Supplementary information Supplementary figures Supplementary Figure S1. Characterization of the superconducting films. a) Atomic force microscope (AFM) measurements of the NbN film morphology after deposition onto silicon-on-insulator substrates with a root-mean-square (RMS) roughness of 1.6Ǻ. b) AFM measurement of a fabricated detector device with Hydrogen silsesquioxane (HSQ) protection layer. c) Critical current values for nanowire devices fabricated in this work (green markers), compared against literature values (blue markers). Red dashed line: linear fit to literature values, blue dashed line: linear fit to the experimental data in this work. p. 1
Supplementary Figure S2. Scanning electron migrographs of fabricated detector devices. The images show sections of nanowire detectors on top of silicon nanophotonic waveguides. The NbN wires are the light regions on top of the clearly defined waveguide structure. The high resolution images show uniform wire width throughout the detector length. p. 2
Supplementary Figure S3. Low-temperature measurement setup. a) Measurement scheme used to determine the SSPD performance. Pulsed optical light is generated using an electro-optical modulator driven by a 500MHz pulse generator. The modulated light is further attenuated using calibrated optical attenuators before being fed into the device using an optical fiber array. The detector circuits are biased with a battery-powered current source. Detected signals are analyzed using a high-speed oscilloscope and a to,ecorrelated single photon counting module. b) Schematic of the custom cryostat setup showing the location of the sample chamber inside the dewar. p. 3
Supplementary Figure S4. Calibration of the optical attenuators. Measurement of the individual attenuator linearity with varying input power and photorecievers. Two independent attenuators are used to supply up to 120dB of optical power reduction. The upper panels show the results for the first attenuator unit, the lower traces the results for the second unit. Panels from left to right correspond to results from different photodetectors. Both units show good linearity, independent on input optical power. p. 4
Supplementary Figure. S5. Calibration of the cascaded attenuators. a) The measured response of the two cascaded attenuators (unit #1 and unit #2) for high input optical powers. The plotted curves correspond to increasing attenuation levels from unit#2. b) The corresponding measurement from a) performed with single photon counting units, illustrating that the attenuators preserve linearity also at very low optical power. Cutoff regions are due to the count rate limit at high input, as well as at very low input powers due to the detector dark counts. p. 5
Supplementary Figure S6. Chip layout of fabricated devices. Optical micrographs of two sections of a fabricated chip, showing the arrangement of individual circuits. Shown are several on-chip detectors, as well as dedicated calibration coupler devices used to analyze the performance of the optical input/output ports. Different coupling wavelengths are obtained by varying the period of the grating, where the period is increased across the chip from the left to the right columns. The inset shows an SEM image of the coupling region. p. 6
Supplementary Figure S7. Calibration of the grating coupler transmission. Shown is the measured transmission through several calibration coupler devices for statistical analysis. The left column shows the transmission loss for up to 120 calibration coupler devices. The central coupling wavelength is varied between 1520nm and 1560nm. The right column shows the measured variation in the central wavelength where the highest coupling efficiency occurs. p. 7
Supplementary Figure S8. Dependence of the critical current on detector length. Shown is the measured dependence of the critical current I c on detector length for three sets of detector devices with a designed width of 70nm, 85nm and 100nm. The data traces are taken at identical experimental conditions, measured on sets of devices with equal nanowire width. The data shows that an increase in detector length preserves the critical current measured on shorter devices. p. 8
Supplementary Figure S9. An alternative detector design. a) Optical micrograph of a fabricated circuit showing optical input circuitry (waveguides, grating couplers and 50/50 splitter), RF contact pads and the SSPD in the top half of the figure; b) An SEM image of the on-chip meander detector located between the contact pads. This traditional meander structure is 4µm wide and shows detector wires of 100nm width with a gap of 100nm. NbN covered regions are colored in red. p. 9
