Voltage-Controlled Fast and Low-Loss Single-Photon Cross-Bar Switch Using Integrated Photonics

A high-speed, low-loss modular cross-bar switching element suitable for single photons is demonstrated. Entanglement preserving voltage-driven switching of single photons is achieved with a unique combination of ultra-fast and low-loss characteristics (less than 50 ps 10%–90% transition time and greater than 90% transmission), and we present a roadmap towards even lower losses. The switch properties are well matched to the wavelength, bandwidth and lifetime of photons generated by spontaneous four-wave mixing sources also realized in silicon photonics. Such a switch can enable reconfigurability of each single photon and addressing of each time bin, and benefit future quantum photonic circuits.


I. INTRODUCTION
T HE use of photonic microchips for the generation and manipulation of single photons is advancing the trend towards scaling up sources and realizing a programmable switching network for an optical quantum technology platform [1]. Cross-bar switches see Fig. 1(a) are the building block for many types of networks, including large-scale optical networks [2]. A scalable approach to low-loss cross-bar switching of single photons has been shown using integrated photonics based on millisecond or microsecond scale thermo-optical effects [3], [4], [5], [6], [7], [8] or micro-mechanical motion [9], but the switching time is many orders of magnitude longer than the duration of photons generated using integrated photonics or the time bin used in modern quantum key distribution [10], [11]. A slow switch lowers the throughput and also inhibits the implementation of feed-forward, as long delays with high resolution are difficult for integrated photonics. On the other hand, switches with a high loss will drastically limit the scale-up and utility of a quantum network. To overcome this bottleneck, here we design a fast and low-loss approach to voltage-driven single-photon switching on a microchip at 1550 nm wavelengths. This work addresses the sub-50 ps time scales which is one-half of a time bin using a nominal 10 GHz clock rate used in quantum key distribution [11], or the lifetime of photons generated at these wavelengths by compact integrated devices [10], [12], [13], [14].
The integrated optics platform we use is silicon photonics, which is compatible with scalable manufacturing trends in the microelectronics industry. Our approach uses the voltage-driven electro-optic (EO) effect [15], which is enhanced by using a micro-resonator geometry [16], as shown in Fig. 1(b). Silicon photonics can also be used to efficiently generate photon pairs on a microchip [12], [13], [14], and in classical optical switching [17], [18]. Our work brings together perspectives from these different topics. The microdisc switch devices were fabricated using a multi-project wafer process and uses only conventional materials and techniques used in silicon wafer manufacturing [19]. The microdisc contains an embedded p-n junction which is used in the depletion mode of operation, where its resonance wavelength can be rapidly shifted by a reverse-bias voltage with minimal current flow. The diameter of the microdisc was 4 μm and is intended for future applications in on-chip photonic circuits. Although feeder waveguides were also fabricated and were used to test various aspects of the performance using fibers and laboratory instruments, the switch itself occupies a compact footprint of less than 20 μm 2 , excluding the area of the electrical contact pads. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ Fig. 2. (a) The finesse (F) is calculated as a function of the waveguideresonator coupling coefficient (|t|) and resonator loss (α, units: dB.cm −1 ) using the terminology described in the Supplemental Materials. The region indicated in white corresponds to experimentally measured values of F. For this region, the (b) through-port transmission extinction ratio (ER) and (c) drop-port insertion loss (IL) are calculated. The point labeled "X" is discussed in the text.
In Section II, we discuss a key aspect of our devices compared to their conventional use. Section III provides information about the experimental setup, and the subsequent sections focus on different aspects of the device, including switching of single photons, preservation of entanglement, switching speed and (onchip) insertion loss. Section IX compares this switch with others made using silicon photonics. This report is an extended version of results first presented in [20].

