On-chip generation and dynamic piezo-optomechanical rotation of single photons

Integrated photonic circuits are key components for photonic quantum technologies and for the implementation of chip-based quantum devices. Future applications demand flexible architectures to overcome common limitations of many current devices, for instance the lack of tuneabilty or built-in quantum light sources. Here, we report on a dynamically reconfigurable integrated photonic circuit comprising integrated quantum dots (QDs), a Mach-Zehnder interferometer (MZI) and surface acoustic wave (SAW) transducers directly fabricated on a monolithic semiconductor platform. We demonstrate on-chip single photon generation by the QD and its sub-nanosecond dynamic on-chip control. Two independently applied SAWs piezo-optomechanically rotate the single photon in the MZI or spectrally modulate the QD emission wavelength. In the MZI, SAWs imprint a time-dependent optical phase and modulate the qubit rotation to the output superposition state. This enables dynamic single photon routing with frequencies exceeding one gigahertz. Finally, the combination of the dynamic single photon control and spectral tuning of the QD realizes wavelength multiplexing of the input photon state and demultiplexing it at the output. Our approach is scalable to multi-component integrated quantum photonic circuits and is compatible with hybrid photonic architectures and other key components for instance photonic resonators or on-chip detectors.

The layer sequence of the sample is displayed in a schematic of the ridge waveguide cross-section in Supplementary Figure 1a. The layer sequence was as follows: first, a 1500 nm thick Al0.2Ga0.8As cladding layer is grown on a (001)-GaAs substrate. The waveguiding layer consists of a 300 nm thick GaAs layer with a layer of (In,Ga)As QDs in its center. As shown Supplementary Figure 1a, the nominal etch depth to define the ridge waveguides was 150 nm. Supplementary Figure 1b shows the optical field distribution of the fundamental TE mode within the GaAs guiding layer (thick lines). The calculation assumes vacuum as the topmost layer and Al0.2Ga0.8As as cladding. The waveguide itself is 2.1 µm wide. The effective refractive index $%% can be calculated with the effective index method 1 . For this we used the refractive indices of the III-V compounds and their temperature dependencies reported in references 2-4 .

Supplementary Figure 2 -IQPC design -Full IQPC layout with all design parameters labeled.
Supplementary Figure 2 shows the full design of the IQPC with the dimensions labeled. In addition, the positions of the IDTs to excite SAWs are indicated (size of the IDTs not to scale). The design is 3342 µm long (z) and 32.1 µm (x) wide. The IQPC comprises output waveguides, tapers, S-bends, multimode interference (MMI) couplers, which form an integrated Mach-Zehnder interferometer (MZI). The circuit is designed for optimum SAW modulation 5 . Key design parameters were as follows: the MMI lengths are chosen according to &&' = 3/2 ( , with ( being the beat length 6 , given by ( ≈ ) + !"" , ! -.
. Here, $ is the effective waveguide width, taking into account the Goos-Hänchen shift 7 .
Furthermore, it is important to note that the center of the MZI arms in the acousto-optic region are separated by (2 + 1)Λ /01 /2 ( integer, Λ /01 , SAW wavelength) along x-direction. For maximum modulation contrast 8 and the most compact design we set = 1 . In the MZI section, another important parameter to consider are the waveguide width, compared to Λ /01 . Here, the ratio is ≈ 0.16, ensuring a well-defined modulation of the refractive index in each arm that can be safely assumed to be constant across the waveguide cross-sections.