Supplementary Figure S10. Cavity ringdown measurement in the through port. The cavity ringdown of on-chip microring resonators in the through port is analyzed for devices with different coupling gap. In the overcoupled case (a)) most of the incoming light is coupled into the ring, therefore the first pulse is small compared to light emerging out of the ring. Consecutive pulses coming out of the ring are strongly damped due to the loss into the feeding waveguide. The ratio between the initial two pulses changes when the coupling ratio is reduced (b)), leading to a pronounced through pulse and several consecutive pulses in the undercoupled case(c)). The round-trip delay of 73ps between the pulses is defined by the resonator length of 5.8mm. p. 10
Supplementary Methods Device fabrication The detector devices are fabricated from standard silicon-on-insulator (SOI) substrates manufactured by SOITEC with a silicon top layer of 220nm and a buried oxide layer of 3µm thickness. In order to enhance coupling of light guided inside the waveguides to the superconducting top layer, the silicon waveguiding layer is thinned down to expand the optical mode in the vertical direction. The thinning is achieved by dry-oxidizing the substrates and subsequently removing the resulting oxide top layer in buffered oxide etchant. The final top silicon thickness is then reduced to 110nm, as also used in previous experiments [42]. The prepared wafers are then covered with 3.5nm of NbN using DC magnetron sputtering. During the deposition no buffer layer is used at a substrate temperature of 850 C [43]. The prepared substrates are cleaned and heated to 120 C on a hotplate to remove residual water content. An optical lithography step is performed using lift-off resist (LOR5A) on top of 500nm photoresist (Shipley 1805) to define contact pads and alignment marks for subsequent electron-beam lithography steps. A 5nm chromium adhesion layer and 200nm gold are deposited using ebeam evaporation under ultra-high vacuum conditions. Lift-off is performed to define the metal structures in N-Methyl-2- pyrrolidon (NMP). A first electron-beam lithography step is performed using a 100kV EBPG 5000+ ebeam lithography system by VISTEC. In order to obtain high resolution hydrogen silsesquioxane (HSQ) ebeam resist in 2% concentration is employed to define the detector meander structures. Following development a first reactive ion etch step in an Oxford Plasmalab 80 system is performed to etch through the thin NbN film, using CF 4 chemistry. The step is timed carefully in order to not attack the silicon layer underneath. A second ebeam lithography step is then performed to define the nanophotonic circuits, using HSQ in 6% concentration in order to obtain a thicker resist layer on the order of 100nm (which is required for the subsequent RIE step). The photonic structures are then transferred into the silicon layer using RIE in chlorine atmosphere using inductively coupled etching in an Oxford 100 system. After fabrication the devices are inspected for lateral imperfections using high-resolution scanning electron microscope (SEM) images as shown in Supplementary Figure S2. p. 11
Several devices are screened and analyzed for lateral constriction of the meander width. From the high resolution SEM images scanned over long detector wires we find no wire defects which would be significant compared to the detectors dimensions. In order to characterize the uniformity of the film thickness we perform high resolution atomic force microscopy (AFM) measurements. First, we measure the surface morphology of the NbN thin films after deposition on the SOI substrates. The results are presented in Supplementary Figure S1a). From the AFM scans we determine an average RMS surface roughness of 1.6Ǻ. The measured value has to be compared to the RMS roughness of 1.1Ǻ determined on bare SOI substrates before the NbN deposition, indicating that the ultra-thin NbN layer closely matches the underlying silicon surface. From the measurements we estimate that thickness variations of the NbN film do not exceed a few percent. In addition the nanowires of the final detector devices are covered by a layer of HSQ ebam resist as shown in Supplementary Figure S1b), protecting the patterned NbN films from degrading during subsequent nanofabrication steps. We furthermore measure critical current (I c ) values of fabricated devices. In Supplementary Figure S1c) we compare the results for devices with a designed nanowire width of 70nm, 85nm and 100nm to critical current values reported in the literature for state-of-the-art nanowire detectors. Assembled are data records (blue markers) for detector devices with comparable film thickness (3.5nm-5nm) and high reported detection efficiency. In our devices we obtain relatively high critical current values for all fabricated wire widths. Even though there is a spread over the measured critical current, the obtained values compare favorably against the I c values measured in traditional SSPDs. As shown in Supplementary Figure S1c), the critical current values depend linearly on the width of the detector wires in first order approximation. In the figure above, the red dashed line is the best linear fit to the literature values, while the dashed blue line is the corresponding linear fit to our data. The Ic values measured for the thinnest wires (70nm) show a slight deviation from the linear fit, which results from a narrower nominal width after electron beam lithography. As expected the fitted slope intersects with zero, stating that with decreasing wire width the critical current decreases to zero. Furthermore, the higher slope p. 12
