Cavity-Enhanced and Ultrafast Superconducting Single-Photon

Oct 19, 2016 - By integrating the nanowire into a photonic crystal cavity, we recover high absorption efficiency, thus enhancing the detection efficie...
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Letter pubs.acs.org/NanoLett

Cavity-Enhanced and Ultrafast Superconducting Single-Photon Detectors Andreas Vetter,*,†,‡ Simone Ferrari,†,§ Patrik Rath,†,§ Rasoul Alaee,‡ Oliver Kahl,†,§ Vadim Kovalyuk,†,∥ Silvia Diewald,⊥ Gregory N. Goltsman,∥,# Alexander Korneev,∥,¶ Carsten Rockstuhl,†,‡ and Wolfram H. P. Pernice†,§ †

Institute of Nanotechnology (INT), Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany Institute of Theoretical Solid State Physics (TFP), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany § Institute of Physics, University of Münster, 48149 Münster, Germany ∥ Department of Physics, Moscow State Pedagogical University, Moscow 119992, Russia ⊥ Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany # National Research University Higher School of Economics, Moscow 101000, Russia ¶ Moscow Institute of Physics and Technology (State University), Moscow 141700, Russia ‡

S Supporting Information *

ABSTRACT: Ultrafast single-photon detectors with high efficiency are of utmost importance for many applications in the context of integrated quantum photonic circuits. Detectors based on superconductor nanowires attached to optical waveguides are particularly appealing for this purpose. However, their speed is limited because the required high absorption efficiency necessitates long nanowires deposited on top of the waveguide. This enhances the kinetic inductance and makes the detectors slow. Here, we solve this problem by aligning the nanowire, contrary to usual choice, perpendicular to the waveguide to realize devices with a length below 1 μm. By integrating the nanowire into a photonic crystal cavity, we recover high absorption efficiency, thus enhancing the detection efficiency by more than an order of magnitude. Our cavity enhanced superconducting nanowire detectors are fully embedded in silicon nanophotonic circuits and efficiently detect single photons at telecom wavelengths. The detectors possess subnanosecond decay (∼120 ps) and recovery times (∼510 ps) and thus show potential for GHz count rates at low timing jitter (∼32 ps). The small absorption volume allows efficient threshold multiphoton detection. KEYWORDS: Superconducting nanowire single-photon detector, nanophotonic circuit, multiphoton detection, photonic crystal cavity fficient on-chip photon detection sensitive down to the single-photon level is essential for integrated photonic applications, enabling the realization of complex optical circuits and functionalities. Key requirements for integrated singlephoton detectors (SPDs) are high detection efficiencies and timing performance, low detector noise, and a scalable fabrication procedure with a low level of imperfections. SPDs which excel among all of these performance metrics are needed for optical quantum computing1−3 and quantum communication4 but equally for selected and challenging classical nanophotonic applications.5−7 A promising solution for efficient on-chip SPD are waveguide-integrated superconducting nanowire single-photon detectors (SNSPDs).8−10 On-chip SNSPDs exploit evanescent near-field coupling of a guided optical mode to an absorptive nanowire on top of a waveguide for highly sensitive detection. When operated below the critical temperature, the transient breakdown of superconductivity upon photon absorption in the

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current-biased nanowire leads to a corresponding signal in the connected readout circuitry.9 A “click” is generated. The onchip detection efficiency (OCDE) of such devices is given by the product of absorption efficiency and internal quantum efficiency (IQE). While the latter depends on bias current, material properties, energy of the absorbed photons, and crosssection of the nanowire,11,12 the absorption efficiency is mainly governed by the coupling strength to the absorptive nanowire and by the interaction length of the photons traveling along the waveguide.13 In order to enhance the absorption efficiency, the interaction length of the coupled system can be increased by elongating the nanowire.10,14 This, however, also increases the detector footprint and reduces the speed. Upon a detection event, the Received: August 9, 2016 Revised: October 16, 2016 Published: October 19, 2016 A

DOI: 10.1021/acs.nanolett.6b03344 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. Cavity-integrated superconducting nanowire single-photon detectors (SNSPD). (a) Colorized scanning electron microscopy (SEM) image of a fabricated device. Photonic elements (blue) allow to send a well-calibrated photon flux to the nanowire (red) connected to gold contact pads (yellow). (b) Colorized SEM image of a microbridge nanowire (red) integrated in a photonic crystal (PhC) cavity consisting of air holes inside the waveguide (blue). (c) SEM images of a U-shape waveguide-integrated SNSPD fabricated for comparison on the same chip.

