A fiber-pigtailed quantum dot device generating indistinguishable photons at GHz clock-rates

3.1 FEM simulations

Figure 1(a) shows an illustration of the fiber-pigtailed hCBG device, with the fiber core symmetrically aligned to the hCBG’s center, hosting the embedded QD. The fiber is separated by a distance h from the QD-hCBG cavity. For this geometry, the optical performance was calculated using finite element method (FEM) simulations with the commercial software JCMsuite [38], using an embedded dipole source to mimic the QD. For details on the FEM simulations, the modelled structure as well as the hCBG cavity design parameters and UHNA3 SMF parameters we refer to the S.I., section S1.

Figure 1:

Device schematic and simulated performance. (a) Illustration of the fiber-pigtailed quantum light source with an UHNA3 fiber aligned to the center of the hCBG with embedded QD. The fiber-to-hCBG distance h and the lateral misalignment between CBG and fiber Δ _XY are indicated. (b) FEM simulation of Purcell factor F _P (red) and single-photon fiber-coupling efficiency η _FC−SPS (blue) of QD emission into the UHNA3 fiber at h = 350 nm. The free space performance with F P no − fiber and lens-efficiency η NA 0.8 no − fiber (green) into a lens with NA=0.8 is indicated. (c) Simulated F _P (red) and η _FC−SPS (blue) for varying h-values at λ=939.5 nm. The simulated F P no − fiber of the QD-hCBG without the fiber is indicated. The target fiber-hCBG distance of h = 350(50) nm is marked. The simulated Q and V _M for h=350, 500, 800 nm, as well as without fiber are listed. (d) Deviation from the maximum simulated η _FC−SPS value at h = 350 nm and λ=939.5 nm for varying lateral displacements dX _fiber/dY _fiber of the fiber relative to the hCBG cavity’s center. The dotted circle denotes a lateral misalignment of Δ _XY = ±200 nm corresponding to the experimentally achieved precision, while the solid line indicates the size of the hCBG’s central disc with radius R=360 nm.

Figure 1(b) shows the simulated optical properties in terms of Purcell factor F _P, free-space performance of the QD-hCBG cavity into a lens without fiber and simulated dipole power coupled to the UHNA3 fiber’s two degenerate ground modes. For a target value of h _target = 350 nm, simulated F _P-values exceed 30, while direct single photon fiber-coupling efficiencies of η _FC−SPS > 80 % are reached. The experimentally obtained precision of the distance between the QD-hCBG cavity and the fiber core is ±50 nm [37], which is marked in Figure 1(c) with dashed lines. This error margin corresponds to the change of the F _P-values in the range of 10–20 % and has a negligible effect on η _FC−SPS. The simulated η _FC−SPS here corresponds to the coupled power in the two degenerate SMF modes, compared to total emitted power by the embedded dipole, which is equal to the probability of collecting a single photon per excitation pulse, assuming unity QD quantum efficiency and preparation fidelity of the excitation. If Purcell enhancement and efficiency into a lens with NA 0.8 instead of the SMF is considered, the simulated QD-hCBGs performance in absence of the fiber is similar in terms of F _P, with slightly higher efficiencies of η _NA0.8 > 93%. The lens-efficiency corresponds to the fraction of total dipole power collected in the far-field for the corresponding NA, accordingly.

The fiber-to-CBG distance h has a significant influence on the achievable Purcell enhancement, as can be seen from Figure 1(c) for a wavelength of λ = 939.5 nm. F _P-values between 50 and 25 are observed in the simulations for 200 < h < 1,000 nm. This large influence stems from additional vertical confinement to the hCBG mode in vertical direction by the present fiber. As shown in S.I., section S2, placing the fiber-facet at regions of high (low) hCBG mode intensity in vertical direction, causes a decrease (increase) in the mode’s Q-factor by up to 45 %. Since the mode volume stays nearly constant, the h-dependency of Q leads to an h-dependent F _P. The fiber can be considered as effectively becoming part of the hCBG cavity. Noteworthy, the h-dependent Q should allow to access the fiber-to-hCBG distance via mode linewidth measurements in the experiment. Note that the drop in simulated F _P at h < 200 nm originates from a shift in the cavity mode wavelength, since the h-dependent simulation is carried out for a constant wavelength. The cavity mode starts to red-shift to longer wavelengths when the fiber comes in close proximity to the hCBG structure, due to increased effective refractive index. η _FC−SPS is only marginally affected and stays between 80 and 85 % over the investigated h-range, indicating the narrow collimation of the hCBG-mode’s emission at these distances.