of the fit to our data confirms that our devices yield high critical current values compared to literature values. We then investigate the dependence of the critical current on the meander length for wire widths of 70nm, 85nm and 100nm. The devices are measured under identical experimental conditions at temperatures below 2K. As shown in Supplementary Figure S8 no obvious change is observed when the detector length is varied (within experimental error). This suggests that for the wire lengths considered in this work no noticeable degradation of the critical current (as a result of an increase in the number of constrictions) occurs when the detector length is increased. The high I c values allow us to operate the detectors in a high current regime, where high output pulse amplitudes are obtained. The above measurements therefore suggest combined that our devices offer uniform nanowires due to the compact detector design and reduced meander length. Calibration of the measurement setup Prior to device measurement the setup is calibrated in terms of attenuator performance and on-chip optical power. We employ both CW measurements and measurements with pulsed optical excitation. The measurement setup is illustrated in Supplementary Figure S3, showing the used pulsed optical source as well as the cryostat layout. During CW measurements the EO-modulator is removed. The sample is mounted on a moveable three-axis stage, allowing for reproducible positioning with closed-loop controllers. Fiber array and RF probes are aligned head-to-head and are adjusted with respect to the sample. In order to obtain calibrated optical power values we use tunable laser sources at 1550nm (New Focus 6428 and Santec TSL-210) combined with optical attenuators. We employ two identical attenuators (Tektronix OA5002), which provide up to 60dB attenuation each. Both instruments are calibrated separately as well as jointly. Fixed optical input power is fed into the attenuators and the output is measured with a calibrated low-noise photodetector (Newport Integrating Sphere 818-IS-1). When scanning detectors with high dark count rates we employ pulsed measurements in addition to CW excitation. In that case light from the tunable laser source is modulated with a high-speed lithium niobate p. 13
electro-optical modulator, driven by a pulse generator (HP8133a). The modulator provides extinction ratio in excess of 25dB between off and on-states. During the offstate, the signals are not registered during data acquisition, thus guaranteeing that no leakage light reaches the SSPDs. This configuration allows us to freely select both the duty cycle as well as the pulse duration. By employing two calibrated attenuators the average number of photons per pulse can be precisely controlled. Thus in combination with a pulsed characterization scheme, the probability of multi-photon events can be strongly reduced. Hence, the absolute number of dark counts registered during a measuring interval is reduced by the duty cycle compared to CW measurements, which allows us to characterize the detection efficiency very close to the critical current. Calibration of the optical attenuators In order to exclude detector influence, we measure the attenuation with several detectors as well as for varying input power. Both attenuators are calibrated separately to confirm the expected linearity particularly for higher attenuation values. Measured results are shown in Supplementary Figure S4. The upper panels show the measured attenuation for the first unit, obtained with three different photoreceivers (Tektronix OCP5002, hp81536a#1, hp81536a#2). The attenuation is measured for input powers from the tunable laser source employed in the detector measurements (Santec TSL-210) at input power levels of 0dBm and -10dBm. The lower traces show the results for the second attenuator unit. For both input powers the traces lie on top of each other. Furthermore, the transmitted power decreases exponentially with increasing attenuation value, as expected. Therefore over the specified attenuation region linear scaling is confirmed, in particular for high attenuation values. In order to make sure the equivalent performance is achieved at single photon levels we also calibrate the attenuators using gated single photon detectors (Id Quantique 200), which reproduce the higher intensity results as expected for passive devices. In Supplementary Figure S5a) we show the measured attenuation for the cascaded attenuators, again for different power levels. p. 14
