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Abstract
We demonstrate a silicon photonic transceiver circuit for high-speed discrete variable quantum key distribution that employs a common structure for transmit and receive functions. The device is intended for use in polarization-based quantum cryptographic protocols, such as BB84. Our characterization indicates that the circuit can generate the four BB84 states (TE/TM/45°/135° linear polarizations) with >30 dB polarization extinction ratios and gigabit per second modulation speed, and is capable of decoding any polarization bases differing by 90° with high extinction ratios.
© 2017 Optical Society of America
1. Introduction
Secure communications has become increasingly important in modern times, affecting daily life in areas such as internet communications, bank transfers, and power grid security, as well as more traditional areas such as national security [1]. In addition to conventional methods of cryptography, people have been looking towards quantum cryptography (QC) to ensure absolute security [2–5]. QC is based on the idea that a single quantum cannot be cloned [6, 7], and so any attempt at eavesdropping will manifest as increased error rates in data.
In 1984, C. H. Bennett and G. Brassard proposed the first QC protocol, now known as BB84 [8]. This approach uses public channels to distribute keys from one person (ALICE) to (BOB). ALICE and BOB communicate by using a pair of two-level quantum states that are in different bases. They assign binary bit values to each quantum state and then ALICE sends data using randomly chosen bases. BOB records the data using his own set of randomly chosen bases. When ALICE and BOB choose the same basis, data is successively transferred, but when they choose different bases, no information is received. Afterwards, they announce their chosen bases (but not the measured state) to determine which transmitted bits were received correctly and to look for evidence of eavesdropping.
Recent efforts have realized systems for DV-QKD that use linear polarization states of light as the basis states, and polarization encoding/decoding DV-QKD has moved from feasibility proof with transmission >1 km [9] to full demonstration over 200 km link [10]. Most existing systems use discrete optical components, creating systems that are rather bulky and require significant space on an optical table. One way to decrease the required footprint is to turn to integrated optical systems. In [11] the authors demonstrated a DV-QKD system based on silica-based planar circuit. An alternative approach to integrated DV-QKD transceiver is silicon photonics (SiP) [12–15]. SiP has experienced phenomenal transformations demonstrating high performance modulators [16], detectors [17, 18], light sources [19, 20], and passive devices [21]. SiP circuits for polarization encoding/decoding entanglement distribution [22, 23] have been reported. Researchers also have demonstrated SiP polarization encoding/decoding DV-QKD transmitters [12, 13]. In this paper, we present a SiP DV-QKD transceiver circuit that can rapidly encode data into four linear polarization states of light (transverse electric (TE)/transverse magnetic (TM)/45°/135°) with high extinction ratios. In comparison to other works on SiP based QKD [12, 13, 15, 22–24], our device employs a common structure to realize both transmit and receive functions. It integrates an adiabatic/diabatic polarization beam splitter (PBS) [25], polarization splitter rotators (PSRs) [26], carrier-depletion phase shifters, amplitude adjustments, and a Mach-Zehnder modulator (MZM). Devices such as these should pave the way for high-speed DV-QKD systems.
2. SiP circuit design
Figure 1(a) shows the schematic of the SiP transceiver, and Fig. 1(b) shows the microscope image of a fabricated device on a 4 × 1.3 mm2 die. When the circuit is operating as a transmitter (TX), both the amplitude and phase of light are adjusted in the waveguide branches to create an arbitrary state of polarization (SOP) at the output. Among all the output SOPs, we are especially interested in the BB84 states, namely TE, TM, 45°, 135° linear polarizations. TE polarized light is coupled into a 2 × 2 MZM from either the bar or cross input waveguide. The MZM consists of a pair of carrier-depletion phase shifters φ1 and φ2 and two directional couplers connected by waveguides to create an interferometer structure. A second pair of MZMs is included to adjust the amplitudes of the light and ensure signal equalization or to implement advanced communication protocols such as decoy state [27]. Phase shifters φ3 and φ4 offer independent control of phase in the two branches. Light from the two branches is combined in a two-stage process. Each stage has one input that passes TE light without affecting it and one input that targets TM polarized light, but the physical processes differ in each. In the first stage, a PSR relying on mode hybridization transfers power from an input TE mode into an output TM mode in the bottom waveguide branch [26, 28]. The TE polarized light in the top waveguide branch propagates through the bar port of a PSR without any change in its polarization. The second stage is a PBS that has waveguides for TE and TM light. TM light is evanescently coupled onto the TE waveguide, but TE light on the second input remains in its initial waveguide [25].
