- Email: [email protected]
Single-photon interference using silica-based AMZI with phase modulation
Optics and Laser Technology 122 (2020) 105837
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
Single-photon interference using silica-based AMZI with phase modulation a,b
a,b
Meizhen Ren , Xiao Li ⁎ Junming Ana,b, a b
a
a
a
T
a,b
, Jiashun Zhang , Liangliang Wang , Yue Wang , Yuanda Wu
,
State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
H I GH L IG H T S
TOPM can modulate the phase difference between the double pulses. • The visibility was dependent on the temperature. • The visibility was dependent on the polarization of the input light. • The observed maximum visibility was 98.38%. • The • The stability of the PLC-based AMZIs was demonstrated.
A R T I C LE I N FO
A B S T R A C T
Keywords: Quantum key distribution Integrated optics Asymmetric Mach-Zehnder interferometer
An asymmetric Mach-Zehnder interferometer (AMZI) which comprised a variable optical attenuator (VOA), a thermo-optic phase modulator (TOPM) and a delay line of 740 ps was designed and fabricated using silica-based planar lightwave circuit technology. Two identical AMZI chips were connected in series to demonstrate the single photon interference in the middle pulse. The experimental results showed the TOPM can modulate the phase difference between the double pulses. The single photon interference visibility was dependent on the temperature and the polarization of the input light. The observed maximum visibility was 98.38% when the temperature of temperature controller (TEC) was 10 °C. And the interference visibility was dependent on the polarization of the input light. The AMZI could form the basis of the passive decoder in the future quantum cryptography systems.
1. Introduction Quantum key distribution (QKD) allows two remote parties (e.g., Alice and Bob) to generate a secret key, with privacy guaranteed by quantum mechanics. Since Bennet and Brassard introduced the BB84 protocol in 1984[1,2], extensive efforts have been devoted to extending the transmission distance. In the fiber-based QKD systems, quantum information is encoded in the relative phase between adjacent two pulses. Townsend et al. first demonstrated 10 km transmission of single interfering photons using the piezoelectric transducer in the AMZI [3]. The next breakthrough was made by using Faraday mirrors to autocompensate the polarization drift and the transmission length was extended to 23 km [4]. Kimura et al. demonstrated single-photon interference using temperature-dependent phase modulation of AMZIs over 150 km [5]. Then a BB84 QKD system was developed by inserting three fiber-optic phase modulators, two in Alice′s and one in Bob′s apparatus
⁎
[6]. The system was stable and backscattering-free with no active compensation. But the insertion of the extra devices might increase the loss of Bob′s apparatus and the quantum bit error rate (QBER). This difficulty was solved by Yoshihiro et al. [7]. They developed a new decoding method, which can eliminate the phase-modulator in Bob′s apparatus. So we can name this method as passive decoding method. This method has several advantages which can reduce the loss, increase the key generation rate, eliminate the phase-modulator in Bob′s apparatus and improve the security. The cost for these advantages is to use a more sophisticated photon detector. Besides, a modulator-free quantum key distribution transmitter chip was developed to simplify the transmitter [8]. Integrated chips are promising in the practical application of QKD network [9,10]. Recently the passive decoding method is widely used in the integrated QKD systems. It extensively provides multi-protocol operation and multiple time-bin selection [11–13]. In this method, there are two
Corresponding author. E-mail address: [email protected] (J. An).
https://doi.org/10.1016/j.optlastec.2019.105837 Received 16 July 2019; Received in revised form 4 September 2019; Accepted 11 September 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 122 (2020) 105837
M. Ren, et al.
Fig. 1. The structure diagram of the AMZI.