The results confirm that the concatenation of our attenuator units again scales linearly with attenuation in db, as in the single attenuator case. At very high attenuation levels the noise floor of the photodetector is reached. In addition we also confirm the high-intensity results at single photon levels, using ID Quantique 200 single photon counters. The results are shown in Supplementary Figure S5b). The previous linearity results are reproduced, for a lower dynamic range due to the photon counter. At higher power levels the count rate is limited by the detector, whereas at low intensity levels the results are shadowed by the dark counts of the detector. From the above analysis we conclude that the attenuators do indeed perform the linear optical operation as expected, at high intensities as well as single photon levels. Therefore laser power coupled into the cascaded attenuators can be reduced to lower photon counts by increasing the attenuation level of each unit. Calibration of transmission of the on-chip grating couplers We next evaluate the statistical performance of our grating couples. We fabricate a large number of calibration couplers as shown in Supplementary Figure S6 for two sections of a fabricated sample. The calibration couplers consist of a grating coupler input and output port, connected by a 300µm long nanophotonic waveguide. By measuring the transmission through the device the coupling loss can be measured in dependence of wavelength [46]. Because of the short device length the propagation loss in the waveguide connecting the couplers is negligible. We obtain statistical coupling data by analyzing more than 100 devices. The coupling loss is measured for both the maximum transmission as well as the mean transmission over the optical bandwidth of the coupler. Because the device obeys optical reciprocity, the coupling loss at both ports is identical. This is also confirmed by measuring the transmission in reverse direction (from output port to input port), where identical transmission loss is obtained. Furthermore, we fabricate three-port devices with two output couplers for a balanced detection as described in the main text. Also in this case we obtain identical transmission in both output couplers, confirming the expected optical reciprocity. By varying the period of the grating coupler, we also determine the coupling loss at different wavelengths. The actual device geometry is shown in the SEM p. 15
image in the inset of Supplementary Figure S6. From the combined data we obtain the coupling loss spread of the input/output ports. Results are shown for 120 measured devices in Supplementary Figure S7. The devices are distributed among the detector devices on the chip and thus give a representative picture of the coupling loss over the chip area. Broken calibration coupler devices are identified by SEM inspection and excluded from the analysis. In the left column of Supplementary Figure S7 we show the measured transmission loss for several detector devices. The panels from top to bottom correspond to different designed coupling wavelengths. From the results we determine a mean coupling loss of -13.1dB for the couplers design for 1554nm. The coupling loss corresponds to the point of maximum transmission, indicated by the blue curves in Supplementary Figure S7. From the data points we extract a standard deviation of 0.7dB. We also measure the average coupling loss over the bandwidth of the coupler, shown by the red traces in Supplementary Figure S7. In this case we obtain an average coupling loss of -16.4dB. In this case the standard deviation of the coupling loss amounts to 0.6dB, which is slightly below the maximum coupling loss value. The number quoted in the main text with respect to the grating couplers is the standard deviation of the coupler transmission in db, which is obtained from measurements of the transmission through many dedicated calibration coupler devices on the same chip. We routinely obtain statistical spread on this order due to repeatable e-beam writing conditions, but wanted to make sure that the same numbers are valid on the measured chip. The calibration coupler devices are placed very close to the detector devices and therefore written under identical conditions (exposed together). The standard deviation is n N obtained as σ = var = 1 ( T mean( T) ) n 2 for each coupler transmission T n in the measured ensemble with N measurements. We then measure a 1-sigma deviation in the absolute coupling loss of 0.7dB. We also determine the mean value and standard deviation for the pulse transmission. In this case the standard deviation is even lower (0.6dB) and the mean is reduced, because of the Gaussian profile of the coupler transmission. Of course, for a given device, the transmission can be measured with much better confidence, by performing direct transmission measurements. The power extracted p. 16