II. DESIGN PRINCIPLES
Although the physical structure of the EO microresonator is similar to that used in EO modulation, the design goals and operating principles are both different. Before discussing the principles of the device from a theoretical and simulation perspective, we highlight the importance of finesse in low-loss switching using microresonators as a general design principle. The finesse (F) of a microresonator is proportional to the number of round trips made by light before it escapes the resonator. Generally, for an application such as fast switching, finesse is an appropriate quantity to use, rather than the quality factor (Q) or linewidth, although they are related. Finesse focuses solely on the mirror reflectivity for a Fabry-Perot cavity, or the coupling coefficient for a microring-waveguide geometry. The designer has more control over this parameter, since the waveguide loss is typically fixed within a relatively narrow range by the foundry process (α ≈ 10 dB.cm −1 in our case). Finesse is used when the transient buildup of light in a resonator is the focus of study whereas Q also involves the geometrical size and governs parameters such as the nonlinear mixing efficiency and parametric oscillation threshold, which are not relevant here [21].
An EO microresonator used as high-bandwidth modulator typically has a low finesse (F ≈ 50 [22], or even as low as F ≈ 1 [23]), whereas a key aspect of our device is that it has a finesse above 500 while still achieving sub-50 ps transition times. Fig. 2(a) shows a contour plot of F in the parameter space defined by |t|, the field through-coupling coefficient of the coupler between the ring and the waveguide (assumed to be the same for both couplers), and α, the circulation factor which describes field propagation in the resonator. High values of F are achieved only when |t| and α are both close to unity, and lead to a low insertion loss. However, values of F that are too high will result in bandwidths that are too narrow for the characteristics of typical photon-pair sources.
Based upon the expected value of the doped-silicon propagation loss coefficient, the finesse (F) range describes which slice of the composite region shown in Fig. 2(a) should be chosen. The point labeled "X" at edge of this slice in Fig. 2(c) includes this value of α and is reached by using values of |t| that are close to unity. As further discussed below, it represents the minimum insertion loss that is achievable, and this requires a finesse in the range of 500-550 for this value of α. If α were smaller or greater, then the slice of F values should shift to the top-right and bottom-left corners of Fig. 2(a).
Bounded by these constraints, we simultaneously achieve in our experiments a high value of F, low loss, and ultra-fast switching speed. The white-colored diagonal slice indicates the range 500 < F < 550 that corresponds to our experimental devices (see Section IV). For the combination of values of |t| and α which satisfy this constraint, Fig. 2(b), (c) show the calculated through port extinction ratio (ER), and the drop port insertion loss, which we label IL (on) . The point labeled "X" has IL (on) = 0.0056 dB (99.9% transmission) and can be reached by changing the coupling coefficient. For this point, the target value of loss is quite reasonable and has already been achieved in the fabricated devices. Similar to achieving ideality in passive resonators [24], perfectly achieving the ideal coupler will require iterative fabrication improvements beyond the scope of this report.