peak 25 mW and frequency 50 MHz were introduced into the SMF pigtail of chip-A from the high speed pulsed laser. The input pulse was linearly polarized, but the polarization azimuth was along a random direction. The chip-A and chip-B were mounted on the same TEC platform. And the entire system was enclosed in an aluminum box with the heat preservation cotton. The input pulse was divided into two coherent output pulses by chip-A, one passing through the short arm and the other through the long arm. The two optical pulses were attenuated so that their average number of photons was on the order of single photon. After traveling through chip-B, the two faint pulses created three pulses in the output ports. And the first and last pulses were independent of the relative phase between the two propagating pulses, whereas the middle pulse depended on the relative phase. The voltages on the VOA of chip-A and chip-B were controlled by the RIGOL DC power supply. The keithley 2400 sourcemeter controlled the voltage on the TOPM of chip-B. The personal computer controlled the the infrared single photon detector (SPD) and the keithley2400 through the serial port and GPIB line. To make sure accuracy, the two faint pulses were tested by the SPD. The synchronous signal from the pulsed laser was used to trigger the SPD. So the SPD could measure the photon counts at different delay times offset from the trigger time. The single photon counts of the SPD is the accumulative detection counts per second. The delay time resolution of the SPD is 10 ps. When the voltage on the VOA of chip-A is 7.4 V, the test result is depicted in Fig. 4. The photon counts in the one of double pulses were approximately 3.5 × 104. So the average number of photons per pulse μ was less than the order of 0.1. This can obtain a reasonable approximation to a single photon source. Now the attenuator whose attenuation was 75 dB, was composed of SMF and adjustable flanges. The delay time between the two pulses was 800 ps. The test value of delay time was more than the designed value, which was because the delay time resolution and the delay time jitter of the SPD is 10 ps and about 50 ps respectively. So the difference 60 ps between the test and designed values was within the range of test error. When the voltages on the VOA of chip-A and chip-B were 7.4 V and 7.9 V respectively, they both were on the balanced state (The test details are in the supplementary research data). The three pulses output from chip-B were tested by the SPD. When the temperature of TEC is 5 °C, a typical distribution of the three pulses plotted as a function of delay time is shown in Fig. 5. The first pulse in Fig. 5 transmitted from the short arms of chip-A and chip-B. The third pulse arose from photons that have travelled the long arms of chip-A and chip-B. The middle pulse was the superposition of two pulses. One of the pulses transmitted from the short arm of chip-A and the long arm of chip-B. The other one transmitted from the long arm of chip-A and the short arm of chip-B. So the middle pulse will exhibit interference, depending on the phase difference of chip-A and chip-B. The interval times between the three pulses are 800 ps as expected. When the delay time was 11600 ps, the peak of the middle pulse was detected. The location of the middle pulse was independent of the temperature of TEC. To observe interference, the amplitude of the middle pulse was investigated by setting the delay time of the SPD at 11600 ps and scanning the voltage on the TOPM of chip-B. A typical series of experiments was preceded by adjusting the
important functions which influence the performance of the whole system. One is to modulate the power ratio of the two pulses, the other is to modulate the phase difference between the double pulses. In addition, the modulation of power is also important for decoy-state in QKD systems and can be used to prepare different intensities for the light source [14]. The passive method is also useful in decoy-state QKD [15]. In this letter, we propose an AMZI which have the two functions simultaneously. We have demonstrated single-photon interference with high visibility. The interference visibility of the system is dependent on temperature and the polarization of the input light. The devices were fabricated using the silica-based PLC technology. The waveguide core geometry was designed to be 6 × 6 μm, which can optimize coupling loss to single-mode fibers at around 1550 nm. Fig. 1 shows the schematic diagram of the device. The geometric path difference ΔL of the AMZI is 152.51 mm, which can generate 740 ps delay time. The AMZI comprises two parts. The first part is a VOA to adjust the power ratio of the two arms in the second part, which can make the output double pulses have balanced amplitude. The second part not only is to generate double pulses, but also is to modulate the phase difference between the double pulses by the TOPM. The TOPM was used to set the optimum operating point for data decoding using the thermo-optic effect. 2. Experimental results We first measured the insertion loss of the AMZI which is defined as the ratios of the input power into the fiber coupled to the chip and the total output power from the fibers coupled to the two output ports. The insertion loss of chip-A and chip-B are 1.83 dB and 2.24 dB respectively. Then the chips were butt-coupled by fiber arrays with single mode fiber (SMF) pigtails. After the chips were adhered to the printed circuit boards (PCB), the heaters of chips were connected with the PCB by wire-bonding. Fig. 2 shows the packaged chip on the PCB. 2.1. Temperature The experimental setup for investigating the effect of different temperatures of TEC on the performance of AMZI is shown in Fig. 3. Two AMZI chips were connected in series by the SMF to produce a QKD interferometer system. 1550 nm pulses with pulse width 50 ps, pulse
Fig. 2. The packaged AMZI chip. 2
Optics and Laser Technology 122 (2020) 105837
M. Ren, et al.
Fig. 3. The schematic diagram of the QKD interferometer system: the effect of the temperature of TEC.