Fig. 1 (a) Schematic of a SiP transceiver circuit for polarization encoding/decoding DV-QKD protocols. PBS, polarization beam splitter, PSR, polarization splitter rotator, φ, carrier depletion phase shifter, Amp, amplitude adjustment, MZM, Mach-Zehnder modulator. TE-polarized light is coupled from the right and various components split, shift, and rotate it to create arbitrary SOPs at the output when the circuit is running as a transmitter (TX). A receiver (RX) uses the same structure as the TX, but light propagates in the opposite direction. The input polarization state determines the output port. (b) Microscope image of the SiP transceiver circuit. The die size is 4 × 1.3 mm2 (c) IV curve of a carrier depletion phase shifter with ~-11 dBm of light coupled in.
When the circuit is operating as a receiver (RX), the encoded TE/TM/45°/135° polarized pulses are coupled into the SiP circuit from the PBS. The PBS splits the TE component of the input into the top waveguide branch, and the TM component into the bottom branch. The TM component is rotated to TE polarization by a PSR. The TE component remains unchanged and propagates through a PSR. The phase shifters on the MZM, φ1, φ2 and the phase shifters, φ3, φ4 between the PSRs and the MZM determine the measurement basis on the RX. We are able to achieve high extinction ratio (ER) between the bar and cross output waveguides for both rectilinear (TE/TM) and diagonal (45°/135°) bases by changing the phase introduced by φ1-φ4. They can also be adjusted to decode any two polarizations differing by 90°, with an arbitrary rotation angle, for example, that present in long stretches of a single mode fiber.
Figure 1(c) shows the IV curve of a carrier depletion phase shifter in the SiP circuit with ~-11 dBm of light at 1565 nm wavelength coupled in. These carrier depletion phase shifters are 1.25 mm long and consist of p-n junctions with ~5 × 1018/cm3 doping level achieved by arsenic and phosphorous implantation. They enable high speed operation of the SiP transceiver, much faster than thermal phase shifters. The figure of merit VπL is ~0.8 V·cm when the phase shifter is reverse biased or ~0.13 V·cm when forward biased. The carrier depletion phase shifters are more energy efficient compared to thermal phase shifters because of the very low current applied to the p-n junction, even in forward bias.
3. Polarization encoding
3.1 Measured SOPs for BB84
We connected the output of a TX module to a polarimeter using a single-mode fiber, and measured the SOP as we looped through a range of voltages applied to φ1 to φ4. Each measurement returns a normalized four-element Stokes vector, as defined in [29]. We repeated this measurement for a range of wavelengths, and presented the result on a Poincare sphere in Fig. 2. Each point in space corresponds to an SOP on the (s1, s2, s3) axes, with labels for special degenerate cases of polarization. It is seen that at shorter wavelengths, only a fraction of the sphere is covered, but it gradually covers up as we move to longer wavelengths. We also note that for BB84 we are not necessarily interested in covering the entire sphere, but only points at locations H, V, 45° and 135° (at the back of the sphere).
Fig. 2 Measured SOPs for different wavelength input, presented on a Poincare sphere: (a) 1520 nm, (b) 1550 nm and (c) 1585 nm. RCP, right-hand circular, LCP, left-hand circular, H, horizontal, V, vertical.
Figure 3 shows the variation of three Stokes parameters as a function of applied voltage from a test device. We coupled continuous-wave light at 1565 nm wavelength into the bar port of the MZM, and then swept the voltage applied to the phase shifters φ2 and φ4 in the bottom branch of the circuit. The amplitude adjustments were held constant. We found that we could produce near-ideal TE light with a Stokes vector S = when we biased the MZM bottom arm and bottom phase adjustment at −1.70V and −1.50V, respectively. We then calculated a polarization extinction ratio (PER) as
Further analysis of the data in Fig. 3 reveals optimum settings for the remaining BB84 states with PERs of ~14.7, ~32.6, ~35.1 dB, for TM, 45°, 135° polarizations, respectively. We also measured the degree of polarization (DOP) for each setting. This figure gives an idea how polarized the light is, regardless of the SOP. It is found aswith a maximum value of 1. The measured DOP is higher than ~0.9885 in Fig. 2 (d) at the output. Therefore, we can confidently say that the SiP TX does not depolarize the light appreciably as it encodes the output SOP.Fig. 3 Dependence of Stokes parameter on the bias voltages of MZM bottom arm φ2 and bottom phase shifter φ4. (a) Rectilinear Stokes parameter s1, (b) diagonal Stokes parameter s2, (c) circular Stokes parameter s3, and (d) degree of polarization (DOP). The phase shifters are reverse biased and the 1565 nm optical input is coupled into the SiP circuit from the bar port in the measurement.