Further insights into the use of small-radius microresonator modulators used as add-drop switching devices may be obtained from a model of the single waveguide-coupled ring-resonator shown in Fig. 3 (the two-waveguide case is discussed at the end of this section). Using the same notation as [25], the normalized complex electric-field amplitudes of the single-mode waveguide before and after the coupler are labeled as a 1 and b 1 , respectively. The normalized transmission past the resonator is where α is the circulation factor and t and κ are the electric field coupling coefficients of the directional coupler between the ring and the waveguide. The round-trip phase accumulated by light propagating once around the ring is θ = βL + φ t where β is the mode propagation constant, L is the circumference of the ring, and φ t is the phase shift of t. The circulation factor is defined as α = exp(−αL/2) and represents the amplitude attenuation experienced in one round-trip, with the conventional per-unitlength (intensity) absorption coefficient written asα. Thus, the fractional internal intensity loss per circulation is 1 − α 2 . The resonance condition, θ = m 2π, where m is an integer, has been discussed elsewhere and results in T = 0 if |t| = α (critical coupling) [25]. The bar-state insertion loss is obtained by evaluating (1) away from resonance. For analytical simplicity, consider θ = m2π + π/2, labeled "off-resonance" (abbreviated in subscripts to "o.r."), whereupon (1) becomes Equation (2) can be written as a Taylor series around critical coupling (α = |t|), Although critical coupling may not be perfectly achieved in practice, we can study the leading-order behavior of T o.r. as critical coupling is approached. Defining the resulting parameter as the insertion loss, we obtain IL ≈ 10 log 10 2 Equation (4) shows that the bar-state insertion loss is proportional to α 2 , i.e., to exp(−αL) and is lowered (improved) by reducing L, the circumference of the resonator. There is no cross-state insertion loss defined in the one-waveguide case, but the analysis for an add-drop (two-waveguide) resonator configuration leads to similar-looking expressions with a few algebraic substitutions (t → t 1 , α → αt 2 ) [25]. Using microresonators with a small circumference is especially important in high-speed modulator structures, which use heavily-doped semiconductors, since the numerical value ofα is dominated by the doping, and can be quite large [26], [27], [28]. Note that a microring or microdisc resonator with a small L has a large free-spectral range (FSR). The FSR of our device exceeds 59 nm around 1550 nm. Experimentally, it is not necessary to tune by one-quarter of the FSR. This reference point is convenient for explaining the same trends which are also seen at smaller detunings using a numerical calculation.

III. EXPERIMENTAL DETAILS
The feeder waveguides on the photonic microchip are singlemode rib waveguides of height 230 nm in silicon which support propagation in the transverse-electric (TE) polarization, with the electric field polarized in the plane of the wafer. The high index contrast of silicon as a waveguide core material with a silicon dioxide cladding supports a low bending loss even for small radii of a few micrometers [29], [30]. A slot was etched in the center of the disc, with dimensions about 2 μm × 0.3 μm to suppress higher-order modes. A vertical p-n junction was used for the microdisc, which improves the modulation efficiency [31], [32] and the fabrication tolerance [33]. To reduce dopant-induced optical loss, only about one-half of the perimeter was doped with p (BF 2 , 4 × 10 13 cm −2 , 380 keV) and n (As, 4 × 10 13 cm −2 , 70 keV) dopants, and the regions of the disc near the waveguides were left undoped [34]. The estimated capacitance is about 10 fF, with a switching energy E s = CV 2 = 0.36 pJ for a voltage swing of 6 V. No adiabatic tapering of the radius was used in this device. A circle of radius 1 μm in the center of the disc was more heavily p-n doped, and low-resistance ohmic electrical contacts to metal (aluminum) electrodes were provided through tungsten vias.
Light was coupled onto the silicon photonic chip with fabricated inverse-taper features at the edge of the chip, and lenstapered single-mode fibers whose position was controlled using piezo-driven micropositioners. Visual monitoring using an infrared camera on a microscope was used to help in the alignment. Photon pairs were generated using spontaneous four-wave mixing (SFWM) in a silicon microring resonator, following a procedure similar to that described in [14]. A continuous-wave, narrow-linewidth diode laser was used as the pump for the SFWM process. The silicon photonic microchip containing the SFWM microring was different from the one containing the switch, but the silicon microfabrication process was similar. By using separate chips, the resonance wavelength of the microresonator could be varied by changing the temperature of the chip. The temperature of each chip mount was controlled by a thermo-electric controller (TEC).
Additional experimental details are presented in the following sections when discussing specific aspects.

IV. DEVICE CHARACTERIZATION
The transmission spectrum of the microdisc was measured using TE-polarized light, showing an FSR of 59.1 nm. Fig. 4, panel (a) shows a wavelength scan of the resonances, and in panel (b), the spectrum are shown for two different values of the reverse bias voltage, −0.5 V (blue line) and −6.5 V (red line). The loaded resonator quality factor Q was 1.34 × 10 4 at a reverse bias voltage of −0.5 V, and 1.42 × 10 4 at a reverse bias voltage of −6.5 V. In the former case, the resonance FWHM was 14.5 GHz, and in the latter case, it was 13.6 GHz. Thus, the finesse (F) was 510 at −0.5 V, and 542 at −6.5 V.