Fig. 4. The two pulses on the order of single photon transmitted in the quantum channel.
Fig. 6. The single photon interference pattern of the middle pulse at the temperature of 5 °C.
Fig. 5. The three pulses output from chip-B.
temperature of TEC. Single photon counts were acquired as a function of the voltage on the TOPM of chip-B under different temperatures. Note that the dark count background was not subtracted. Fig. 6 shows the single photon interference pattern obtained at the temperature of 5 °C. The interference visibility of 86.03% was calculated from the observed maximum and minimum photon counts. The interference visibility at different temperatures are shown in Fig. 7. The interference visibility reached the maximum of 98.38% and the minimum of 43.03% when the temperature of TEC was 10 °C and 20 °C respectively.
Fig. 7. The interference visibility versus the temperature of TEC.
2.2. Stability In the QKD systems, the stability is an important issue. To demonstrate it, we set the temperature of TEC at 10 °C so that the maximum visibility could be observed. Then we monitored the visibility within four hours and the visibility was measured every 20 min. Fig. 8 shows the measured visibility as a function of time. The visibility varied
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connected like Fig. 3. The transmission process of the pulses was also similar to Fig. 3. The output state of polarization (SOP) of the polarization controller could be tracked to one of the basis SOPs spanning the Stoker space: LP0° (1,0,0), LP45° (0,1,0), LP90° (−1,0,0), LP135° (0,−1,0), RHC (0,0,1), LHC (0,0,−1). The schematic diagram of SOP on the poincare sphere is shown in Fig. 10(b). When the SOP of polarization controller was tracked to LP0°, the temperature of TEC is 5 °C, the voltages on the VOA of chip-A and chipB were 7.4 V and 7.9 V respectively, the three pulses output from chip-B were tested by the SPD. The distribution of the three pulses plotted as a function of delay time is shown in Fig. 11. Because the attenuation of the attenuator was also adjusted to 75 dB, the amplitudes of the first and last pulses were lower than Fig. 5. When the delay time was 11460 ps, the peak of the middle pulse was detected. The curve was moved parallelly because of the addition of polarization controller in the optical path. The location of the middle pulse was independent of the output SOP of polarization controller. Then the amplitude of the middle pulse was investigated by setting the delay time of the SPD at 11460 ps and scanning the voltage on the TOPM of chip-B. A typical series of experiments was preceded by tracking the different SOPs and adjusting the temperature of TEC. The results of the interference visibility are shown in Table 1.
Fig. 8. The stability of the PLC-based AMZI.
between 95.69% and 99.45% within four hours, the variation was less than 3.76%. The phase could keep basically stable within four hours. So the PLC-based AMZI has sufficient visibility and time-stability performance. In addition, the above experiments were carried out through an attenuator. In order to emulate the operation of a real system, we measured the performance of the PLC-based AMZIs over 20 km singlemode fiber G.652 with transmission loss 3.8 dB@1550 nm. The three pulses transmitted were shown in Fig. 9(a). The curve was broaden compared with Fig. 5 due to the dispersion of the fiber. The tested visibility was 97.95%. In order to emulate different lengths of fiber, a variable attenuator was inserted after the 20 km fiber. This can emulate the transmission of dispersion-shifted fiber G.653 with very low dispertion. The visibility was measured with increasing the attenuator 1.9 dB (that is, increasing 10 km fiber) every time. The results are shown in Fig. 9(b). The visibility decreased to 89.7% when the emulated fiber length increased to 50 km, as shown in black curve. It should be noted that the dark count background was not subtracted and the dark count background of SPD was about 150. The visibility with background subtraction was shown in red curve in Fig. 9(b). The visibility varied between 93.9% and 99.3% within 80 km. So the PLC-based AMZIs could keep a high visibility within 80 km.