Supplementary Note 1.2 -Interdigital transducer design
The IDTs used in the experiments presented had a Split-2 finger design to suppress internal reflections. The design wavelength was Λ /01 = 5.6 µm (corresponding to a frequency of 520 MHz). The IDTs consist of 1400 fingers (aperture = 120 µm) distributed evenly over a total length of 1960 μm. In the optical part, a laser (wavelength 660 nm) (Laser 1) is focused by an objective lens (NA = 0.81) to a diffraction limited spot on the device under test (DUT). It photo-generates carriers inside QDs which then emit single photons into the waveguide structure (colored red). At the top end of the DUT one lensed optical fiber is positioned to collect the light from the cleaved facet. For preliminary characterization a resonant laser (Laser 2) can be coupled in the IQPCs using a second lensed fiber on the opposite port. The collected signal was dispersed by a grating spectrometer and detected by a liquid nitrogen cooled charged-coupled device (CCD) camera or by single photon avalanche detectors (SPADs). The latter are connected to a time correlated single photon counting (TCSPC) electronics for time resolved detection. The acoustic part comprises two RF signal generators connected to two IDTs (colored golden) to generate SAWs. The two generators are locked by a 10 MHz clock and referenced to the TCSPC to establish a common time base of experiments. For preliminary IDT characterization a network analyzer replaces the signal generators. The fabricated IDTs were characterized employing vector network analysis. The measured transmission at room temperature with the sample being mounted on an impedance matched testboard is shown in Supplementary Figure 6 for the IDT device used as the PM. For the measurement, two IDTs on the same acoustic axis along [110] are used. At the resonance frequency of 519MHz the insertion loss of the delay line is 12.4 dB. As the delay line is symmetrical, this results in an electro-acoustic conversion efficiency of 24% for a single IDT. For low temperatures, the resonance frequency shifts to 525 MHz and the insertion loss increases to 28 dB. The increase of the insertion loss is attributed to an additional damping by the cryostat caused by longer rf-cables and a non-mode-matched electrical connection of the sample to the RF-cables due to spatial restrictions in the cryostat assembly. Overall, at low temperatures about 13% of the applied rf-power is transferred to the IDT electrodes. The electrical drive powers rf,PM and rf,SM specified in the main text are not corrected for this additional attenuation and correspond to the power applied to the cryostat connectors. The unmodulated device is designed in the cross-coupling configuration shown in Supplementary  Figures 7a and b, where the color-coded normalized optical field intensity is plotted as a function of position. The main panels show simulations of the light propagation obtained from beam propagation method (BPM) calculations. In these simulations, we assume an optical wavelength of @ABCDEF,G = 876.5 nm (Supplementary Figure 7a) and @ABCDEF,H = 880.5 nm (cf. Supplementary Figure 7b Figure 7b), respectively. As shown, the unmodulated, passive device is indeed designed in a crosscoupling configuration, i.e. Input A of the MZI and is coupled out via Output B. Conversely, Input B is coupled out via Output A. Next, we confirm the successful fabrication of such designed device using two single QDs located in different inputs and detecting the emission from the two outputs using a lensed optical fiber. Supplementary Figure 7c-d show measured emission spectra of two single QDs located in Input A and Input B, respectively. When the QD in Input A is excited (cf. Supplementary  Figure 7c), we detect a strong emission signal at Output B (right panel) while the intensity coupled out at Output A (left panel) is strongly suppressed. When switching to a QD in Input B (cf. Supplementary  Figure 7d), the situation is reversed, and a strong signal is detected from Output A (left panel) and a weak signal from Output B (right panel). Without SAW-modulation, the fabricated MZI near-ideally maps an inversion of the input photonic qubits |0⟩ → |1⟩ and |1⟩ → 0⟩ with high fidelities of 0.90 and 0.96, respectively. Figs S6 e and S6 f show the corresponding qubti rotations on the Bloch sphere. Supplementary Figure 8a shows the calculated optical transmission intensity when the refractive index difference ∆ $%% between the two interferometer arms in the acousto-optic interaction region increases linearly. The grey background area marks the modulation achieved in the experiment (cf. Figure 2c of the main manuscript) with ∆ 7EI = −∆ 7CJ marking the range of the effective refractive index change ∆ $%% that causes the optical phase shift G/L . Here, ∆ M is the static refractive index difference between the MZI arms which causes the device characteristic optical transmission pattern observed in the experiment. ∆ ′ is the increment of refractive index change for which the default, cross coupling configuration of the device is restored. Using these parameters, the time dependent transmission can be expressed as

Supplementary
(1) Here, @AB± ( ) is the intensity of the time dependent optical transmission of the acoustically tuned device 9 and is plotted in Supplementary Figure 8b for both Outputs B with @ABR ( ) and Output A with @ABS ( ) using ∆ $%% = ∆ 7EI = 0.00157.