An additional parameter with a more significant effect on the η _FC−SPS is the lateral displacement of the UHNA3’s fiber-core with respect to the center of the QD-hCBG cavity. The deviation from the maximum efficiency with lateral displacements of the fiber are shown in Figure 1(d), with the indicated alignment accuracy of ± 200 nm of the pigtailing process still yielding > 90 % of the maximum fiber-efficiency.

Note that the simulations in Figure 1 assumed an ideal position of the embedded QD, perfectly centered vertically and laterally in the center hCBG disc. Furthermore, the central mode wavelength λ _C in the hCBG cavity can be varied by ± 10 nm by slightly varying the diameter of the central hCBG disc, without affecting the simulated efficiency significantly.

3.2 Spectral properties

For quantum-optical experiments, the fiber-pigtailed QD-hCBG device is transferred into a closed-cycle He-cryostat, and the 780HP side of the 780HP-UHNA3 patchcord is connected to a fiber feedthrough of the cryostat, followed by a controlled cooldown. The room temperature side of the fiber-feedthrough is connected to a 1:2 fiber-coupler (split ratio: 90:10), whose 90 % arm is connected to a fiber-collimator directing the sample emission to a spectrometer. Spectra and time-resolved measurements are recorded using an attached Si-CCD camera or a single photon nanowire detector (efficiency ∼85 %), respectively. The 10 % arm of the fiber-coupler serves as input for the excitation laser and is either connected to a ∼ 2 ps-pulsed tunable excitation laser with 80 MHz excitation rate, or to a broadband white-light source for reflection measurements. The QD-hCBG before the fiber-pigtailing was characterized using the identical setup and excitation sources, but with the sample’s emission collected using a NA=0.8 microscope objective in the cryostat via a free-space path towards the spectrometer. Detailed information on the setup can be found in S.I., section S2.

The fiber-pigtailed QD device was cooled down while excited with off-resonant pulses at excitation wavelength λ _exc = 793 nm and the emission was recorded on the spectrometer’s Si-CCD camera. Details of the sample’s emission during the cooling cycle are shown in S.I., section S3, indicating that the fiber-to-hCBG alignment was stable throughout the cooldown, and no plastic deformation occurred. The cryostat’s temperature sensor displayed a final temperature of about 4.8 K, which is 0.8 K warmer than for the QD-hCBG device without fiber-attached, indicating a potential increased thermal load. However, we confirmed proper thermalization of the device from its emission spectra (see below).

In Figure 2, spectroscopic data of the selected QD-hCBG cavity before and after the fiber-pigtailing process is presented (sample temperature: T=4.8 K). Figure 2(a) depicts spectra of the fiber-pigtailed QD-hCBG emission after four consecutive cooldowns (FC_CD) and the reference spectrum before fiber-pigtailing, each under off-resonant excitation at λ _exc = 793 nm and excitation power P _exc ∼10–100 nW. The emission spectrum prior to the pigtailing (grey line) shows dominant positive trion states (multiple lines associated with excitonic X²⁺ and other higher hole states, the dominant X⁺ and two lines corresponding to biexcitonic XX⁺ transitions), commonly observed for the investigated InAs QDs and dependent on their background doping [39]. The assignment of the emission lines to specific QD states was confirmed by conducting excitation power- and polarization-resolved measurements after the first cooldown of the fiber-pigtailed device (see S.I., section S5. for details).