Note that this is an example measurement to demonstrate the polarization encoding function of a transceiver circuit using reverse biased φ2 and φ4. In real operation, rather than varying the bias voltage of the phase shifters, we also have the flexibility to choose among different combinations of phase shifters, and change the bias polarity to have the four BB84 states with high PER from the output port. For instance, we applied forward bias on φ1 or φ2 and reverse bias on φ3 or φ4 in another test on the same device, from which we obtained data in Fig. 3. With optimum settings, the PERs for TE/TM/45°/135° polarizations are ~31.2, ~34.2, ~37.3, ~37.6 dB respectively, when the optical input was coupled into the transceiver from the cross port.
3.2 Speed of polarization modulation
Another major challenge for the TX SiP circuit is the high data-rate modulation of the output SOP. We tested the speed of polarization modulation using the setup shown in Fig. 4(a). In this measurement, we did not use the amplitude adjustments. We applied a non-return-to-zero (NRZ) signal to φ1. According to the static SOP test result shown in Fig. 4(b), the NRZ signal can change the output SOP between the TE and TM polarizations if we apply a proper DC bias on φ4 and DC offset on φ1. We coupled the light from the optical output waveguide using a piece of polarization maintaining (PM) lensed fiber. The fundamental TE and TM modes were aligned to the slow and fast axes of the PM fiber, respectively. The PM lensed fiber is connected to a fiber polarizer which only transmits the TE polarization (20 dB PER). The TE polarized component is measured by a high speed photodetector. This setup enabled us to carry out eye-diagram and classical bit-error rate (BER) measurements to characterize the speed of the output polarization modulation between TE and TM modes. Figure 4(c)-4(e) show the eye-diagrams of polarization modulation at 6, 8 and 10 Gbps data-rates with a clear traces in each case. However, the estimation of the extinction ratio (ER) at a high data-rate from the eye-diagram was limited by the experimental setup because the photodetector used in the measurement has a ~3 V DC output offset, which is much larger than the signal amplitude. Therefore, we had to use an AC coupled oscilloscope in the experimental setup which removed the zero reference in the eye-diagram by returning a negative voltage when the output SOP was TM polarized. In addition, the resolution of the RF amplitude will limit the PER performance of the device as we will not be able to access the exact bias points required for high purity states. On the device side, an impedance mismatch between the carrier depletion phase shifters and the RF wiring leads to frequency dependent excitation levels that affect the output SOP. However, our previous results have shown the bandwidth of our 1.25 mm long carrier depletion phase shifters is expected to be >14 GHz [30], and we would expect improved performance in this case. From a structural point of view, the hybrid couplers in the MZM structure could limit the dynamic PER. The split ratio of hybrid couplers displays greater wavelength dependence than the other components in the SiP circuit and phase modulation naturally produces a wavelength shift of the propagating light. However, we simulated the change in PER from the measurement of the on-chip test structures and estimated less than 1 dB difference in the PER when operating at the optimum wavelength and detuned by ± 20 GHz.
Fig. 4 (a) Experimental setup to measure the eye-diagrams and BER of polarization modulation by the SiP TX. (b) Static SOP 2-D map with bias on φ1 and φ4. (c-e) Eye-diagrams of polarization modulation at 6, 8 and 10 Gbps data-rate.