from the two output ports on the same device are identical within 0.2dB (5%) in the absence of detectors. Procedure used to determine the on-chip detection efficiency After verification of the linearity of the setup both at low power level (with power meters) and at the single photon level (with ID Quantique single photon detectors) we align the sample to the fiber array and RF probe, which are mounted head-to-head. Subsequently, we measure the optical transmission through the device at the target temperature, in both the control port and the through port (which passes underneath the detector). Knowing the coupling into the device, we evaluate the optical power on the waveguide (as also previously done in our measurements on gradient optical forces, for a detailed description see our previous work [42,45]. Independently we confirm the splitter operation using Mach-Zehnder Interferometers [42,45]. In these we realize on-chip interference with extinction ratio approaching 33dB, thus also indicating that the splitter has a splitting uncertainty far below 0.1%. The 50/50 splitter is further tested with a balanced device without NbN cover, which also confirms that the splitter works near-ideal (besides it being a very simple device to fabricate). Thus the splitter transmission loss T s is given as T s = 3dB. The overall transmission T through the device is now composed of three parts: a) the coupler transmission at the input T 1, the transmission through the splitter T s at the 50/50 partition and the transmission at the output coupler T 2. Thus the total transmission through the calibration port is given as P cal = P in *T=P in *T 1 *T s *T 2 and the power going to the detector is P d = P in *T 1 *T s From the transmission measurements we find at the used wavelength for detection calibration of 1545nm an overall transmission loss of T = 29. 37dB and hence the coupler loss as T cp = 13. 19dB (assuming T cp = T 1 = T 2 ); thus the power coupling loss to the waveguide leading to the detector is T = T T = 16. db ). wg cp s 19 In the next step we measure the optical power coupled into the device. First, the optical loss from the laser, through the modulation setup and the fibers is measured and confirmed with independent photodetectors. We measure average optical input power p. 17
before the attenuators of -10.15dBm (close to 100µW). Then we measure the power attenuation given by the optical attenuators. We calibrate the attenuators independently and jointly. The attenuation is measured for high laser input powers as well as reduced input powers without deviation from the expected value. On top we also obtain the attenuation under very low photon number input using single photon counters, again with identical attenuation value. The attenuation is measured to be Att = 72. 61dB. We then determine the photon count rate on the waveguide leading to the detector. Knowing the input wavelength of 1545nm, the photon energy is given as E ph = ħ ω = 1.2857e 19J. Using the input power, the transmission coefficient to the detector and the attenuation, the optical power on the waveguide leading to the detector is P P wg = 1.27e 13W, which is equivalent to a photon flux of wg Fph = = 9.9e5Hz (or E equivalently 0.0198 photons per pulse). Then after choosing the proper biasing condition for the detector the photon count rate is measured with the PicoHarp300. The discriminator value is adjusted until no change in count rate is reliably observed, which is simple due to the large signal we get because of the high critical current values (28µA, 400mV pulse height). We monitor the count rate over prolonged periods of time to establish the real count rate. The maximum count rate registered close to I c is F = max 9.01e5 Hz. ph Experimental determination of the device timing jitter The timing jitter of our devices is obtained from using a digital oscilloscope (Agilent Infiniium 54855A) in histogram mode. The oscilloscope provides electrical bandwidth of 6GHz, which is the limiting bandwidth because of the used wide bandwidth electrical amplifiers (15GHz) as described in the main text. The timing jitter is measured by triggering the oscilloscope at the point of maximum slope of the incoming pulses from the SSPDs. From the time trace of the pulse front we obtain a pulse slope of 8µV/ps for the device before electrical amplification, given the measured critical current of the detector of 28µA and return current of 5µA. The pulse amplitude rises up to 1.1mV. Using a thermal noise estimate at 300K for our oscilloscope bandwidth of 6GHz, the p. 18