When measured with classical light (at about 1 mW input optical power level), the optical transmission on resonance (extinction ratio) was measured to be −7.6 dB, showing that about 83% of the photons were coupled out of the input waveguide at 1550 nm. This capture efficiency is similar, for example, to the 80% efficiency reported for the coupling efficiency of a quantum-dot-waveguide system [35], and also for ultrasmall resonators [23]. Small-radius microresonators show device-todevice variations across a wafer; we have not yet performed measurements on a large ensemble of devices at this time. For this device, the resonance null at 1610 nm was deeper (-10 dB) but other devices may show a deeper null at 1550 nm than at the longer wavelength. Analysis of the spectrum showed that this resonator was in the slightly under-coupled regime. By reducing the waveguide-resonator gap by about 40 nm, the critical coupling condition would be more closely achieved at 1550 nm in the same device, and the reduced gap would still be compatible with a foundry photolithography process and not require electron-beam lithography. In principle, 100% waveguide capture efficiency is possible at critical coupling, which has been demonstrated using movable fiber tapers [36], [37], [38], but is also possible through design iterations and post-fabrication trimming [39], [40], [41], [42], [43].

V. SWITCHING OF SINGLE PHOTONS
Entanglement-preserving switching of single photons was demonstrated using photon pairs generated using spontaneous four-wave mixing (SFWM) in a silicon microresonator device. Such a source could easily be integrated on the same microchip as the switch, although here, we used our previously-studied source devices [14], [44] to allow a detailed characterization of the switch by itself. The operating wavelength of the switch was thermo-optically tuned to match the wavelength of the signal photon generated by SFWM. The SFWM source was operated at about 1550.74 nm (near room temperature, about 21 • C) and the switch disc was operated at about 1550.78 nm at 44 • C (wavelength shift of about 1.58 nm from the resonance at room temperature).
Digitally-generated electronic control signals drive the switch between cross and bar states. Setting the appropriate voltage levels for cross and bar operation requires knowing the wavelength of the incoming photons. This is usually the case in quantum photonics, especially when photons are generated using processes such as spontaneous four-wave mixing and spontaneous parametric down-conversion wherein the pump determines the wavelengths of the signal and idler photons by strict energy conservation and narrowband filters are set to specific wavelengths.
The idler photons of the SFWM pair bypassed the chip. The output photons were coupled off chip into a single-mode fiber with un-optimized coupling loss from diced edges of about 5 dB per facet using polarization-maintaining fiber [Coherent PM2000D], and detected using a pair of high-efficiency NbN superconducting nanowire single photon detectors (SNSPD) made by Single Quantum. The detectors were operated at 0.8 K in a closed-cycle cryostat with a sorption stage [Photon Spot, Inc.]. A pair of ultra-low noise cryogenic amplifiers [Cosmic Microwave Technology, Inc.] were used to amplify the signals generated by the SNSPDs at a cold stage. Start-stop histogramming was performed using a time-to-digital converter (TDC) instrument (quTAG, qutools GmbH) with time-bin resolution of 4 ps. The TDC also used a 10 MHz electrical trigger generated by the AWG, which was digitally synchronized with the control pulses. The detection of the photons was used as the "start" signals and the clock signal was used as the "stop" signal in constructing start-stop histograms. In some measurements, each photon detection event was also time-stamped. The actual number of photons accumulated in a bin of width 4 ps at the highest count rates was about 2 × 10 5 . Fig. 5(a) shows the schematic of the experiments performed to study coincidences-to-accidentals ratio (CAR) for the cross and bar states (sub-panel labeled "c.1") and a measurement of energy-time entanglement after switching (sub-panel labeled "c.2"). For the CAR measurement, panel (b) shows a typical signal-idler cross-correlation measurement (at the lowest CAR value; other points have a higher peak value) and panel (c) shows the scaling of CAR versus singles rates for single photons in both the drop (cross) and thru (bar) ports. The fitted lines follow the conventional form described elsewhere [14]. A small difference is seen between the cross and bar states, favoring the latter. In the bar state, the microdisc is placed off resonance with the wavelength of the incoming photons.