In addition, we measured error free operation for >5 mins, when the data-rate was 6 Gbps or lower. The BER at 8 and 10 Gbps were 2.5 × 10−11 and 9.0 × 10−10 /s, respectively. This classical BER illustrates that the bandwidth of the circuit, mainly the carrier depletion phase shifters and wiring parasitics should not place a limit to a DV-QKD link system with < 2 GHz clock rate which is mostly determined by the recovery time of single photon detectors. Its contribution to the quantum bit error rate is negligible and not taken into consideration in the estimation of the secret key generation rate in section 5.
4. Polarization decoding
When a SiP circuit operates as an RX under the BB84 protocol, we require the circuit capable of splitting the two states of the rectilinear (TE/TM) or diagonal (45°/135°) basis with a high extinction ratio (ER). That is, for one set of bias values on the MZM and phase shifters φ3 and φ4, the ratio of the power at the two outputs of the RX should clearly discriminate the TE vs. TM polarization at the input. With a second set of values for the MZM and phase shifters φ3 and φ4, the ratio of the two outputs should clearly show 45° vs. 135° polarization.
Figure 5 shows the 2-D maps of bar and cross port ER measured at 1565 nm wavelength. Figure 5(a)-5(d) have φ1 and φ4 reverse biased. A quick glance shows regions where we can find optimum ER for a given polarization state. For practical operation, though, we must use bias conditions that simultaneously give high ER for both polarization states of a given basis set. Therefore, in order to locate the optimal operation condition, we compare the ERs at the same bias points for complementary cases, like Fig. 5(a) and 5(b) or Fig. 5(c) and 5(d), etc. We define the lower absolute ER of the two polarizations as the operational ER. Thus, the optimal operational ER for TE and TM polarizations in Fig. 5(a) and 5(b) is ~18.4 dB when φ2 is biased at 0 V and the φ3 is 5.75 V reverse biased. The optimal single state and operational ERs are shown in Table 1 for each of the BB84 polarization states for reverse bias settings. The column 6 in Table 1 shows the optical insertion loss when the circuit is biased at the optimal operational ER setting. This insertion loss is normalized with the fiber to fiber (F2F) loss of a through waveguide on the same chip. The corresponding RX F2F loss is listed in column 7. We used lensed fibers with 3.5 µm diameter spot to couple light into/ out of the circuit in the test. The lensed fibers produced a spot size that was larger than the waveguide mode and thus introduced coupling loss due to mode mismatch. An alternative way for coupling is using high numerical aperture (NA) fibers. A numerical study showed that fibers with optimized NA would be capable of decreasing the coupling loss to ~0.5 dB for TE and ~1.5 dB for TM cases. Compared to the ~15.2/ 6.0 dB F2F loss of TE/TM modes measured from the through-waveguide used for normalization, high NA fibers can significantly decrease the loss for the DV-QKD link based on our SiP transceiver.
Fig. 5 RX extinction ratio (ER) between bar and cross output waveguides as a function of bias voltages of MZM arms and the phase shifters. In (a)-(d), both the MZM top arm φ1 and the bottom phase shifter φ4 are reverse biased. The optical input is TE/TM/45°/135° polarized in (a)-(d), respectively. In (e)-(h), the MZM top arm φ1 is forward biased and the bottom phase shifter φ4 is reverse biased
Table 1. Summary of RX decoding functionality for reverse bias conditions
The modulation efficiency is enhanced in carrier-depletion phase shifters under forward bias conditions [31, 32]. Figures 5(e)-5(h) show the 2-D maps of the ER for the bar and cross ports measured at 1565 nm wavelength when φ4 is reverse biased and φ1 is forward biased. The optimal single state and operational ERs and the optical insertion loss with forward bias on MZM top arm are listed in Table 2. When we apply forward bias on the MZM arms, it is easy to achieve >20 dB ER for both bases. The forward bias on carrier-depletion phase shifters does not introduce a much higher insertion loss than the reverse bias because the phase shifters are able to introduce a π phase shift at a bias not much higher than the turn-on voltage of the p-n junction. In this situation, the absorption due to free carriers is not yet significant.
Table 2. Summary of RX decoding functionality for mixed bias conditions
Additional to rectilinear and diagonal bases, the SiP circuit is capable of decoding polarizations differing by 90° with an arbitrary rotation angle. This function has been proposed in [33] and we tested decoding over arbitrary angles in 15° increments at 1550 nm wavelength. We changed the rotation angle of the optical input using a PM lensed fiber and rotating the slow axis respect to the horizontal direction. In this measurement, φ1 and φ4 were both reverse biased. The experimental results are shown in Fig. 6, and the optimal operational ER and the corresponding bias setting are listed in Table 3.