Figure 2:

Emission properties of the QD-hCBG device before and after fiber-pigtailing. Shown are measurements from four different cooldowns (FC_CD) #1 (red), #2 (blue), #3 (green) and #4 (orange) of the fiber-pigtailed device and the hCBG before fiber-coupling as reference (grey). Dashed grey lines indicate the long-wavelength cut-off of an bandpass filter used in the measurements. (a) Normalized emission intensity of the fiber-pigtailed device under pulsed off-resonant excitation (λ _exc = 793 nm) respective QD states are indicated. (b) Normalized emission intensity under pulsed p-shell excitation. (c) Normalized white-light reflection spectra for linear H- (solid) and V-polarisation (dashed line).

The spectrum for the fiber-pigtailed QD-hCBG device under similar excitation conditions of the first cooldown in red, however, appears noticeably different, with dominant QD emission lines identified as the charge-neutral states X and XX as well as the negative trion X⁻. The observed change to the dominant X⁻ prevails for the cooldown runs #2–4, accompanied by a considerable blue-shift relative to cooldown run #1 and further reduced intensity from the positive trions under off-resonant excitation.

As X⁺ dominated the spectrum under off-resonant excitation in the uncoupled device, the spectrum was taken with a bandpass filter that focused on the spectral region around the trion. Therefore the QD states at longer wavelengths are not visible in the reference spectrum before fiber-pigtailing. However, as can be seen in S.I., section S4, if the intensity scale is logarithmic, it can be seen clearly that the observed emission lines stem from the same QD.

The successful fiber-pigtailing is additionally confirmed by the emission spectra under quasi-resonant excitation in Figure 2(b), revealing near-identical spectra throughout cooldown runs #2–4. Moreover, we observe wavelength shifts for the X⁺ state of +0.25 nm for cooldown #1 and −1.55 nm for the cooldowns #2–4 relative to the reference spectrum before fiber-coupling. The wavelength of the excitation laser at P _exc ∼3 μW was set to the p-shell resonance for the X⁺ state, as identified from photoluminescence excitation (PLE) scans before and after pigtailing (see S.I. section S5). The PLE scans additionally confirm the observed wavelength shifts of the X⁺ transition by showing a corresponding shift in the λ _exc of the p-shell, indicating that it is in fact a spectral shift resulting from a change of the QD’s spectral fingerprint rather than a measurement artifact (e.g. due to changes in the alignment of the detection path).

Figure 2(c) shows white-light reflection measurements before and after pigtailing of the QD-hCBG device. The H- and V-polarized cavity modes are visible as dips in the recorded reflection spectra. In addition, the white-light illumination also excited the QD states, which enables a straightforward analysis of the spectral detuning between cavity and quantum emitter. The spectrum before the pigtailing confirms the good alignment of the X⁺ emission with the hCBG’s cavity mode. For a quantitative analysis, the cavity modes positions are extracted from a Fano fit [40], causing the central mode wavelength λ _M to be shifted slightly relative to minima of the reflection dips. Interestingly, the cavity mode appears considerably red-shifted after cooldown run #1 of the fiber-pigtailed device (compared to the measurements before pigtailing), while a relatively stable blue-shift is observed for the cooldown runs #2–4.

Due to the fact that both the QD emission and the hCBG modes exhibited a red-shift during cooldown #1 compared to before the pigtailing, while the cooldowns afterwards showed a blue-shift, a temperature-induced shift is unlikely, not least as the proper thermalization of the fiber-pigtail was confirmed by comparing the temperature dependence of the emission intensity during the cooldown runs with theoretical predictions (see. S.I. section S3). We thus identify strain as the origin of the observed shifts in emission wavelengths and also the changes in dominant emission lines. A reasonable explanation could be that the induced strain affects the availability of excess holes required for a dominant X⁺ emission under off-resonant excitation, enabling excess electrons from nearby donors instead causing X⁻ to be the dominant line. Under p-shell excitation, the X⁺ transition still remains dominant. The strain is likely built up due to the different thermal expansion coefficient of the hCBG substrate (i.e. GaAs, SiO₂ and Au, see Figure 1(a)) and fiber-pigtail (i.e. silica and UV-adhesive). The strain could also explain the shifts in mode wavelengths between the cooldowns, by changing the (effective) refractive index of the combined fiber-hCBG microcavity. For a rough estimation based on FEM simulations, we find that a refractive index change Δn < 0.2 % is already sufficient to create the observed mode shifts. Such a Δn is well within reach for already small amounts of strain [41].