obtained 70.5µV rms translate into 70.5µV*2.355 at FWHM. Thus the measurement limited jitter is therefore given as 20.7ps, which is close to the measured detector jitter of 18.4ps. The true device timing jitter may be even lower than the measured value shown in Fig.4 due to restrictions from the electrical instrumentation. Alternative detector design For comparison with the travelling wave detector design we also fabricate additional detector chips following a more traditional detector layout similar to normal-incidence SSPDs. In this case the SSPD is arranged in a long meander form which results in a subwavelength [44] multi-mode interference (MMI) structure as shown in the optical micrograph in Supplementary Figure S9a). In such a configuration only one electron-beam lithography step is required, assisted by an additional optical lithography step with less stringent alignment tolerance requirements. Differing from the SSPD design introduced in the main text and the fabrication routine outlined above, the meander structure is transferred both into the NbN and the underlying silicon substrate by a combined CF4/Cl2 etching step as shown in the SEM image in Supplementary Figure S9b). The meander wire thickness is kept at 100nm, while a filling factor of 50% is used for the MMI, therefore the gap between neighboring meander-wires is also 100nm as shown in the inset in Supplementary Figure S9b). From FDTD simulations of this alternative design we estimate 20dB attenuation over a MMI length of 10µm. However, the MMI also provides reflection loss at the input, as well as scattering loss along the sub-wavelength grating. In addition, part of the incoming waveguide is covered by unwanted NbN due to necessary alignment offset designed for optical lithography. Therefore the overall detection efficiency is reduced, as shown in Figure 2 in the main text (purple markers), reaching a best efficiency of 3% close to the critical current. In addition, the longer meander length leads to a detector decay time on the order of 5ns, for a 4µm wide MMI. Ballistic photon cavity ring-down In order to analyze the time-domain ring-down we consider the excitation of a microring resonator by an optical mode propagating along the waveguide. The coupling between p. 19
the waveguide and the cavity electrical fields are described by the coupling constant κ and the transmission coefficient t. α is the linear attenuation inside the resonator caused by absorption, scattering and radiation. Because of time reversal symmetry and energy 2 2 conservation we have t + κ = 1. For a high Q cavity, both α and κ are small. When discrete optical pulses (instead of a continuous wave) are launched into the resonator, the resonator response for a cavity with a ring-down time constant τ 0 can be analyzed directly in the time-domain. For pulse propagation with a pulse duration τ p < τ 0, we need to treat the pulse as a ballistic particle. Instead of using electrical fields, we consider the optical intensity to describe the light propagation. As a result the optical power circulating inside the cavity will not build up. The 1 st pulse (or input pulse) will have an optical power after passing the cavity given by: I = 2 0 t I i (S1) Similarly the n th pulse will reemerge from the cavity with a power of 2 2 2n 2 I n = (1 t ) t exp( nl) α I ( S2) i Therefore the intensity ratio observed in Supplementary Figure S8 between pulses is given by I I n 0 2 = (1 t ) t 2 2n 4 exp( αnl) I ( S3) i For the very first pulse emerging from the ring (n=1), the ratio can be larger than one if t is small, which corresponds to very strong coupling. The theoretical framework is validated experimentally by measuring ballistic transport in the through-port of an optical resonator with a cavity length of 5.8mm. The cavity length again gives rise to a round-trip time of 73ps as in the main text. As shown in Supplementary Figure S10a), when the resonator is strongly coupled to the input waveguide the transmission parameter t is small. Therefore a large fraction of the incoming light is coupled into the resonator and the directly transmitted input pulse is small in amplitude compared to the first pulse coupled out of the resonator. When the p. 20
coupling into the ring resonator is reduced by increasing the coupling gap, the intensity ratio between the transmitted input pulse and the pulse train coupled out of the ring resonator is reversed. In Supplementary Figure S10b) we show the time-domain trace for a slightly overcoupled resonator. In this case the intensity coupling constant is smaller and therefore the transmitted pulse is comparable in amplitude to the pulse coupled out of the ring resonator. When the coupling gap is further reduced to operate the device in the undercoupled regime (Supplementary Figure S10c)), the amplitude of the directly transmitted pulse is much larger than the following pulse train, due to the weak interaction between the input waveguide and the ring resonator. Supplementary References 42. Li, M. et al., Harnessing optical forces in integrated photonic circuits, Nature 456, 480-484 (2008). 43. Cherednichenko, S., Yagoubov, P., Il'in, K., Gol'tsman, G., and Gershenzon, E. in Eighth International Symposium on Space Terahertz Technology. (ed R. Blundell, Tong, E.) 245. 44. Schmid, J. H. et al, Subwavelength Grating Structures in Silicon-on-Insulator Waveguides, Advances in Optical Technologies 2008, 685489-685496 (2008). 45. Li, M. et al., Tunable bipolar interactions between guided lightwaves, Nature Photonics 3, 464-468 (2009). 46. D. Taillaert, et al., Compact efficient broadband grating coupler for silicon-oninsulator waveguides, Opt. Lett. 29, 2749-2751 (2004). p. 21