Fig. 6 dependence of ER between bar and cross output waveguides on the bias voltages of MZM arms and the phase adjustments when the optical input is linearly polarized. (a)-(f) show the input of rectilinear, 15°/105°, 30°/120°, diagonal, 60°/150°, 75°/165° bases, respectively.
Table 3. Optimal operational ER of different polarization bases
This function of the SiP circuit ensures that the RX is capable of decoding the BB84 states transmitted through a long single mode fiber in a link, which may rotate the SOP, but maintains close to linear polarization for reasonable distances.
5. Estimation of secret key rate
Based on the above performance of our SiP transceiver, we estimate the quantum bit error rate (QBER) and secret key generation rate of a DV-QKD link system implementing BB84 using Eq. (11) in [34] and Eq. (12) in [27]. We employed the specifications of a commercial superconducting nanowire single photon detector [35]. Additionally, we assumed the error correct function f = 1, which means perfect correction [36], optimum expected photon number of the signal, which maximize the ratio of the single photon gain to the overall gain, and ideal coupling from fiber to detector. The parameters used in the estimation are listed in Table 4, and the result is illustrated in Fig. 7. With an optimal fiber to waveguide coupling loss of 1.5 dB, we expect a maximal transmission distance of ~127 km. The absolute key generation rate is proportional to the system clock rate, which is limited by the reset time of the single photon detector.
Table 4. Parameters used in secret key rate estimation
Fig. 7 Estimated secret key generation rate and QBER implementing BB84 protocol. The parameters used in the estimation are listed in Table 4. The optimal expected photon number is calculated using Eq. (12) in [34]. The maximal transmission distance is ~127 km in single mode fiber.
6. Discussion
Our measurements indicate that the SiP circuit is capable of polarization encoding/decoding for the BB84 DV-QKD protocol. Although our devices show clean, high-speed performance, there are a few areas that could be modified that would improve the operation. One area to concentrate on is the optical splitters in the MZM. The directional couplers in the transceiver circuit have a strong wavelength sensitivity. The optimal wavelength of the directional couplers in the test circuits was ~1586 nm and mismatched with the PBS that was centered closer to 1550 nm. Replacing directional couplers with either adiabatic or multimode interference couplers would ensure a split ratio closer to 50:50 across a wider bandwidth. This is important because of the spectral bandwidths of the PBS and PSR used in the circuit. We believe the misalignment between the optimal wavelength of directional couplers and the bandwidths of PBS and PSR resulted in the uncovered fraction of Poincare spheres in Fig. 2(a) and 2(b) and the <20 dB ERs in the polarization decoding measurement.
Our SiP circuit employs carrier-depletion phase shifters. Although they introduce some optical loss in operation, their strength is in their higher speed operation compared to thermal phase shifters [38]. Nowadays, high speed performance of transceivers is essential for DV-QKD links. The slow reset time of single photon detectors [39] used to limit the QKD system clock rate to MHz level. With the recent progress in superconducting nanowire single photon detectors, it has been accelerated to GHz [24]. Consequently, there is a demand for high speed polarization encoding/decoding, which can be satisfied by the carrier-depletion phase shifters. Our carrier-depletion phase shifters could be further improved using standard high-speed modifications such as optimized wiring (i.e. coplanar striplines) or travelling wave electrodes [30]. The phase introduced by a carrier depletion phase shifter is sensitive to environmental and temperature changes, thus a closed loop compensation system is required for a DV-QKD link using our SiP transceiver. The SiP circuit has phase shifters φ3 and φ4 between the MZM and the PSRs. They offer independent phase control in the top and bottom branches of the circuit, which can compensate for imperfections in the PBS/PSR or the MZM.
One major factor deciding the QBER and the secret key generation rate is the RX F2F loss. As mentioned in Section 4, the RX circuit indicates reasonable insertion loss after being normalized with a through waveguide. However, the waveguide to fiber coupling loss is yet non-ideal in the measurements presented in this paper. We are capable of resolving this issue by using high NA fibers for coupling according to our numerical study.