Strain-induced changes of the emission wavelength of InAs QDs have been reported for monolithic samples in combination with permanently adhered fiber-systems [42]. The significant change from predominantly positive to negative trion emission observed in our work for the hybrid samples under off-resonant excitation, however, was not reported yet. While a detailed understanding of these changes in state-occupation will require further research efforts, the fact that X⁺ and X⁻ show these variations might point towards background dopants or defect levels providing excess-charge-carriers close to the QD being affected by the strain. Furthermore, the X⁺ emission being inhibited under off-resonant excitation at λ _exc=793 nm, while showing considerably brighter emission in p-shell excitation, hints towards the specific energy levels of these defects. A possible factor that benefits the observation of these effects in the present hCBG sample, might be its thin GaAs-membrane on thin SiO₂ spacer, enabling an efficient strain-transfer from the glued fiber to the QD position. Since the central disc is free-standing and should be neither in contact with glue nor fiber (due to the ion-beam milling of the fiber core and cladding), this strain-transfer is supported by the underlying layers which extend over a larger areas covered by ferrule and glue.

It is worth noting that both the X⁺ and mode wavelengths appear to remain constant after the first cooling and warming cycle. Especially the cavity-mode wavelengths after the cooldown runs #2–4 of the fiber-pigtailed device are more similar to each other, indicating that the strain conditions are still different compared to before, but remain constant after the first temperature cycle.

3.3 Efficiency and Purcell enhancement

After confirming that the employed fiber-pigtailing method allows for deterministic coupling of a selected QD-hCBG, we now investigate the quantum optical properties of the fiber-pigtailed QD device. Figure 3(a) shows time-resolved measurements during cooldown #2 for the X⁺ under p-shell excitation, and for X⁻ under off-resonant excitation. Additionally, a time-resolved measurement of the X⁺ before the pigtailing is shown. A T ₁(X⁺)=77(1) ps for the FC-device under p-shell excitation is extracted by an exponential fit. This is slightly longer than the 55(1) ps before the pigtailing. A typical T ₁ time of positive trions in p-shell excitation in the surrounding membrane of the sample is 680(111) ps, which corresponds to F _P = 12.4(2.2) before, and 8.8(1.4) for the fiber-pigtailed device. T ₁(X⁻) under off-resonant excitation is found to be 1.780(1) ns, which is attributed to a large spectral mismatch of X⁻ to the mode (see. Figure 2(c)).

Figure 3:

Time-resolved measurements before and after the pigtailing. (a) Lifetime-measurement with extracted T ₁-times from exponential fits for X⁺ in p-shell excitation before (grey) and after (blue) the fiber-pigtailing. The measurement for the X⁻ after the pigtailing (purple) in off-resonant excitation is also shown. (b) Measured T ₁-times of X⁺, mode Q-factors and QD-mode spectral mismatch Δλ. (b) Second-order-auto-correlation g ⁽²⁾(τ)-measurements and g ⁽²⁾(0)-values from comparing the integrated events at τ = 0 to the integrated neighbouring peaks at 12.5 ns time-window. Measurements for X⁺ and X⁻ for respective excitation conditions are shown. The integration time-window around τ = 0 ns is indicated. (d) g ⁽²⁾(0)-values of the X⁺ under p-shell excitation before the fiber-pigtailing and for pigtailed cooldowns.