VI. PRESERVATION OF ENTANGLEMENT
The photons come from a pair-generation process in a silicon photonic device which generates energy-time entanglement that can be quantified using the two-photon visibility in a Franson interferometer. Experiments reported here test whether these quantum properties are deteriorated, which could happen in several ways. For example, certain types of all-optical switches which use a strong pump beam could experience scattering of the pump into noise that interferes with the signal and decreases the interference visibility. The large amplitude-phase coupling parameter for III-V electro-optic switches causes strong amplitudephase coupling and hence a distortion on one of the two photons, which would also be evident in such a test.  the delay-line interferometers (DLI). As the phase in the second DLI was scanned, the (normalized) coincidences in the central peak are shown in panel (e) for two different settings of the first DLI. The singles counts are also shown in the lower panel, and do not show interference (as is expected). Two other phase settings in the first DLI were also measured (not shown here, for clarity The Clauser-Horne-Shimony-Holt S parameter [45] was calculated from a set of sixteen coincidence measurements, using a set of four voltages on each of the two DLI's shown schematically in Fig. 5, panel (c.2). Each set took about 600 seconds of acquisition time. The phase of each DLI was varied by an electrical voltage in the range of 0-75 V. The four voltages were chosen to be approximately equal to phase settings of 0 • , 45 • , 90 • and 135 • where 180 • results in a full period of the two-photon coincidence interference curve. After calibration, the actual phase settings that were used by the discrete voltage settings were found to be 3.8 • , 48 • , 92 • and 139 • . Since the state was not exactly that which should generate a maximal violation of the Bell inequality, we expect a small reduction of |S|, but these settings were sufficient for the present purposes. The four probability correlation functions were calculated and the Clauser-Horne-Shimony-Holt S parameter was found to be |S| = 2.45 which is above the limit |S| ≤ 2. These results show that that the photons, even after passage through the switch, retain their quantum properties (energy-time entanglement) to a high degree that easily permits a violation of Bell's inequality.

VII. SWITCH TRANSITION TIME
For measuring the switch transition time, single photons of 80 ps duration (full-width at half maximum, FWHM) were obtained by heavily attenuating modulated pulses from a laser, using the setup shown schematically in Fig. 6. This approach substantially reduces the source jitter compared to using a spontaneous source of heralded photons, or a stream of single photons from a quantum dot at these wavelengths, and provides a more accurate characterization of the switch transition time. A continuous-wave, narrow-linewidth diode laser was tuned to the resonance of the microdisc resonator near 1550 nm. Pulses were carved using a modulator with 40 GHz bandwidth and 29 dB extinction ratio, driven by a low-jitter arbitrary waveform generator (AWG) [Tektronix AWG70002B] and RF amplifier [Keysight N4985A-P15]. The repetition rate was 100 MHz and the pulse duration (full-width at half-maximum, FWHM) was measured to be 80 ps. The pulses were attenuated using a programmable optical attenuator so that the average optical power coupled to the chip was -82.6 dBm and the average power into the microdisc was -91.6 dBm. This resulted in an average of 0.05 photons per pulse, i.e., the input pulse stream predominantly comprised single photons with a multi-photon probability per pulse less than 3%. The microdisc was driven by control signals comprised of voltage pulses from an arbitrary waveform generator (AWG) which were synchronized with the optical pulses. Storage times between 200 ps and 1.2 ns were set by programming the AWG with patterns consisting of two pulses (a write pulse and a read pulse). The time interval between the write and read control signals could be incrementally adjusted with 40 ps step resolution and 1 ps skew adjustment. The control pules (for both write and read) were 80 ps FWHM duration. A high-bandwidth RF bias tee was used to apply a constant reverse-bias DC voltage of -3.5 V to the disk switch, and the control signal pulses generated by the AWG were added to the DC bias with a 6 V swing. Each electrical pulse was 80 ps in duration. These control signals were applied to the contact pads on the microchip using high-bandwidth probes. The electrical control signal and optical pulse as measured on a high-bandwidth oscilloscope are shown in Fig. 6(b) and (c); the relative delay includes the contributions of RF cables, optical fibers and controllable optical delay lines to synchronize the control pulse with the arrival of the photons at the switch. The electrical waveform shown in Fig. 6(b) is a scaled version of the applied control signal which ranges from net reverse bias voltage levels of −0.5 V and −6.5 V for the two switch states. Photons were detected after switching by a fiber-coupled superconducting nanowire single-photon detector (SPD) made by JPL, with about 60% system detection efficiency and 18 ps FWHM jitter at 1550 nm.