When building a polarization encoding/decoding DV-QKD optical fiber link system, polarization rotation and polarization mode dispersion (PMD) in single mode fiber have the potential to affect the key rate and distance. In section 4, we demonstrated the RX decoding of linear polarizations differing by 90° with an arbitrary rotation angle. Therefore, the RX is capable of decoding BB84 states from the TX by calibrating the polarization rotation in the transmission channel before the key exchange. In addition, the PMD of our calculated maximal ~127 km transmission distance in fiber can result in up to ~0.5 ps temporal delay between the TE and TM components [37], thus changing linear polarization to elliptical. We believe after the input polarization is decomposed by the PBS, φ3 and φ4 are capable of compensating PMD in the transmission channel. Specifically, the silicon waveguide with 400 × 230 nm2 cross-section in our SiP transceiver indicates stronger PMD than the fiber channel due to group indices that are 4.45 and 3.68 for the fundamental TE and TM modes respectively. The waveguide length from the RX input to the PSR which rotates the fundamental TM mode to TE is ~2 mm, which introduces a ~5.0 ps temporal delay. The demonstration of polarization decoding in section 4 provides a solid proof that the waveguide PMD has been compensated.
The circuit also includes intensity adjustments having an MZM structure with a carrier depletion phase shifter on each arm. They offer the function of independent intensity attenuation in the top and bottom waveguide branches. Thus, they are capable of balancing the intensity variation of the BB84 states. Furthermore, they enable the circuit to work under more advanced protocols than BB84, e.g. decoy state which is able to overcome the photon-number-splitting attack for BB84 [40].
The power consumption of a modulator is approximately given by αCV2f, where C is the capacitance, V is the applied voltage, f is the clock frequency (bit rate), and α is the utilization factor, which is 0.25 for random data. Operating in reverse bias for an estimated capacitance of 1 pF (0.83 fF/µm) [41], V = 7 V, f = 1 GHz gives a power consumption of 12.5 mW. (So far, the highest clock rate of DV-QKD link is ~1 GHz [15].) For a 25 Gbps data communications link, a 1.4 V modulating voltage will give the same power consumption. Many of the low voltage demonstrations for data communications systems do not operate over a full π phase shift, so those systems have an advantage in power consumption for a given device and any comparison must take that into account.
Our figure of merit, VπL, of ~0.8 V·cm is among the lowest of silicon photonics transceivers [42], but there are a few methods to further reduce the voltage. We can operate partially in forward bias but still less than the built-in field, so the device remains as fast as in reverse bias, limited by carrier sweep out versus recombination [43]. We can tune opposite phase shifters differentially with one partially into forward bias to reduce the reverse bias on another; we didn’t investigate this method because of the need to modify 4 voltages simultaneously, two for each section of the device (see Fig. 1a). We can modify the doping in our device to create greater carrier changes versus voltage [44]. Lastly, because the key rate is low compared to the device capabilities, we can lengthen the device, which reduces the power consumption because of the square term in the voltage versus linear term in capacitance. However, some of these examples (e. g. forward bias, increased doping, increased length) increase the optical loss. In the TX, additional loss may be tolerable, but in the RX an increase in loss may prove to be a poor trade-off for decreased power consumption. So, while there is room for improvement in reducing the voltage through modified device design, care must be taken to make sure the changes do not adversely affect the key rate or distance in the QKD application.
7. Conclusion
We demonstrate a silicon photonics integrated transceiver capable of implementing the BB84 DV-QKD protocol for both the TX and RX. The transceiver is designed and fabricated on Sandia National Laboratories’ silicon photonic platform. As a TX, it is capable of encoding BB84 states with >30 dB PER and has a low classical BER of 9.0 × 10−10 s−1 when modulated at 10 Gbps data rate. As an RX, it is capable of decoding BB84 states with >20 dB ER, and in addition, is capable of decoding polarizations differing by 90° with an arbitrary rotation angle. We estimated an ideal secret key generation rate of a DV-QKD link system based on the SiP transceiver implementing the BB84 protocol, assuming state of the art fiber coupling (1.5 dB) to the chip and single photon detector. The maximal transmission distance is calculated to be ~127 km.
Funding
United States Department of Energy’s National Nuclear Security Administration (DE-AC04-94AL85000).
Acknowledgments
Sandia is a multi-mission laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
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