reflectors, designed with the narrow part atop the waveguide. Due to its compact size and straight geometry, our nanowire design is less susceptible to fabrication imperfections11,27 and avoids the effect of current crowding,28,29 i.e., the reduction of the critical current IC emerging in curved nanowire geometries, compared to the established U-shape nanowire geometry (Figure 1c). The spatial separation of front reflector, nanowire, and back reflector allows us to describe the optical response of the system with a Fabry−Perot model that governs the amplitude of the lowest order guided mode in the waveguide. The model takes into account multiple reflections at the individual photonic elements.30 In the model, we relate analytically the scattering and absorption properties of the nanowire and the reflection and transmission properties of the front and back reflector to the overall spectral response and the loss contributions. The single mode waveguide and the PhCs are optimized for transverse electric (TE)-like polarization. The individual reflection and transmission coefficients for the lowest order TE polarized guided mode at the PhCs and the nanowire, rij and tij, are obtained from full wave finite-element simulations and are evaluated at the transition from section i to j. First, for illustrative purpose, we apply the model only to the subsystem consisting of the nanowire and the back reflector (Figure 2a). Subsequently, the model is extended to describe the entire detector, including the front reflector. The combined reflection coefficient r24 of the nanowire and the back reflector is subject to Airy’s formula31

time needed for a complete recovery of the original detection efficiency is limited by the kinetic inductance.15 This quantity is proportional to the nanowire length. Therefore, a longer nanowire raises the absorption efficiency but increases the recovery time as well. This trade-off between detector speed and absorption efficiency is inherent to SNSPDs. Different approaches to enhance the detection speed have been adopted, including the use of superconducting materials with low kinetic inductances16,17 or parallel nanowire geometries.18−21 In the former concept, the fundamental limit for the recovery time is imposed by the material properties of the superconducting film. The latter approach, based on a cascade-switching mechanism, suffers from operation instabilities and signal after-pulsing, imposing a limit on the attainable recovery time.22 Here, we overcome the trade-off between absorption efficiency and detector speed by aligning the superconducting nanowire made from niobium nitride (NbN) perpendicular to the waveguide and not parallel, as considered thus far. Together with the contact pads, this gives the detector a microbridge geometry.23,24 Such a design renders the detector fast, but because of a strongly reduced interaction length it only provides low absorption efficiency. To nullify this drawback, we capitalize on a coherent perfect absorber (CPA) concept25 and integrate the nanowire into a suitably designed optical cavity.26 The cavity is made from photonic crystal (PhC) elements consisting of air holes etched into the waveguide. The back mirror of the cavity is perfectly reflecting at the frequency of operation. The front mirror is only partially reflecting. Thereby, the entire cavity is designed such that directly reflected light at the front mirror destructively interferes with light that experience multiple round trips in the cavity. Since the only escape path for the photon energy is dissipation in the nanowire, the absorption is strongly enhanced thanks to CPA. The entire device is a part of a silicon-on-insulator (SOI) nanophotonic circuit and thus fully integrated. Figure 1a shows the detector design, comprising of photonic components and electric contact pads. A close-up view of the detector inside a waveguide cavity is provided in Figure 1b. The absorptive nanowire is situated in between front and back

r24 = r23 +

t 23t32r34e 2iφ3 1 − r32r34e 2iφ3

(1)

2π

where φ3 = neff (λ) λ l3. The effective refractive index neff of the guided mode is extracted from mode simulations, while λ indicates the wavelength and l3 is the distance between both elements. The front reflector is integrated in complete analogy into the model, considering the combined response of the back reflector and the nanowire given by r24. Consequently, the total B

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Figure 2. (a) Pictorial representation of the Fabry−Perot model. r and t denote the complex reflection and transmission coefficients, respectively. Simulated values are provided in the SI. The coefficient r24 for a combination of nanowire and back reflector can be obtained by adding up multiple reflections, leading to Airy’s formula. (b) Energy dissipation in the cavity as a function of the two phases φ2 and φ3, i.e., using eqs 1 and 2. Reflectors and nanowire are simulated at a wavelength of 1550 nm. The upper graph shows the data along the dashed line. For negligible out-scattering losses, the absorption efficiency of unity can be achieved. (c) Spectrum of the detector showing distinct resonances. The design is optimized for a wavelength of 1550 nm. The absorption in the nanowire without cavity amounts to 5.8%, while out-scattering losses contribute 0.5%.

reflection coefficient rtot of the assembled detector design is given by rtot = r12 +

(5.4%) per pass. Out-scattering losses are estimated as 0.15 dB (3.5%) per pass. Waveguide crossings are a well-investigated issue in integrated photonics,32−35 and sophisticated design approaches to reduce losses to 0.03 dB have been demonstrated likewise for our selected fully etched SOI waveguide geometry.36 The validity of the nanowire absorption model has been also verified by fabricating selected elements and characterizing them. Comparison to the simulated predictions showed a good agreement (see SI). The Fabry−Perot model provides a clear guideline for designing the coherent perfect absorber. Considering the presence of the junction and out-scattering at other elements of the cavity, an actual absorption of 55% of the impinging light in the nanowire can be reached. Using full wave simulations of the actual structure to obtain the respective optical coefficients of each subelement, we derive all geometrical details of the entire device. Based on these designs, we realized microbridge detectors with various configurations of PhC cavity and nanowire geometry (Figure 1b) as well as U-shape nanowire detectors (Figure 1c) to directly compare their performance. The nanowires are fabricated from 4 nm thick NbN films, deposited by reactive magnetron sputtering on 220 nm thick silicon atop a 3 μm buried oxide layer. In three lithographical steps, the detector design is transferred to the chip. Focusing grating couplers (Figure 1a) are used to couple external laser light into the photonic integrated circuit and to collect light transmitted through a reference branch. A balanced waveguide design allows to calibrate the incident photon flux at the detector’s site by correcting for coupling and propagation losses37 (see SI). Optical fibers and a RF contact probe provide optical and electrical connection to the device under consideration. A multiaxis piezo nanopositioner enables to access several devices in succession. Device characterization is performed inside a helium flow cryostat with a base temperature of 1.7 K. More details about the fabrication procedures and measurement setups are provided in the SI. As indicated in Figure 2c, the absorption spectrum of the cavity-integrated detectors exhibits a pronounced resonance. In the following, we focus on the detector design revealing the best on-chip detection efficiency (OCDE) of all devices under examination. The OCDE is defined as the ratio of the count rate to the impinging photon flux on the cavity (Figure 1a) and hence an appropriate quantity to characterize the complete