2.4. Different phase points of the middle pulse In the real QKD system, it is not essential to set all phase points on the interference curve. Generally, we only need to acquire four phase points, such as, 0, π/2, π and 3π/2. In the experiments of section A, the interference visibility reached the maximum of 98.38% when the temperature of TEC is 10 °C. When the voltages on the TOPM of chip-B were 5.4 V, 6.8 V, 8.6 V and 10.2 V respectively, the interference curve reached the minimum, the average of the maximum minus the minimum, the maximum, again the average of the maximum minus the minimum. And these four voltages corresponded to the phase difference between chip-A and chip-B of π, 3π/2, 2π, 5π/2. An example with typical pulse shapes is shown in Fig. 12. 3. Discussion The perfect interference occurs when two interfering pulses recombine at the output coupler with the same polarization [16]. The photon counts in the middle pulse is
2.3. Polarization
N = N1TE + N2TE + 2 N1TE N2TE cos(ΔϕTE ) + N1TM + N2TM
In the experiments of section A, we found the polarization of the input light affected the amplitude of the middle pulse significantly. So we implemented the setup in Fig. 10(a) to investigate the effect of the polarization of the input light. The input pulses were first polarization controlled before input to the chip-A. The other apparatuses were
+ 2 N1TM N2TM cos(ΔϕTM ) N1TE = N1TM = N1/2 N2TE = N2TM = N2/2
Fig. 9. (a) The three pulses output from chip-B over a real fiber of 20 km (b) The visibility versus the emulated fiber distance. 4
(1)
Optics and Laser Technology 122 (2020) 105837
M. Ren, et al.
Fig. 10. (a) Schematic diagram of the QKD interferometer system: the effect of the polarization of the input light (b) The schematic diagram of SOP on the poincare sphere.
where N1 and N2 are the photon counts of the two interference pulses, N1TE and N1TM are the photon counts of one of the two interference pulses for TE and TM modes, N2TE and N2TM are the photon counts of the other one interference pulse for TE and TM modes, ΔϕTE is the relative phase delay between the two arms of AMZI in the TE polarization mode and ΔϕTE = 2πnTEΔL/λ0, ΔϕTM is the relative phase delay between the two arms of AMZI in the TM polarization mode and ΔϕTM = 2πnTMΔL/ λ0. The difference of the modal phase mismatch between TE and TM Δϕ = ΔϕTE − ΔϕTM = 2πΔnΔL/λ0. polarization modes is TE TM Δn = n − n is the modal birefringence. nTE and nTM are the modal refractive index for TE and TM modes in the silica waveguides, Ls and Ll are the geometrical path length of the short and long arm of AMZI (s:short and l:long), ΔL = Ll − Ls is the geometrical path-length difference of the AMZI. λ0 is the wavelength in vacuum. ΔϕTM can be expressed as Fig. 11. The three pulses output from chip-B when the SOP was tracked to LP0°.
ΔϕTE = ΔϕTM + Δϕ Then
Table 1 The interference visibility under different temperatures and input SOPs. Temperature/°C
N = N1 + N2 + 2 N1 N2 cos
Polarization
= N1 + N2 + 2 N1 N2 LP0°
LP45°
LP90°
LP135°
RHC
LHC
92.87% 92.01% 82.23% 97.40% 94.96% 31.71% 97.58% 90.46% 86.68%
96.99% 91.12% 52.46% 37.39% 51.89% 71.47% 75.95% 52.57% 83.56%
91.76% 88.84% 66.01% 96.46% 92.14% 37.26% 97.44% 84.56% 86.73%
97.28% 90.89% 74.88% 28.42% 48.25% 67.10% 66.53% 46.40% 74.96%
91.54% 72.77% 96.94% 42.32% 53.45% 81.86% 63.31% 43.12% 79.06%
92.88% 68.41% 96.94% 48.44% 57.73% 76.11% 71.10% 41.48% 73.64%
(2)
(
ΔϕTE + ΔϕTM 2
cos(ΔϕTM
) cos (
ΔϕTE − ΔϕTM 2
+ Δϕ/2) cos(Δϕ/2)
) (3)
The interference visibility is 5 7.5 10 12.5 15 17.5 20 22.5 25
V=
N1 N2 Nmax − Nmin cos(Δϕ/2) =2 Nmax + Nmin N1 + N2
(4)
It is obvious that the visibility depends on N1, N2 and Δϕ . It depends only on Δϕ when N1 = N2. The interference visibility reached the maximum whenΔϕ = 2mπ and the interference visibility reached the minimum when Δϕ =(2 m + 1)π, where m is an integer. ΔϕTM changes with the voltage on the TOPM. The silica waveguides have the birefringence and the thermo-optic effect, so the modal birefringence Δn is temperature dependent. Hence the interference visibility is temperature-dependent. According to the formula (4) and the interference visibility was 86.03% when the temperature of TEC was 5 °C, Δϕ could be got as 0.34π. And ΔϕTM changes linearly with the square of the voltage. N1 = 6339 and N2 = 6381 could be get from Fig. 5. Then the fitting curve of Fig. 6 is shown in Fig. 13 through setting the appropriate coefficient for ΔϕTM and the square of the voltage. In addition to the maximum value of the fitted curve, the curve fitted well with the test data. According to the data in Table 1, we calculated the mean square deviation of the interference visibility between the different input SOPs. The mean square deviation achieved the minimum value when the temperature was 5 °C. In other words, the input SOPs have less impact on the interference visibility at the temperature of 5 °C. Corresponding to each input SOP, the interference visibility reached the maximum at a special temperature. For example, the interference visibility reached the maximum of 97% at the temperature of 20 °C for the input SOP of
Fig. 12. The typical pulse shape for different phase difference between chip-A and chip-B.