The time stamps were recorded by a time-to-digital converter (TDC) calibrated to have less than 10 ps jitter. The AWG also provided an electronic synchronization signal for the TDC. Fig. 6 shows the results of both cross and bar switch transitions, measured by moving the optical fiber between two output ports and accumulating the results over several pulses. To measure the step response of the disc modulator to digital driving voltages, optical transmission was measured while a sequence of voltage pulses generated by the AWG were applied to the microdisc. Averages were taken over six recorded waveforms. The average 10%-90% fall time, indicated by transitions between the levels indicated by the dashed lines, was 34 ps and the average 10%-90% rise time was 48 ps in response to the control signals. The carrier dynamics in depletion-mode silicon devices are dependent on the bias voltage and the asymmetry is expected. This does not have an effect on the photons as the switch will have fully transitioned in less than one-half of the nominal time bin of 100 ps. The SPD jitter has not been deconvolved from these measurements; therefore, the quoted rise and fall times are conservatively stated.

VIII. ON-CHIP INSERTION LOSS CHARACTERIZATION
The on-chip insertion loss determines the scalability of the EO switch device. For characterizing the insertion loss of the switch accurately, we fabricated an on-chip loop structure using the microresonator as an add-drop switch, as indicated in Fig. 7. A first control pulse from the AWG captures a photon from the bus waveguide, and a second pulse releases it from the loop after a programmed delay interval between the pulses. In between these pulses, the switch is held in the bar state, so that the photon recirculates in the loop a number of times until it is switched out, with a gradual loss due to absorption. The waveguide dispersion is insignificant in these experiments. The group-velocity dispersion (GVD) coefficient of the waveguide was simulated to be about D ≈ 4500 ps/nm-km. Propagation of an intially-unchirped 50 ps input pulse through 10 round trips only results in a spreading of less than 0.05 ps, which is negligible compared to the pulse width. The AWG can only generate pulses with delays that are integer multiples of 40 ps which is its step resolution. After storage for a variable delay (multiples of the loop round trip time which is about 100 ps), photons were detected by a single-photon detector and recorded by a time-to-digital converter (TDC).
The TDC performed real-time histogramming of the photon detection events in start-stop mode, with the photon detection events being the "start" signal and a clock signal as the "stop" signal. Histograms of start-stop durations were collected and subsequently analyzed using offline computer processing (see Section VIII-A). We performed this experiment for a set of six hold time intervals up to 1.2 ns, obtaining sufficient data to extract the loss per round trip from the histograms. The magnitudes of the peaks from a set of measurements are plotted versus the hold time Δt pk in Fig. 7(b). The slope of the fit is 0.72 dB (loss per round trip), of which 0.45 dB is the waveguide loss calculated using the length and a previously calibrated loss coefficient for the passive waveguide. This results in a switch loss in the bar state of 0.27 dB, and using this value in the model, the switch loss in the cross state is calculated to be 0.44 dB. A small asymmetry in the bar and cross insertion losses can, in fact, be used in designing large-scale networks [46]. A comparison of the insertion loss of this switch with other high-speed electro-optic switches in silicon photonics is presented in Section IX.