t12t 21r24e 2iφ2 1 − r21r24e 2iφ2

(2)

2π

with φ2 = neff (λ) λ l 2 , being a function of l2, the distance between front reflector and nanowire. At vanishing transmittance through the cavity (which is achieved with a sufficient number of holes in the back reflector and choosing a set of parameters such that the frequency of operation lies within the Bragg gap of the PhC back mirror), in combination with the two phases φ2 and φ3, the reflection coefficients r12 and r21 have to be adapted to minimize rtot at the resonance wavelength. The minimal total reflection implies maximum absorption of light in the nanowire, given by 1 − |rtot|2. No reflection occurs if light which is directly reflected at the front reflector (as described by the first term) interferes destructively with multiple reflections of the system of nanowire and back reflector (second term). Figure 2b depicts the dissipated energy as a function of the relative phases φ2 and φ3 for an optimized front reflector design. Such a Fabry−Perot model greatly reduces the simulation overhead, since it allows to individually optimize nanowire, front and back reflector with respect to reflectance, transmittance, and losses. Moreover, we obtain an analytic understanding of CPA in the structure. Selected results that compare prediction obtained with the Fabry−Perot model and with full wave simulations are shown in the Supporting Information (SI). Apart from out-scattering losses due to the impedance mismatch of Bloch and guided modes at the interface between the PhCs and the waveguide sections,30 the main contribution to losses arises from the silicon remaining underneath the electrical connection of the nanowire (Figure 1b). We note that these silicon side-wings only serve the purpose to provide structural integrity and remain after fabrication of the devices. This supporting structure can be considered as another waveguide crossing. The lateral mode confinement is reduced at the junction, and the resulting mode mismatch causes outscattering and coupling to the crossing structure. For typical dimensions (nanowire width 100 nm, thickness 4 nm), the simulated absorption of the nanowire amounts to 0.23 dB C

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Figure 3. (a) Spectrally resolved on-chip detection efficiency (OCDE) for different devices with varying distance l2 between front reflector and nanowire. The nanowire width is 90 nm, and the bias current is set to 0.9IC for each individual detector; all other parameters are kept constant. Solid lines present a Lorentzian fit to the measured data. Varying l2 between 1 and 2 μm leads to resonance wavelengths of 1516.2, 1517.1, 1523.9, 1529.6, 1532.6, and 1535.7 nm, with quality factors of 247, 218, 208, 275, 272, and 280, respectively. Inset: Resonance wavelength as a function of the distance between front reflector and nanowire. Data points in gray are not indicated in the main plot. Gray solid lines indicate the change of the resonance wavelength with varying distance l2 and represent a guide for the eye. (b) OCDE and DCR on logarithmic scale for selected devices at the respective resonance wavelength as a function of normalized bias current. The same symbols as in panel a are used. The DCR is indicated for a single device with an integration time of 1 h per data point. Blue circles denote no dark count within this time interval. We attribute the variation in the DCR to short-lived electronic noise inherent to our setup, rather than to the detector itself. Inset: OCDE on linear scale. Error bars are omitted for clarity.

(∼34 μA) on the same chip. A further investigation of latchinglimited operation could be performed by determining the experimental critical current of microbridge nanowires with artificially increased kinetic inductance, e.g., by prolonging the nanowire. Nevertheless, efficient photon detection is possible because the OCDE can reach saturation in our devices. The dependence of the OCDE on the normalized bias current IB/IC (Figure 3b for selected devices) exhibits a monotonous rise with increasing bias current.10,12,42 The OCDE starts to saturate near the experimental critical current, as can be seen in a linear scale (inset of Figure 3b). Such saturation allows biasing the nanowire at currents below Ilatch without compromising the detection properties as efficiency and speed. A broad saturation behavior is observed even for a nanowire width of 110 nm for detectors fabricated on a different chip (see SI), starting from bias currents of IB ∼ 0.7IC. We attribute this variation to differences in the internal quantum efficiency due to the quality and/or stoichiometry of the NbN film. The maximum OCDE of 30% is compared to our model of the detector layout under consideration. Simulations reveal a maximum possible absorption efficiency of 55% at resonance, limited by out-scattering losses. This value is obtained from simulations of the nanowire alone and by comparison to the ratio of absorption to out-scattering losses (see SI). The OCDE can be improved by better adapted reflectance of the front reflector, further minimizing transmittance through the cavity, and higher IQEs depending for example on nanowire width. In addition, longer detectors would increase Ilatch and allow higher bias current but decrease the detector speed. A direct comparison between the findings of the Fabry−Perot model and experimental data is challenging because of the uncertain etch depth of the PhC holes, affecting both amplitude and phase of reflection and transmission coefficients (see SI). However, CPA strongly enhances the absorption in the device by more than an order of magnitude compared to devices without a cavity. Improving the absorption efficiency would allow to approach the performance of SNSPDs in U-shape geometry featuring a comparable nanowire width of 100 nm,