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Optics and Laser Technology 122 (2020) 105837
M. Ren, et al.
Fig. 13. The fitting curve of the single photon counts of the middle pulse at the temperature of 5 °C.
doi.org/10.1016/j.optlastec.2019.105837.
LP0° and LP90°. The interference visibility reached the maximum of 97% at the temperature of 5 °C for the input SOP of LP45° and LP135°. The interference visibility reached the maximum of 96.9% at the temperature of 10 °C for the input SOP of RHC and LHC. The test interference visibility may not reach the best because the temperature step was 2.5 °C in the experiment. It should be noted that there was a sudden drop for every input SOP at a specific temperature range. For example, the visibility dropped from 94.96% to 31.71% for LP0° when the temperature increased just 2.5 °C. Similarly, the visibility dropped from 91.12% to 52.46% for LP45°. I think the reasons for this phenomenon were as follows. Because no polarization maintaining fiber was used between the polarization controller and the AMZI chip, for any of the six basis SOPs, it can be split into two polarization modes (TE and TM modes) corresponding to the polarization direction of the waveguide. Then there will be a similar curve like Fig. 7 for any of the six basis SOPs. The curve had steep and flat areas. In steep areas, the visibility changed significantly within a small temperature change.
References [1] C.H. Bennett, G. Brassard, Quantum cryptography: Public key distribution and coin tossing, Theoret. Comput. Sci. 560 (2014) 7–11. [2] C.H. Bennett, F. Bessette, G. Brassard, L. Salvail, J. Smolin, Experimental quantum cryptography, J. Cryptol. 5 (1992) 3–28. [3] P.D. Townsend, J.G. Rarity, P.R. Tapster, Single photon interference in 10 km long optical fibre interferometer, Electron. Lett. 29 (1993) 634–635. [4] A. Muller, H. Zbinden, N. Gisin, Quantum cryptography over 23 km in installed under-lake telecom fibre, Europhys. Lett. (EPL) 33 (1996) 335–340. [5] T. Kimura, Y. Nambu, T. Hatanaka, A. Tomita, H. Kosaka, K. Nakamura, Singlephoton Interference over 150 km transmission using silica-based integrated-optic interferometers for quantum cryptography, Jpn. J. Appl. Phys. 43 (2004) L1217–L1219. [6] Y. Nambu, K.I. Yoshino, A. Tomita, One-way quantum key distribution system based on planar lightwave circuits, Jpn. J. Appl. Phys. 45 (2006) 5344–5348. [7] Y. Nambu, T. Hatanaka, K. Nakamura, BB84 quantum key distribution system based on silica-based planar lightwave circuits, Jpn. J. Appl. Phys. 43 (2004) L1109–L1110. [8] T.K. Paraïso, I. De Marco, T. Roger, D.G. Marangon, J.F. Dynes, M. Lucamarini, Z. Yuan, A.J. Shields, A modulator-free quantum key distribution transmitter chip, NPJ Quant. Inform. 5 (2019) 42. [9] C.-Y. Wang, J. Gao, Z.-Q. Jiao, L.-F. Qiao, R.-J. Ren, Z. Feng, Y. Chen, Z.-Q. Yan, Y. Wang, H. Tang, X.-M. Jin, Integrated measurement server for measurement-device-independent quantum key distribution network, Opt. Express 27 (2019) 5982–5989. [10] M.G. Thompson, Large-scale integrated quantum photonic technologies for communications and computation, Optical Fiber Communication Conference (OFC) 2019, OSA Technical Digest, Optical Society of America, 2019 W3D.3. [11] P. Sibson, C. Erven, M. Godfrey, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M.G. Tanner, C.M. Natarajan, R.H. Hadfield, J.L. O’Brien, M.G. Thompson, Chip-based quantum key distribution, Nat. Commun. 