A. Data Processing
Since perfect critical coupling was not achieved in this test structure, some of the input light reached the detector along the same waveguide and created precursor signals in the histograms. Physically, the precursors do not affect the photons circulating in the loop. Mathematically, however, the impulse response of a single-photon detector is not a delta-function in time, but has an exponential tail on the same time scale as the programmed delay between the two control signals which store and release a photon from the loop. Therefore, the effect of this tail needs to be factored out of the histogrammed measurements in order to correctly assess the storage time. Also, because some of the input light leaked directly through to the detector without entering the loop, the first measured data point in Fig. 7 is excluded from the linear fit.
The data shown in Fig. 7 are the results of separate measurements on the same device, as the delay between the "write" and the "read" control pulses was varied between 200 ps and 1.2 ns. (A single round trip, of duration 100 ps, is inaccessible because of the 40 ps resolution of the AWG.) In each case, a baseline histogram was also collected by increasing the delay between the control pulse to a large value (10 ns), well in excess of the storage capacity of the device. The second pulse was shifted to a long relative delay rather than turned off completely to avoid changing the average bias conditions which can shift the resonance of the microresonator. The baselines represent the ringdown of the loop when the switch was held in the "cross" configuration. By subtracting the baseline histogram from the data histogram, we obtain a histogram of normalized counts which only represents the trapped photons in the "bar" configuration. Stated another way, the data histograms measure the device response under a cross-bar two-step switching protocol, whereas the baseline histograms measure the device response under the cross pulse only. Subtracting the latter from the former gives the device response in the bar state, which cannot otherwise be measured externally. Fig. 8(a) shows a representative data trace, using the bin number of the histogram recorded by the TDC instrument on the horizontal axis, which is inverted (right-to-left) with respect to the time delay. The vertical axis shows the normalized counts, which are defined as the measured data acquired with voltages of −0.5 V and −6.5 V control signals, from which the baseline trace was subtracted, thus placing the background noise floor at zero average value. The inset in panel (a) shows the oscillatory waveform in the precursor region followed by the readout of a stored photon after a delay (the time axis is reversed with respect to the bin number). The oscillation in the precursor arises because the on-resonance input is filtered by the transfer function of the microresonator.
Subtraction is a noisy mathematical operation when performed on real-world signals. We help identify the real data by considering the effect of shifting the baseline (but not the data) histograms by one time bin (±4 ps) when performing the baseline subtraction. To understand why this useful, first consider the mathematical subtraction of two very similar signals, x 1 (t) and x 2 (t). In this case, the triad of signals {x 1 (t) − x 2 (t), x 1 (t) − x 2 (t ± δ)} where δ = 4 ps is small compared to the width of the pulse (approximately 50 ps) described by x 1 (t) or x 2 (t). Consequently, the difference between these signals is just noise, and will be very different from each other, with oppositely-oriented positive and negative swings. On the other hand, if a signal y(t) contains a real feature not present in x(t), then the triad of signals {y(t) − x(t), y(t) − x(t ± δ)} will be similar to each other.
Indeed, this is what was observed, as shown in Fig. 8(b). The waveforms to the left of 100 ps on the relative time axis are noisy precursors which are often positive as negative, and average to almost zero. On the other hand, the real data, as shown by the peak at 1 ns, is insensitive to these mathematical shifts of the baseline. In Fig. 8(b), three traces are shown corresponding to zero or one time bin (±4 ps) shifts of the background. In plotting Fig. 4 (main paper), a triangular windowing function was used: the baseline traces that were shifted by one time bin were also weighted by a factor of one-half relative to the unshifted baseline. Note that the peaks of the signal are not affected by this operation.