detector design for on-chip single-photon detection. The nanowire width is 90 nm, as confirmed by SEM imaging, and all devices exhibit consistent critical currents IC around 23 μA at 1.7 K. The waveguide geometry features an asymmetric PhC cavity consisting of a seven-hole front reflector and a 13-hole back reflector (Figure 1b and 3b). The reflectors are followed by a linear tapering with hole radii between 70 and 100 nm and center-to-center distances between the holes of 320 to 400 nm, as obtained from finite-element optimization to reduce outscattering losses (see SI). In the following we compare the figures of merit obtained for our detectors to waveguideintegrated SNSPDs in U-shape geometry, as given by Pernice et al.,10 which are used, e.g., for the characterization of on-chip single-photon emitters.38 We vary the spatial separation l2 between front reflector and nanowire between 1.0 and 2.1 μm in order to tune the resonance wavelength. Figure 3a shows several on-chip detection efficiency spectra obtained by normalizing the count rate to the photon flux impinging on the cavity in dependence of wavelength. The best device features a maximum OCDE of 30% at a wavelength of 1523.8 nm and a bias current IB = 0.9IC. This corresponds to a system detection efficiency (SDE) of 0.89% (see SI). A Lorentzian fit of the spectra reveals a resonance full width at half-maximum (fwhm) of 6.2 nm on average. Due to the limited bandwidth of the grating couplers, only one resonance per detector can be observed. An additional parameter to control the detector operation besides the detector design is the magnitude of the bias current IB, with an upper limit imposed by the experimental critical current IC of the nanowire. Fast SNSPDs typically suffer from detector latching, i.e., a feedback mechanism which renders the nanowire normal conducting and insensitive to subsequent photons at bias currents above a latching current Ilatch.39−41 Our results indicate that here the experimental critical current IC is limited by Ilatch rather than the depairing critical current of the nanowire. This hypothesis is supported by slightly lower critical currents compared to the U-shape geometry in previous work (∼28 μA10) and the higher values found in U-shape detectors D

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Figure 4. (a) Averaged pulse shapes for different nanowire geometries (width 100 nm) in microbridge and U-shape design biased at a current of 0.9IC. Solid lines represent exponential fits to the data. Inset: 1/e decay times, obtained from the exponential fits, as a function of the kinetic inductance which is renormalized to the longest U-shaped nanowire.15 The black line represents a guide for the eye. (b) Single- and multiphoton detection with a cavity-integrated microbridge nanodetector. The detection probability is plotted on a log−log scale as a function of the average photon number in an attenuated laser pulse for different bias currents IB. Detection regimes are indicated by linear fits.

about 80 ps.19 The compact design provides a roughly four times smaller decay time compared to 10 μm long U-shape devices reported by Pernice et al.10 with decay times down to 455 ps. We did not observe detector latching up to bias currents near the critical current, because the low kinetic inductance leads to a lower heat load induced to the nanowire compared to larger nanowire geometries.41 After the successful recording of a detection event, the SNSPD requires a finite recovery time before it is able to detect the next photon with high detection efficiency.43 The recovery time is determined by the return of the bias current to the detector,15 i.e., the combination of rise and decay time it takes to recover the detection efficiency to the steady-state value after a detection event. For our microbridge nanodetectors, the recovery time is not dominated by the decay time only,12 and thus the rise time of the signal contributes significantly. To estimate the maximum possible count rate, we thus define the recovery time τrec,90 as the required time for the OCDE to recover to 90% of its initial value. At 92% of the initial bias current, 90% of the initial detection efficiency has recovered, corresponding to an OCDE of 21.2% for the same device investigated before (see Figure 3b). We obtain a value of τrec,90 ∼ 510 ps, with an upper limit most likely imposed by our available readout equipment. This implies that our microbridge nanodetector is capable of reliably detecting single- and multiphoton pulses with count rates of about 2 GHz, while ensuring detection efficiencies above 20%. We experimentally verified the high detection rate using a GHz pulsed laser source in combination with single-shot measurements recorded at a fast oscilloscope for a device exhibiting a resonance at 1535.4 nm (red data points in Figure 3a and b). From evaluating the number of events (blue diamonds) in a certain time span exceeding a selected threshold level, we obtain a maximum count rate of 1.20 GHz, corresponding to the repetition rate of the light source. We note that in this measurement the number of photons per pulse is high in order to reliably trigger in a detection event. Therefore, these measurements do not correspond to singlephoton sensitivity. Correspondingly, the bias current has to be reduced in order to maintain superconductivity in the nanowire. Besides detector speed, the timing accuracy or timing jitter is a crucial aspect of single-photon detection, particularly for