The measured T ₁-times of the X⁺ for the consecutive cooldowns of the pigtailed device are displayed in Figure 3(d). The observed spectral mismatch of X⁺ wavelength and closest cavity mode and the measured cavity mode Q-factor as λ _M/w _M are additionally listed. The pigtailed device shows a considerably larger T ₁(X⁺) during cooldown #1, while interestingly also exhibiting a clearly increased Q compared to before the pigtailing. However, while the spectral mismatch between X⁺ and mode was −0.44(0.50) nm before, the pigtailed device showed a mismatch of +1.53(0.50) nm during the first cooldown. We attribute the longer T ₁-time to the larger spectral mismatch after the first cooldown. With the strain conditions settled after the first temperature cycle, the following cooldowns yield very similar T ₁ times, alongside X⁺-mode mismatches between −0.62(0.50) nm and 0.15(0.50) nm. While the observed spectral mismatch is close to the value before the pigtailing, the Q-factors are clearly reduced for the cooldowns #2 to #4. We attribute the slightly higher T ₁ times after the fiber-pigtailing to the decreased Purcell enhancement by the reduced Q caused by the distance-dependent effect of the fiber on the F _P here as predicted in Figure 1(c).

The decrease in experimental Q between before the pigtailing and for cooldown #1 is approximately 390/260 ≃ 1.35, which is also close to the relation between the simulated Q before the pigtailing and at h _target = 350 nm of 430/320, considering that the overall Q was reduced slightly through imperfect fabrication. This indicates that before cooldown #1, the distance of fiber and hCBG cavity was potentially close to the target value. After the warmup and following cooldowns #2 to #4, the experimental Q drops to 0.71× the Q-factor before the pigtailing, which means that the fiber-to-hCBG distance for the pitailed device afterwards might be up to 200 nm larger than the h _target of 350 nm. We note that the expected strain-related refractive index change causing the spectral shift of the modes results in a negligible change in Q as confirmed from the simulations, hinting further towards a fiber-distance related effect. The resulting T ₁-times before and after the pigtailing during cooldowns #2 to #4 exhibit a similar relation of 0.72, implying that the change in T ₁ could stem from the distance-dependent reduced F _P by the lower Q. Future work simulating the strain conditions [43] could answer the question of how much T ₁ is additionally affected by the strain itself. Note that the device does not reach the simulated F _P of 30 and more already before the coupling, likely due to a non-ideal spatial integration of the QD.

To proof the non-classical photon statistics of the photons emitted by the fiber-pigtailed QD device, we performed experiments in Hanbury–Brown–Twiss (HBT) type configuration. Figure 3(c) shows the resulting second-order auto-correlation histograms g ⁽²⁾(τ) and corresponding g ⁽²⁾(0)-values obtained by integrating the coincidences within a 12.5 ns wide window around τ = 0 and comparing this number with the integrated coincidences of the neighbouring peaks.

A multiphoton-suppression value of g ⁽²⁾(0) = 0.007(2) is obtained for the X⁺ under p-shell excitation, while the X⁻ shows g ⁽²⁾(0) = 0.045(6) in off-resonant excitation. The higher multiphoton suppression obtained for X⁺ is benefited by the possible quasi-resonant excitation compared to the above-band excitation for X⁻, and also the significantly shorter T ₁(X⁺). For X⁻, the long T ₁ time leads to significant residual events around τ=0 in the g ⁽²⁾(τ)-measurement at 12.5 ns pulse separation.

As a final comparison of before and after the pigtailing, Figure 3(d) shows the obtained g ⁽²⁾(0)-values pf X⁺ for each case. The multi-photon suppression in the fiber-pigtailed cases are slightly better than before the pigtailing, with comparably small error due to the short lifetime and thus high statistics in the corresponding time-bins of the histograms. The difference between the before and pigtailed case is most likely not significant, given the fact that the measurements were some time apart, leading to different lab conditions like stray light, and detector dark counts. The error for the respective g ⁽²⁾(0)-values does only account for the statistical error for the integration of the histogram, and does not take such systematic deviations into account.

