 4: (a) Measured raw $V_\mathrm{HOM}$ (filled circles) and corrected $V^\mathrm{corr}_\mathrm{HOM}$ (open circles) for varying X$^+$$T_1$ times under p-shell and s-shell excitation. The plotted theory curves are according to equation (\ref{['eq:VHOM_T1']}) with respective $\Gamma$-values. (b) Corresponding $g^{(2)}(0)$-values for the data in (a). (c) Corresponding $T_2$-time extracted from fits of the central HOM-dip for the data in (a). (d) Measured raw $V_\mathrm{HOM}$ (filled circles) and corrected $V^\mathrm{corr}_\mathrm{HOM}$ (open circles) for varying X$^+$ transitions with varying $F_\mathrm{P}$ under p-shell excitation. The plotted theory curves are according to equation (\ref{['eq:VHOM_Temp']}), taking the $T$-dependent $T_1$-time due to temperature tuning of the embedded QDs into account. The indicated $F_\mathrm{P}$-values are measured at $T=4$ K and $T=45$ K for the respective cavities.
• Figure 5: Time-resolved measurements in (quasi-)resonant excitation at 1.28 GHz repetition rate. (a) Lifetime measurements of a QD-hCBGs cavity with $T_1<50$ ps under p-shell and s-shell excitation . (b) Second-order auto-correlation $g^{(2)}(\tau)$-measurement and (c) Two-photon interference $g^{(2)}_\mathrm{HOM}(\tau)$ under p-shell excitation for the QD-hCBG cavity in (a). (d) Second-order auto-correlation $g^{(2)}(\tau)$-measurement and (e) Two-photon interference $g^{(2)}_\mathrm{HOM}(\tau)$ under $\pi$-pulse s-shell excitation for the QD-hCBG cavity in (a). (f) Measured count-rates for an increasing number of excitation pulses (and correspondingly higher excitation rate $f$), normalized by the 1-pulse result for p-shell (red) and s-shell (blue) excitation.