which provide on-chip and system detection efficiency of 87% and 2.1%, respectively.10 To characterize the noise performance of our device we measure the detector dark count rate (DCR). The DCR for a typical detector (marked with red symbols in Figure 3a) is depicted in the lower part of Figure 3b, corresponding to the right axis. We measured the DCR under the same conditions as the OCDE, while metal caps cover the optical fibers leading into the cryostat. All devices presented here exhibit very low DCRs, typically below 1 Hz. We attribute this low dark count level mainly to the low bias currents at the operation point we are able to choose due to the saturation of the OCDE. In fact, the typical exponential growth of the DCR near IC23 is cut off, indicating that in our devices Ilatch limits IC. In addition, several improvements arise from the compact nanowire footprint. Embedding the nanowire into the cavity leads to reflection of guided stray light over a large span of the spectrum (off resonance),26 and the absorption of light which is coupled freespace from the fiber array to the active nanowire area is reduced by a factor of 60 compared to the U-shape design (length 120 μm). The small footprint of the nanowire leads to low kinetic inductance compared to traditional U-shape designs and governs the timing characteristics of our cavity-integrated microbridge nanodetectors. To showcase the outstanding speed of our SNSPDs, we compare the electrical readout pulses of nanodetectors to those of U-shape SNSPDs (Figure 4a). Pulse traces for detectors of both designs exhibit a sharp rise and an exponential decay in time.9 The 1/e decay times τdec, as obtained from exponential fits, amount to 4.7 ns (3.4 ns) for the long U-shape devices [total nanowire length 160 μm (120 μm)] and 206 ps for the compact microbridge nanowire (as depicted in Figure 1b, length between the contact pads 20 μm). Employing faster amplifiers results in a best value of 119 ps among all characterized devices, obtained for a 90 nm wide nanowire. We further suspect that our measurements are still limited by the bandwidth of the readout electronic, especially the amplifiers (4 GHz, see SI). Even lower decay times are within reach using faster electronics. Up to our knowledge, such decay times corresponds to the smallest decay times reported in the literature of waveguideintegrated SNSPDs10 relying on the use of only a single nanowire, while parallel strips show minimum decay times of E

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floor typically observed in such measurements. For waveguideintegrated SNSPDs in U-shape geometry, multiphoton detection up to the three-photon level has been demonstrated before.52 We would like to emphasize that the multiphoton detection scheme presented here does not correspond to photon-number resolution (PNR). While PNR detectors feature a readout signal characteristic for the number of detected photons, SNSPDs are threshold detectors that can only discriminate between “less than n photons” and “n or more photons”. From our observations we expect that both the efficiency of detecting multiphoton states as well as an extension of the detection regime toward higher photon numbers is possible using wider nanowires. All of the results described here are obtained for a width of 90 nm. Wider nanowires are better suited for multiphoton detection52 because the detectors can be operated with higher bias currents while still exhibiting multiphoton detection capability, resulting in enhanced detection probabilities for small n. In summary, superconducting nanowires integrated into a waveguide cavity provide a viable route to achieve ultracompact and efficient single-photon detection at high rates and ultralow dark count rates. Short nanowires exhibit limited inherent absorption but show faster timing characteristics arising from their small kinetic inductance. Embedding the photon-sensitive nanowire into a photonic crystal cavity enhances the absorption efficiency in a wavelength range adaptable by design while acting as an optical filter for other wavelengths. Finite-element simulations support the design of photonic elements and pave the way to further enhance the detection efficiency by reducing out-scattering losses. Combining photonic crystal cavity and compact nanowire geometry culminates in a strong enhancement of the detection efficiencies on resonance compared to stand-alone nanodetectors, exhibiting outstanding decay and recovery times. The small detector footprint leads to dark count rates below 1 Hz and the efficient detection of multiphoton states as a threshold detector. The latter enables the realization of efficient autocorrelation detectors at adaptable threshold levels,53 while the small decay times allow to establish time-multiplexed singlephoton detection schemes.54,55 These results pave the way toward arrays of compact waveguide-coupled detectors, providing a monolithic scalable platform for applications in on-chip quantum optics and time-correlated single-photon counting.