The measured multiphoton suppression for the pigtailed QD-hCBG device of below 1 %, obtained via direct integration of the measured g ⁽²⁾(τ)-histogram, is the best performance for a directly fiber-coupled device under these excitation conditions reported so far, if compared to the value of ∼1.5 % in Ref. [19] by Northeast et al. and ∼3.7 % in Ref. [28] by Snijders et al. It should be noted, however, that we used a slightly narrower spectral filter (bandwidth: 100 μeV or 0.07 nm) in our experiments compared to Ref. [19] (∼0.1 nm), while the experiments in Ref. [28] did not use any spectral filtering at all, which was possible thanks to the resonance fluorescence excitation scheme (cross-polarized excitation-detection configuration) employed in their fiber-pigtailed device. Since arbitrarily high spectral filtering will always improve the measured g ⁽²⁾-value, we point out that the 100 μeV filtering settings are still 2–3 times broader than the zero phonon line of the pigtailed X⁺, and only discard small portions of the phonon sideband, a filtering comparable [44] or less strict [12], [45] than other works in literature.

After confirming the single-photon nature of the fiber-pigtailed QD device’s emission, its efficiency can be estimated by analyzing the photon flux detected at the single photon detector in the experimental setup and taking into account transmission losses from the fiberpigtail to the detection system. The observed countrates R ^before before and R ^FC after the pigtailing (in this case for cooldown #2) are listed in Table 1. A countrate of R X + FC = 300 ( 10 ) kcps (kilo clicks per second) is obtained for the X⁺ under p-shell excitation (P _Sat ∼ 3 μW) on the SNSPDs, while the X⁻ reaches R X − FC = 1.20 ( 5 ) Mcps at off-resonant excitation with λ _exc = 793 nm (P _Sat < 15 nW).

By dividing the measured countrates from Table 1 by the excitation repetition rate of f = 80 MHz, the end-to-end efficiency at the detectors is η _overall = R/f, yielding η _overall(X⁺) = 0.375 % and η _overall(X⁻) = 1.50 %. To compare these efficiencies to the simulated η _FC−SPS in Figure 1(a), we take the setup efficiency η _setup into account. Details about the efficiency estimation can be found in S.I., section S8. Considering the UHNA3-to-780HP splice η _splice = 0.95(1), the fiber-feedthrough at the cryostat η _cryo = 0.60(5) and transmission losses by the fiber-beamsplitter, several fiber-connectors, the spectrometer and the connection to the SNSPDs η _detection = 0.049(1), we obtain an experimental η _FC−SPS into the pigtailed UHNA3 fiber of η fiber X + = 13.4 ( 2 ) % and η fiber X − = 53.7 ( 2 ) % for X⁺ and X⁻, respectively.

The observed η _FC−SPS for X⁻ is already surprisingly close to the simulated efficiency of η _FC−SPS = 85 %, a possible non-ideal lateral alignment between fiber and hCBG device. Furthermore, the off-resonant excitation of the X⁻ reduces the measured efficiency, since e.g. the neutral states are also excited (see cooldown #2 in Figure 2(a)). Note here, that the high efficiency observed for the X⁻ state besides its far detuning from the cavity modes highlights the potential of the broadband capabilities of hCBG devices also for applications benefiting from long lifetimes. The large spectral cavity-emitter detuning substantially increases T ₁(X⁻), while η _FC−SPS remains on a high level.