Supplementary Note 3.5 -Acousto-optic spectral tuning of QDs
We analyze the spectral modulation of the emission of a single QD in the input arms using IDTSM. As shown in the schematic in Supplementary Figure 9a Supplementary Figure 10 shows measurement data from an acoustically modulated QD positioned in a single straight waveguide structure. For comparison, the false color plot shows spectral broadening (vertical axis) of the QD response for increasing acoustic powers (horizontal axis). Again, a temperature dependent shift of the emission spectra for high modulation powers is also observed as discussed above and is discussed in Supplementary Note 3.6. The spectrum for low acoustic modulation (-3 dBm, blue line), moderate modulation (11 dBm, red line) and the unmodulated case (dashed line, intensity not to scale) are highlighted in the panel to the right. In the lower panel the spectral broadening is again plotted in double-logarithmic representation as a function of \ T%,/& in units of √mW. Through a best fit to the data, we obtain = 1.13 ± 0.01. The green symbols show the integrated optical intensity of the main signal decreases to approx. 55% when increasing the RF power to 17 dBm.

Quantum Dots
In Supplementary Figure 11 we plot the energy shift of three self-assembled (In,Ga)As QDs as a function of the temperature of the cryostat cold finger (symbols). The measurement is conducted on a reference sample without IQPCs. The emitted photons are collected through the same objective through which the laser signal is focused on the sample to excite the QDs' emission. The corresponding lines are extrapolations to the experimental data 15 . Using these extrapolations, we obtain a temperature increase to ≈ 55 K for the measured spectral shift in Figure 2b of the main paper. This spurious heating can be suppressed by pulsed SAW excitation schemes 15 .
Supplementary Figure 11 -Temperature dependent spectral shift -Temperature dependence of the spectral response for three QDs (symbols) and fit to the data (lines).

Waveguide transmission
We assessed the dependence of the waveguide transmission on the applied RF power at room temperature and low temperature (7 K).
Supplementary Figure 12 -Impact of SAWs on the photonic transmission -Mean total photonic transmission measured for experiments at room temperature (RT) and at low temperatures (LT) with a SAW applied to modulate the phase.
Supplementary Figure 12 shows the mean of the photonic transmission as a function of applied RF power measured for three devices with MMI lengths of 300.5 µm, 314 µm and 326 µm each and at different optical wavelengths between 910 nm and 970 nm (Laser-2 in Supplementary Figure 4) at room temperature (red, 6 devices). At low temperature (green) the wavelengths of photons emitted by QDs varies from 873 nm to 913 nm between seven individual measurement series. The error bars for the mean transmission values for each SAW power measured are calculated as 1σ. These data show no significant optical transmission loss induced by the SAW generated by IDTPM at RT. At low temperatures, 7 K) a pronounced reduction is observed. This reduction may arise from a reduced emission intensity due to the elevated temperature. The blue symbols show complementary data from the measurement series analyzed in Figure 2c of the main manuscript which shows the same trend. Moreover, the data presented in Supplementary Figure 10 shows a similar reduction of the emission intensity at strong spectral drive supporting our assumption that the reduction of the signal intensity arises from heating.

Supplementary Note 4.2 -Intensity modulation of the two QDs selected for ( ) experiments
Supplementary Figure 14 shows pre-characterization data of the QDs used for the measurements of the second order autocorrelation functions (P) ( ) in Figure 3 of the main paper. Supplementary  Figure 14a presents the experimental configuration with one QD in Input WG-A (red) and another one in Input WG-B (black). The measured signals are collected through Output WG-B. Supplementary Figure 14b shows the measured PL-spectra of both QDs with the emission lines used for measuring (P) ( ) marked. Supplementary Figure 14c shows the time resolved measurement of the intensities of the two QDs with a SAW generated by IDTPM under same conditions as (P) ( ) was measured: the trace for Input A (red line) corresponds to Fig. 3a and the measurement for Input B (black line)