correlation measurements and time-correlated single-photon counting. Using a picosecond pulsed laser source in combination with a digital sampling oscilloscope in histogram mode, the arrival time of detection pulses are measured with respect to the excitation pulse. The full width of half-maximum (fwhm) of the histogram, as obtained from a Gaussian fit, is a measure of the detector’s timing jitter. We find a best value of 32 ps among the examined cavity-integrated microbridge detectors (90 nm wide nanowire,IB = 0.9IC, photon flux 105 photons per second, see SI). This value is on par with current waveguide-integrated SNSPDs12,37 and within a factor of 2 of the record value of 17.8 ps44 for meander SNSPDs and 18 ps for waveguide-integrated U-shape SNSPDs.10 In principle, the improved signal-to-noise ratio (SNR) of the nanowire structure without bends45 and our compact nanowire design46 presented here could result in reduced jitter values. It might be beneficial to artificially increase the kinetic inductance in order to increase the latching-limited critical current and thus improve the SNR. In addition, we suggest that an improvement toward higher uniformity of the fabricated nanowire (e.g., by optimizing the NbN etching) might have the potential to reduce the timing jitter in ultrashort SNSPDs. The optical cavity itself does not contribute to the timing jitter, since the energy stored in circulating photons decays on a time scale below 1 ps26 (see SI). In addition to fast detector speed, our compact nanowire design provides clear advantages for the detection of multiphoton states. If the bias current flowing through the nanowire is low enough or the nanowire is wide enough, the absorption of a single photon is not sufficient to trigger a detection event. Instead, the simultaneous absorption of multiple photons in the same small volume of the nanowire is required to obtain a readout signal.23,47 This leads to different detection regimes, investigated here by exploiting a technique commonly referred to as quantum detector tomography (QDT).48−52 In the microbridge design, the strongly reduced size of the nanowire (compared to U-shape implementations52) renders the simultaneous absorption of photons in the same spatial volume more likely. In addition, the integration of the nanowire into an optical cavity leads to a further improvement of the absorption efficiency, revealing a clear enhancement over previous implementations of nanodetectors.23 We investigate here the single- and multiphoton detection capabilities of the detector already discussed in Figure 4b (90 nm wide nanowire, IC = 22.4 μA). In order to determine the probability of detecting a pulse containing different average numbers of photons per pulse, we use a picosecond pulsed laser (PriTel FFL-40M) at a wavelength corresponding to the resonance of the cavity-integrated SNSPD (see Figure 3a). Figure 4b shows these detection probabilities as a function of the average number of photons per pulse for different bias currents IB on a log−log scale. For bias currents of 0.9 and 0.7 IC, the slope of a linear fit equal to one (m = 1) coincides with the data, corresponding to single-photon sensitivity over a range of 10−5 to 102 photons per pulse. Two-photon detection becomes the dominant contribution for a bias current of IB = 0.5 IC and less than ∼30 photons per pulse. More photons lead to a decreasing contribution of the two-photon regime, and the detector enters the three-photon regime.52 A further reduction of the bias current to IB = 0.4 IC allows the observation of a seven-photon regime (m = 7 in Figure 4b) using only a single nanowire. In addition, the low noise level, as described before, manifests in a vanishing noise

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b03344. Device fabrication, photonic circuitry layout, experimental methods, simulation methods and photonic crystal design, sensitivity analysis, recovery time and readout electronics, saturation of the on-chip detection efficiency, nanowire attenuation, timing jitter measurements, investigation of GHz count rate pulses, comparison of different pulse counters, and a comparison of microbridge and U-shape waveguide-integrated SNSPDs (PDF) F