The observed η _FC−SPS of the X⁺ is significantly lower than expected, however this can be explained considering the fact, that the X⁺ was already limited in brightness prior to the pigtailing: Table 1 shows the observed peak-intensities at the CCD for the X⁺ under p-shell near saturation before the pigtailing with I X + before = 252 ( 10 ) kcps, and with pigtailed fiber as I X + FC = 175 ( 10 ) kcps. Free-space and fiber-setup efficiencies to the CCD were comparable for the measurements, so that the ratio of peak-CCD counts for the X⁺ before and after the pigtailing can also act as a rough estimate for η _FC−SPS. I X + FC / I X + before yields ∼ 0.69 ( 4 ) , which is reasonably close to the simulated η FC − SPS / η NA 0.8 nofiber = 0.91 bearing the aforementioned experimental limitation in mind and thus further indicating a high degree of pigtailing precision. We observed, that the saturated X⁺ brightness for the incorporated QDs in the hCBGs before the pigtailing varied by up to a factor of 4 between QDs, which we attribute to changing dopant and defect layer environments, that provide the charge carries for the X⁺. The fiber-pigtailed device here was primarily chosen for the high Purcell enhancement of the X⁺, rather than the X⁺ brightness, and we plan to optimize both parameters in the future.

The performance of the fiber-pigtailed QD device presented above compares favorably with an earlier report on CBG-based plug-and-play sources by Jeon et al. [34]. We achieve significantly higher F _P and lower g ⁽²⁾(0) for the quasi-resonantly excited X⁺. The improvement in multiphoton-suppression we thereby attribute to the quasi-resonant excitation scheme implemented in our work. Moreover, our fully deterministic technology for QD-device integration and fiber-pigtailing enables us to increase η _FC−SPS of the X⁺ and especially X⁻ state by more than a factor six. This advancement is further facilitated by the optimized hybrid back-reflector design in combination with the UHNA3-fiber and precise fiber-to-hCBG alignment accuracy.

3.4 Photon-indistinguishability

Next, we investigated the photon-indistinguishability of the emission of the fiber-pigtailed device using two-photon interference experiments to access g HOM ( 2 ) ( τ ) in a Hong-Ou-Mandel (HOM) setup. For this purpose we interfered consecutively emitted X⁺ photons in the HOM-setup after spectral filtering via the spectrometer (see S.I., section S2 for experimental details). To quantify the degree of indistinguishability, measurements in co- and cross-polarized configuration are compared. The HOM-experiments are conducted during cooldown #3 for two different temporal delays δt of 2 ns and 12.5 ns for consecutively emitted photons, providing additional insights in possible dephasing mechanisms [46].

The resulting HOM-histograms are shown in Figure 4, while the extracted two-photon visibilities V _HOM are summarized in Table 2. Figure 4(a) yields V _HOM = 0.78(4) for p-shell excitation at 0.5P _sat and δt = 2 ns. Accounting for residual multi-photon emission events, we obtain a corrected value of V HOM corr = ( 1 + 2 g ( 2 ) ( 0 ) ) V HOM = 0.82 ( 4 ) [47], using the g ⁽²⁾(0)-value measured during cooldown run #3 (c.f., Figure 3(d)). Figure 4(b) shows g HOM ( 2 ) under the similar conditions, but for δt = 12.5 ns. The extracted visibility is slightly reduced to V _HOM = 0.75(4) ( V HOM corr = 0.79 ( 4 ) ) at these increased time delays, a commonly observed phenomenon [48] that could be reduced in future works by employing coherent excitation schemes [49]. At saturation power, values of V _HOM = 0.63(4) ( V HOM corr = 0.67 ( 4 ) ) are measured for δt = 2 ns and V _HOM = 0.52(4) ( V HOM corr = 0.55 ( 4 ) ) for δt = 12.5 ns. The further decrease in indistinguishability at elevated excitation power indicates increased decoherence due to excitation power induced dephasing. We note again, that the spectral filtering applied in the measurements conducted here partially filtered out the phonon side bands of the X⁺ emission, but collected all emission from the zero phonon line.

Figure 4:

Two-photon interference measurements for the FC-device. The g HOM ( 2 ) ( τ ) measurements were taken during FC_CD#3 under 80 MHz p-shell excitation at half the saturation power P _sat. Co-polarized measurements are shown in green, cross-polarized measurements in grey. (a) For a separation of δt = 2 ns for the exciting pulses. (b) For a separation of δt = 12.5 ns for the exciting pulses. The HOM visibility V _HOM is obtained by comparing the co- and cross polarized peak areas at τ = 0. The respective integration time-windows are indicated with dashed lines.

