Wavelength-Sensitive Superconducting Single-Photon Detectors on Thin Film Lithium Niobate Waveguides

Lithium niobate, because of its nonlinear and electro-optical properties, is one of the materials of choice for photonic applications. The development of nanostructuring capabilities of thin film lithium niobate (TFLN) permits fabrication of small footprint, low-loss optical circuits. With the recent implementation of on-chip single-photon detectors, this architecture is among the most promising for realizing on-chip quantum optics experiments. In this Letter, we report on the implementation of superconducting nanowire single-photon detectors (SNSPDs) based on NbTiN on 300 nm thick TFLN ridge nano-waveguides. We demonstrate a waveguide-integrated wavelength meter based on the photon energy dependence of the superconducting detectors. The device operates at the telecom C- and L-bands and has a footprint smaller than 300 × 180 μm2 and critical currents between ∼12 and ∼14 μA, which ensures operation with minimum heat dissipation. Our results hold promise for future densely packed on-chip wavelength-multiplexed quantum communication systems.


S-1. Coupling efficiency of the TFLN waveguides.
A room temperature characterization was carried out to evaluate the response of dedicated test structures used to assess optical losses of waveguides without SNSPD.This allowed the systematic characterization (at  !""# ) of grating couplers similar to the ones used for the devices discussed in the main text.Figure S-1 shows the measured transmission of one of these test structures (and the simulated response accounting for the effect of the grating couplers).The  !""# characterization was implemented using single mode fibers positioned in the proximity of the chip surface (instead of the focusing lens mounted in the cryostat described in the main text).After replacing the fiber for a properly positioned lens and adjusting the geometrical parameters of the grating couplers (relying on the result of atomic force microscopy of the fabricated S3 devices), the same simulation tools was used to evaluate the response of the cryogenic device.
The result of the simulation for the cryogenically characterized devices is shown in the inset of Figure 4(a) in the main text.

S-2. Accuracy of the waveguide integrated wavelength meter.
The complete responsivity matrix of the waveguide integrated wavelength meter accounts for wavelengths in the range: 1520 nm -1630 nm and currents from 0 µA to 15 µA.By choosing bias currents setpoints between 5.6 and 7.1 µA (i.e.restricting the study to the subset of the responsivity matrix highlighted in Figure 4(a) in the main text), the normalized average photon count rate  &&&&&& provides a wavelength accuracy of ~ 15 nm on the whole C-and L-bands (see Fig. 4(b) in the main text).After this first rough characterization, the measurement accuracy can be improved selecting a different set of currents ( $%& ′ ).This is shown in Fig. 5 of the main text for four different wavelength ranges.Table S-T1 describes how to choose  $%& ′ to obtain the optimal sensitivity for different wavelength ranges between 1520 nm and 1630 nm.Unless differently specified, the normalization current amounts to  '"(# = 10 µA.
In the first column, R1 represents "range 1", a rough wavelength range obtained through the  &&&&&& measurement as per Figure 4(b) in the main text.Iterating a second time the analysis with different bias currents setpoints ( $%& ′, in the second column of the table), it is possible to reduce the wavelength uncertainty (Δ , see the third column of the table).In some cases, it is worth repeating the process a third time (starting from the information acquired in the second iteration, "range 2" -R2) to further reduce Δ.Here, as in the main text, the uncertainty Δ is defined as one standard deviation of the experimental points from the linear fit.
Different devices were probed (see also Figure S-2).The best accuracy we could measure amounts to ~ 4 nm, corresponding to an uncertainty of ± 2 nm, for the case represented in Fig.
5 (d) in the main text.An uncertainty of ±4 nm was obtained on the whole C-and L-bands.Our measurements are limited by coupling efficiency and electronic noise.Improved results could be obtained with better coupling structures and cryogenic amplification of the detector's output.All the measurements we report on the wavelength meter capabilities were performed using CW laser sources.The wavelength meter performance would be negatively affected by waveguide dispersion if short light pulses were used as optical input.Dispersion free waveguides for the wavelength range of interest could be engineered to retrieve a good wavelength meter performance also in case of short light pulses signals.

S-3. Stability of the measurement set up.
The robustness of our measurements against vibrations and alignment drifts is granted by choosing a proper integration time and by mounting the focusing lens (used to couple the optical signal into the waveguides) monolithically with respect to the chip.In this way the environmental disturbances leading to a small perturbation of the path followed by the input beam correspond to a negligible change in the position where the input is collimated onto the grating coupler.This was tested (for multiple wavelengths) by monitoring the number of counts S6 while inputting constant optical power and keeping fixed the bias current.The result of this analysis is plotted in Figure S-3.

Figure S- 1 .
Figure S-1.Transmission spectrum obtained at room temperature from a waveguide structure

Figure
Figure S-2.PCR map for a different device from the one analyzed in the main text.The

Figure S- 3 :
Figure S-3: Stability of the measurement.(a) Count rate of a device measured over 10 minutes at

Figure
Figure S-4: (a) Mode simulation accounting for a misaligned detector (waveguide thickness =