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(18) Ejrnaes, M.; Cristiano, R.; Quaranta, O.; Pagano, S.; Gaggero, A.; Mattioli, F.; Leoni, R.; Voronov, B.; Gol’Tsman, G. Appl. Phys. Lett. 2007, 91 (26), 10−13. (19) Tarkhov, M.; Claudon, J.; Poizat, J. P.; Korneev, A.; Divochiy, A.; Minaeva, O.; Seleznev, V.; Kaurova, N.; Voronov, B.; Semenov, A. V.; Gol’tsman, G. Appl. Phys. Lett. 2008, 92 (24), 241112. (20) Ejrnaes, M.; Casaburi, A.; Quaranta, O.; Marchetti, S.; Gaggero, A.; Mattioli, F.; Leoni, R.; Pagano, S.; Cristiano, R. Supercond. Sci. Technol. 2009, 22 (5), 55006. (21) Marsili, F.; Najafi, F.; Dauler, E.; Bellei, F.; Hu, X.; Csete, M.; Molnar, R. J.; Berggren, K. K. Nano Lett. 2011, 11 (5), 2048−2053. (22) Marsili, F.; Najafi, F.; Dauler, E.; Molnar, R. J.; Berggren, K. K. Appl. Phys. Lett. 2012, 100 (11), 112601. (23) Bitauld, D.; Marsili, F.; Gaggero, A.; Mattioli, F.; Leoni, R.; Nejad, S. J.; Lévy, F.; Fiore, A. Nano Lett. 2010, 10 (8), 2977−2981. (24) Renema, J. J.; Wang, Q.; Gaudio, R.; Komen, I.; op ’t Hoog, K.; Sahin, D.; Schilling, A.; van Exter, M. P.; Fiore, A.; Engel, A.; de Dood, M. J. A. Nano Lett. 2015, 15 (7), 4541−4545. (25) Liu, N.; Mesch, M.; Weiss, T.; Hentschel, M.; Giessen, H. Nano Lett. 2010, 10 (7), 2342−2348. (26) Akhlaghi, M. K.; Schelew, E.; Young, J. F. Nat. Commun. 2015, 6, 8233. (27) Gaudio, R.; op ’t Hoog, K. P. M.; Zhou, Z.; Sahin, D.; Fiore, A. Appl. Phys. Lett. 2014, 105 (22), 222602. (28) Clem, J. R.; Berggren, K. K. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84 (17), 174510. (29) Henrich, D.; Reichensperger, P.; Hofherr, M.; Meckbach, J. M.; Il’in, K.; Siegel, M.; Semenov, A.; Zotova, A.; Vodolazov, D. Y. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86 (14), 144504. (30) Lalanne, P.; Sauvan, C.; Hugonin, J. P. Laser Photonics Rev. 2008, 2 (6), 514−526. (31) Saleh, B. E. A.; Teich, M. C. Fundamentals of Photonics; Wiley Series in Pure and Applied Optics; Wiley, 2007. (32) Fukazawa, T.; Hirano, T.; Ohno, F.; Baba, T. Japanese J. Appl. Physics, Part 1 Regul. Pap. Short Notes Rev. Pap. 2004, 43 (2), 646−647. (33) Bogaerts, W.; Dumon, P.; Van Thourhout, D.; Baets, R. Opt. Lett. 2007, 32 (19), 2801−2803. (34) Tsarev, A. In 2012 IEEE 11th International Conference on Actual Problems of Electronics Instrument Engineering (APEIE); IEEE, 2012; Vol. 19, pp 151−153. (35) Celo, D.; Goodwill, D. J.; Dumais, P.; Jiang, J.; Bernier, E. In 11th International Conference on Group IV Photonics (GFP); IEEE, 2014; Vol. 23, pp 189−190. (36) Ma, Y.; Zhang, Y.; Yang, S.; Novack, A.; Ding, R.; Lim, A. E.-J.; Lo, G.-Q.; Baehr-Jones, T.; Hochberg, M. Opt. Express 2013, 21 (24), 29374. (37) Rath, P.; Vetter, A.; Kovalyuk, V.; Ferrari, S.; Kahl, O.; Nebel, C.; Goltsman, G. N.; Korneev, A.; Pernice, W. H. P. In Proc. SPIE 9750, Integrated Optics: Devices, Materials, and Technologies XX, 2016; Vol. 97500T. (38) Khasminskaya, S.; Pyatkov, F.; Słowik, K.; Ferrari, S.; Kahl, O.; Kovalyuk, V.; Rath, P.; Vetter, A.; Hennrich, F.; Kappes, M. M.; Gol’tsman, G.; Korneev, A.; Rockstuhl, C.; Krupke, R.; Pernice, W. H. P. Nat. Photonics 2016, in press.10.1038/nphoton.2016.178 (39) Yang, J. K. W. K. W.; Kerman, A. J. J.; Dauler, E. A. A.; Anant, V.; Rosfjord, K. M. M.; Berggren, K. K. K. IEEE Trans. Appl. Supercond. 2007, 17 (2), 581−585. (40) Kerman, A. J.; Yang, J. K. W.; Molnar, R. J.; Dauler, E. A.; Berggren, K. K. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79 (10), 100509. (41) Annunziata, A. J.; Quaranta, O.; Santavicca, D. F.; Casaburi, A.; Frunzio, L.; Ejrnaes, M.; Rooks, M. J.; Cristiano, R.; Pagano, S.; Frydman, A.; Prober, D. E. J. Appl. Phys. 2010, 108 (8), 84507. (42) Kahl, O.; Ferrari, S.; Rath, P.; Vetter, A.; Nebel, C.; Pernice, W. H. P. J. Lightwave Technol. 2016, 34 (2), 249−255. (43) Migdall, A. Single-Photon Generation and Detection; Elsevier, 2009. (44) Shcheslavskiy, V.; Morozov, P.; Divochiy, A.; Vakhtomin, Y.; Smirnov, K.; Becker, W. Rev. Sci. Instrum. 2016, 87 (5), 53117.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

R.A.: Max Planck Institute for the Science of Light, 91058 Erlangen, Germany. Funding

We gratefully acknowledge partial financial support by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173 and Project PE 1832/1-1 and the Helmholtz Society through grant HIRG-0005. G.G., A.K., and V.K. acknowledge support by Ministry of Education and Science of the Russian Federation (contract no. 14.586.21.0007; Project ID: RFMEFI58614X0007). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors want to thank M. Stegmaier, N. Gruhler, S. Khasminskaya, F. Pyatkov, M. Fruhnert, and P. Brenner for useful discussions and technical support. Device fabrication was performed at the Center of Functional Nanostructures (CFN) and the Institute of Nanotechnology (INT) of the Karlsruhe Institute of Technology (KIT).