8 (2017) 13984. [12] P. Sibson, J.E. Kennard, S. Stanisic, C. Erven, J.L. O’Brien, M.G. Thompson, Integrated silicon photonics for high-speed quantum key distribution, Optica 4 (2017) 172–177. [13] A. Tomita, K.-I. Yoshino, Y. Nambu, A. Tajima, A. Tanaka, S. Takahashi, W. Maeda, S. Miki, Z. Wang, M. Fujiwara, M. Sasaki, High speed quantum key distribution system, Opt. Fiber Technol. 16 (2010) 55–62. [14] C.-Z. Peng, J. Zhang, D. Yang, W.-B. Gao, H.-X. Ma, H. Yin, H.-P. Zeng, T. Yang, X.B. Wang, J.-W. Pan, Experimental long-distance decoy-state quantum key distribution based on polarization encoding, Phys. Rev. Lett. 98 (2007) 010505. [15] L. Liu, F.-Z. Guo, S.-J. Qin, Q.-Y. Wen, Round-robin differential-phase-shift quantum key distribution with a passive decoy state method, Sci. Rep. 7 (2017) 42261. [16] Y. Nambu, K.I. Yoshino, A. Tomita, Quantum encoder and decoder for practical quantum key distribution using a planar lightwave circuit, J. Mod. Opt. 55 (2008) 1953–1970.
4. Conclusion In summary, we have demonstrated an AMZI integrated chip that has the potential to form the basis of the passive decoder in the future quantum cryptography systems. This AMZI can modulate the power ratio and the phase difference between the double pulses. The influence factors of single photon interference visibility were investigated, such as temperature, the polarization of the input light. In order to guarantee the stable temperature for the chips, it is necessary to use the TEC platform. And the whole systems should be placed in aluminum box with the heat preservation cotton. These results were useful to improve the long-term stability of the practical fiber-based QKD system. Acknowledgement This work was supported by National Key R&D Program of China (2018YFA0306403), National Nature Science Foundation of China (61805232, 61435013) and K.C. Wong Education Foundation. Appendix A. Supplementary material Supplementary data to this article can be found online at https://
6
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
Single-photon interference using silica-based AMZI with phase modulation a,b
a,b
Meizhen Ren , Xiao Li ⁎ Junming Ana,b, a b
a
a
a
T
a,b
, Jiashun Zhang , Liangliang Wang , Yue Wang , Yuanda Wu
,
State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
H I GH L IG H T S
TOPM can modulate the phase difference between the double pulses. • The visibility was dependent on the temperature. • The visibility was dependent on the polarization of the input light. • The observed maximum visibility was 98.38%. • The • The stability of the PLC-based AMZIs was demonstrated.
A R T I C LE I N FO
A B S T R A C T
Keywords: Quantum key distribution Integrated optics Asymmetric Mach-Zehnder interferometer
An asymmetric Mach-Zehnder interferometer (AMZI) which comprised a variable optical attenuator (VOA), a thermo-optic phase modulator (TOPM) and a delay line of 740 ps was designed and fabricated using silica-based planar lightwave circuit technology. Two identical AMZI chips were connected in series to demonstrate the single photon interference in the middle pulse. The experimental results showed the TOPM can modulate the phase difference between the double pulses. The single photon interference visibility was dependent on the temperature and the polarization of the input light. The observed maximum visibility was 98.38% when the temperature of temperature controller (TEC) was 10 °C. And the interference visibility was dependent on the polarization of the input light. The AMZI could form the basis of the passive decoder in the future quantum cryptography systems.