Although experimental data which would allow for a direct comparison of the photon-indistinguishability before the fiber-pigtailing is not available, we can still compare the performance of the pigtailed device with experimental data of free-space coupled devices under comparable excitation conditions stemming from the same wafer (see S.I., section S7). The HOM-results summarized in Table 2 yield very similar V _HOM for given T ₁-times and inhomogeneous broadening under p-shell excitation, indicating that the photon-indistinguishability is mostly affected by the effects of the fiber-pigtailing on the emitter’s T ₁-time as well as the degree of inhomogeneous broadening.

3.5 GHz clock-rate operation

Furthermore, we demonstrate that the short Purcell-enhanced lifetime of the fiber-pigtailed QD-hCBG cavity enables its operation at clock-rates in the GHz-regime. Using a home-built frequency multiplication setup, we reduced the original repetition period of the 80 MHz laser system from δt = 12.5 ns down to δt = 781 ps corresponding to an excitation repetition rate of f = 1.28 GHz.

Time-resolved measurements of the fiber-pigtailed QD device under p-shell excitation at these GHz frequencies during cooldown run #4 are displayed in Figure 5(a). The short T ₁ time of the X⁺ transition enables a clear separation between consecutive single-photon pulses even at 1.28 GHz clock-rate. Note, that the X⁺-state has been operated far below saturation in this measurement (P _sat/16), due to technical limitations for the transmission of the used self-built frequency multiplication setup.

Figure 5:

Performance of the fiber-pigtailed QD device (X⁺ emission) under p-shell excitation at a clock-rate of f=1.28 GHz. The temporal delay between consecutive single-photon amounts to 1/f = 781 ps. (a) Time-resolved trace of a single-photon pulse train in logarithmic scaling. (b) Photon-autocorrelation g ⁽²⁾(τ)-measurement. (c) Two-photon interference g HOM ( 2 ) ( t ) histograms measured in co- (orange) and cross- (grey) polarized configuration at P _exc=P _sat/16. Dashed lines indicate the 781 ps repetition period.

The corresponding g ⁽²⁾(τ)-measurement is depicted in Figure 5(b), with an extracted g ⁽²⁾(0)-value of 0.035(11), obtained by direct coincidence integration and comparison to neighbouring peaks in a temporal window of 1/f = δt = 0.781 ns. The multiphoton suppression is slightly elevated compared to operation at 80 MHz (compare Figure 3(d)). This is due to the slower bi-exponential decay component of > 600 ps in the time-trace for the X⁺ under p-shell excitation, resulting in a small but noticeable overlap of consecutive single-photon pulses.

Finally, we also conducted two-photon interference experiments at 1.28 GHz clock-rate. The HOM-results are displayed in Figure 5(c) for co- and cross-polarized measurement configurations. From the raw experimental data we extract an photon-indistinguishability of (V _HOM = 0.61(7)) at δt = 0.781 ns and accounting for the finite g ⁽²⁾(0) yields a corrected value of V HOM corr = 0.68 ( 7 ) ).

The obtained values are similar to the photon-indistinguishabilities obtained under 80 MHz p-shell excitation and at significantly higher excitation powers. Considering that both the excitation power per pulse as well as the temporal-separation between interfering photons is considerably smaller, the two-photon interference visibility observed under GHz-driving is lower than intuitively expected.

The aforementioned longer decay component leads to some degree of overlap of neighbouring pulses, reducing the measured indistinguishability. In general, the effect of GHz-driving on the indistinguishability of emitted photons by a quantum emitter is far less explored compared to conventional 80 MHz excitation rates. Recent results indicate that the short time-scales between consecutive pulses can affect the emission from charged QD states [35], which might well be connected to the limited two-photon interference visibility under GHz-drive observed above.