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REFERENCES

(1) Knill, E.; Laflamme, R.; Milburn, G. J. Nature 2001, 409 (6816), 46−52. (2) O’Brien, J. L. Science (Washington, DC, U. S.) 2007, 318 (5856), 1567−1570. (3) Varnava, M.; Browne, D. E.; Rudolph, T. Phys. Rev. Lett. 2008, 100 (6), 1−4. (4) Gisin, N.; Ribordy, G.; Tittel, W.; Zbinden, H. Rev. Mod. Phys. 2002, 74 (1), 145−195. (5) Eraerds, P.; Legre, M.; Zhang, J. Z. J.; Zbinden, H.; Gisin, N. J. Lightwave Technol. 2010, 28 (6), 1−12. (6) Becker, W.; Bergmann, A.; Hink, M. A.; König, K.; Benndorf, K.; Biskup, C. Microsc. Res. Tech. 2004, 63 (1), 58−66. (7) Hadfield, R. H.; Stevens, M. J.; Gruber, S. S.; Miller, A. J.; Schwall, R. E.; Mirin, R. P.; Nam, S. W. Opt. Express 2005, 13 (26), 10846. (8) Gol’tsman, G. N.; Okunev, O.; Chulkova, G.; Lipatov, A.; Semenov, A.; Smirnov, K.; Voronov, B.; Dzardanov, A.; Williams, C.; Sobolewski, R. Appl. Phys. Lett. 2001, 79 (6), 705−707. (9) Natarajan, C. M. M.; Tanner, M. G. G.; Hadfield, R. Supercond. Sci. Technol. 2012, 25, 063001. (10) Pernice, W. H. P.; Schuck, C.; Minaeva, O.; Li, M.; Goltsman, G. N.; Sergienko, A. V.; Tang, H. X. Nat. Commun. 2012, 3, 1325. (11) Kerman, A. J.; Dauler, E. A.; Yang, J. K. W.; Rosfjord, K. M.; Anant, V.; Berggren, K. K.; Gol’tsman, G. N.; Voronov, B. M. Appl. Phys. Lett. 2007, 90 (10), 101110. (12) Kahl, O.; Ferrari, S.; Kovalyuk, V.; Goltsman, G. N.; Korneev, A.; Pernice, W. H. P. Sci. Rep. 2015, 5, 10941. (13) Hu, X.; Holzwarth, C. W.; Masciarelli, D.; Dauler, E. A.; Berggren, K. K. IEEE Trans. Appl. Supercond. 2009, 19 (3), 336−340. (14) Kovalyuk, V.; Hartmann, W.; Kahl, O.; Kaurova, N.; Korneev, A.; Goltsman, G.; Pernice, W. H. P. Opt. Express 2013, 21 (19), 22683. (15) Kerman, A. J.; Dauler, E. A.; Keicher, W. E.; Yang, J. K. W.; Berggren, K. K.; Gol’tsman, G.; Voronov, B. Appl. Phys. Lett. 2006, 88 (11), 111116. (16) Miki, S.; Takeda, M.; Fujiwara, M.; Sasaki, M.; Otomo, A.; Wang, Z. Appl. Phys. Express 2009, 2 (7), 13−16. (17) Schuck, C.; Pernice, W. H. P.; Tang, H. X. Appl. Phys. Lett. 2013, 102, 5. G

DOI: 10.1021/acs.nanolett.6b03344 Nano Lett. XXXX, XXX, XXX−XXX

Letter

Nano Letters (45) You, L.; Yang, X.; He, Y.; Zhang, W.; Liu, D.; Zhang, W.; Zhang, L.; Zhang, L.; Liu, X.; Chen, S.; Wang, Z.; Xie, X. AIP Adv. 2013, 3 (7), 72135. (46) O’Connor, J. A.; Tanner, M. G.; Natarajan, C. M.; Buller, G. S.; Warburton, R. J.; Miki, S.; Wang, Z.; Nam, S. W.; Hadfield, R. H. Appl. Phys. Lett. 2011, 98 (20), 201116. (47) Renema, J. J.; Gaudio, R.; Wang, Q.; van Exter, M. P.; Fiore, A.; de Dood, M. J. A. arXiv: 1607.03088, 2016. (48) Lundeen, J. S.; Feito, A.; Coldenstrodt-Ronge, H.; Pregnell, K. L.; Silberhorn, C.; Ralph, T. C.; Eisert, J.; Plenio, M. B.; Walmsley, I. A. Nat. Phys. 2009, 5 (1), 6. (49) Feito, A.; Lundeen, J. S.; Coldenstrodt-Ronge, H.; Eisert, J.; Plenio, M. B.; Walmsley, I. A. New J. Phys. 2009, 11 (9), 93038. (50) Renema, J. J.; Frucci, G.; de Dood, M. J. A.; Gill, R.; Fiore, A.; van Exter, M. P. Phys. Rev. A: At., Mol., Opt. Phys. 2012, 86 (6), 62113. (51) Elezov, M. S.; Semenov, A. V.; An, P. P.; Tarkhov, M. A.; Goltsman, G. N.; Kardakova, A. I.; Kazakov, A. Y. J. Opt. Technol. 2013, 80 (7), 435. (52) Ferrari, S.; Kahl, O.; Kovalyuk, V.; Goltsman, G. N.; Korneev, A.; Pernice, W. H. P. Appl. Phys. Lett. 2015, 106 (15), 151101. (53) Zhou, Z.; Frucci, G.; Mattioli, F.; Gaggero, A.; Leoni, R.; Jahanmirinejad, S.; Hoang, T. B.; Fiore, A. Phys. Rev. Lett. 2013, 110 (13), 133605. (54) Fitch, M. J.; Jacobs, B. C.; Pittman, T. B.; Franson, J. D. Phys. Rev. A: At., Mol., Opt. Phys. 2003, 68 (4), 43814. (55) Lee, C.; Ferrari, S.; Pernice, W. H. P.; Rockstuhl, C. arXiv: 1606.04826 2016.

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DOI: 10.1021/acs.nanolett.6b03344 Nano Lett. XXXX, XXX, XXX−XXX