The same argument can be made differently: The raw time-bin resolution of 4 ps recorded by the TDC instrument represents a 3x oversampling compared to the intrinsic photon lifetime, τ ≈ 11 − 12 ps, associated with the measured quality factor of the microresonator (Q ≈ 1.4 × 10 4 under 6.5 V reverse bias).
By downsampling the raw data across three time bins, the bandwidths are brought approximately into agreement with each other. Here, we use a triangular windowing function for the weighting coefficients (0.5, 1.0, 0.5) for δ = −4 ps, 0 ps and +4 ps.

IX. DISCUSSION: SILICON PHOTONIC HIGH-SPEED ELECTRO-OPTIC DEVICE COMPARISON
With such a short transition time (< 50 ps), the switch can be assumed to have fully transitioned to the cross or bar states when a photon arrives, even at rates of several hundreds of millions of counts per second, which exceeds the single-photon rates achievable today. Therefore, the dynamics of switching do not chirp or shift the frequency of the photon [47]. Our scheme is simpler and has lower voltage requirements compared to EO frequency shifting of photons [48] and does not require precise synchronization of the switch control with the arrivals of the photons. This "bang-bang" switch operation mode is different from the usual operation of a microresonator-based data modulator [16], which is biased at an intermediate voltage and is almost always in transition between the extrema when driven at the highest speeds. In the "bang-bang" mode, the switch has fully transitioned to one of its two states before the photon arrives, which is distinct from the operation of electro-optic microresonator modulators which imposes frequency sidebands on the spectrum of the photons. Improvements in the on-off switching speed may be achieved by improving the design of the p-n junction, reducing parasitic contributions to resistance and capacitance from electrical pads and wires, and compensating for the electrical roll-off by shaping the driving electrical pulses.
In Table I, a representative selection of silicon photonic electro-optic devices which are capable of high-speed cross-bar switching is reported. All these devices are based on electronic dopants in silicon waveguides, and are capable of much faster operation than thermally-tuned or mechnically-actuated switches. Some of these devices are described as data modulators, but can also perform cross-bar switching. These devices span a wide range of designs including microresonators, coupled microresonators, and Mach-Zehnder interferometer (MZI) structures and have used different silicon foundries in the fabrication process, and thus show range of typical performance than can be expected. Explanatory notes are provided about the insertion loss and transition time, both of which have had different definitions in the literature. Here, those quantities are tabulated with a consistent definition to allow a fair comparison.
When the wavelength of the incoming photons is known, there can be several advantages to using a microresonator over an MZI as a switch in semiconductor optics. Firstly, the voltage required to achieve a large output swing using a microresonator is reduced, compared to the voltage required to achieve π phase shift in an MZI device [25]. Stated another way, given a certain level of driving voltage that can be provided by electronic circuits, a microresonator device can generally achieve better performance compared to an MZI device if the required bandwidth is not too large. Secondly, tuning a microresonator by π phase shift (one-half the free spectral range) is not required since a large change in transmission can be achieved with a smaller phase shift. This makes the driver requirements easier. Finally, the insertion loss is lower when using the microresonator, which is not only beneficial in classical optics, but of even more significance in the single-photon regime.

X. CONCLUSION
In conclusion, we have shown the first integrated photonics single-photon switch which can simultaneously achieve low losses and high speed and performs entanglement-preserving switching at 1550 nm. This voltage-driven, room-temperature switch has less than 50 ps 10%-90% transition time, low loss (0.27 dB for the through port and 0.44 dB for the drop port), and small footprint (less than 20 squared microns) and substantially outperforms other high-speed silicon photonic electrooptic switches. Unlike all-optical switches, this device is free of scattered photon noise and is energy-efficient. A voltage-driven single-photon switch designed and fabricated using silicon photonics is scalable, cost-effective, compatible with foundry fabrication, and benefits from using the low size, weight, and power (SWaP) of a microchip platform to support future large-scale integration trends in both classical and quantum photonics.