1. Introduction Quantum key distribution (QKD) allows two remote parties (e.g., Alice and Bob) to generate a secret key, with privacy guaranteed by quantum mechanics. Since Bennet and Brassard introduced the BB84 protocol in 1984[1,2], extensive efforts have been devoted to extending the transmission distance. In the fiber-based QKD systems, quantum information is encoded in the relative phase between adjacent two pulses. Townsend et al. first demonstrated 10 km transmission of single interfering photons using the piezoelectric transducer in the AMZI [3]. The next breakthrough was made by using Faraday mirrors to autocompensate the polarization drift and the transmission length was extended to 23 km [4]. Kimura et al. demonstrated single-photon interference using temperature-dependent phase modulation of AMZIs over 150 km [5]. Then a BB84 QKD system was developed by inserting three fiber-optic phase modulators, two in Alice′s and one in Bob′s apparatus
⁎
[6]. The system was stable and backscattering-free with no active compensation. But the insertion of the extra devices might increase the loss of Bob′s apparatus and the quantum bit error rate (QBER). This difficulty was solved by Yoshihiro et al. [7]. They developed a new decoding method, which can eliminate the phase-modulator in Bob′s apparatus. So we can name this method as passive decoding method. This method has several advantages which can reduce the loss, increase the key generation rate, eliminate the phase-modulator in Bob′s apparatus and improve the security. The cost for these advantages is to use a more sophisticated photon detector. Besides, a modulator-free quantum key distribution transmitter chip was developed to simplify the transmitter [8]. Integrated chips are promising in the practical application of QKD network [9,10]. Recently the passive decoding method is widely used in the integrated QKD systems. It extensively provides multi-protocol operation and multiple time-bin selection [11–13]. In this method, there are two
Corresponding author. E-mail address: [email protected] (J. An).
https://doi.org/10.1016/j.optlastec.2019.105837 Received 16 July 2019; Received in revised form 4 September 2019; Accepted 11 September 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 122 (2020) 105837
M. Ren, et al.
Fig. 1. The structure diagram of the AMZI.
peak 25 mW and frequency 50 MHz were introduced into the SMF pigtail of chip-A from the high speed pulsed laser. The input pulse was linearly polarized, but the polarization azimuth was along a random direction. The chip-A and chip-B were mounted on the same TEC platform. And the entire system was enclosed in an aluminum box with the heat preservation cotton. The input pulse was divided into two coherent output pulses by chip-A, one passing through the short arm and the other through the long arm. The two optical pulses were attenuated so that their average number of photons was on the order of single photon. After traveling through chip-B, the two faint pulses created three pulses in the output ports. And the first and last pulses were independent of the relative phase between the two propagating pulses, whereas the middle pulse depended on the relative phase. The voltages on the VOA of chip-A and chip-B were controlled by the RIGOL DC power supply. The keithley 2400 sourcemeter controlled the voltage on the TOPM of chip-B. The personal computer controlled the the infrared single photon detector (SPD) and the keithley2400 through the serial port and GPIB line. To make sure accuracy, the two faint pulses were tested by the SPD. The synchronous signal from the pulsed laser was used to trigger the SPD. So the SPD could measure the photon counts at different delay times offset from the trigger time. The single photon counts of the SPD is the accumulative detection counts per second. The delay time resolution of the SPD is 10 ps. When the voltage on the VOA of chip-A is 7.4 V, the test result is depicted in Fig. 4. The photon counts in the one of double pulses were approximately 3.5 × 104. So the average number of photons per pulse μ was less than the order of 0.1. This can obtain a reasonable approximation to a single photon source. Now the attenuator whose attenuation was 75 dB, was composed of SMF and adjustable flanges. The delay time between the two pulses was 800 ps. The test value of delay time was more than the designed value, which was because the delay time resolution and the delay time jitter of the SPD is 10 ps and about 50 ps respectively. So the difference 60 ps between the test and designed values was within the range of test error. When the voltages on the VOA of chip-A and chip-B were 7.4 V and 7.9 V respectively, they both were on the balanced state (The test details are in the supplementary research data). The three pulses output from chip-B were tested by the SPD. When the temperature of TEC is 5 °C, a typical distribution of the three pulses plotted as a function of delay time is shown in Fig. 5. The first pulse in Fig. 5 transmitted from the short arms of chip-A and chip-B. The third pulse arose from photons that have travelled the long arms of chip-A and chip-B. The middle pulse was the superposition of two pulses. One of the pulses transmitted from the short arm of chip-A and the long arm of chip-B. The other one transmitted from the long arm of chip-A and the short arm of chip-B. So the middle pulse will exhibit interference, depending on the phase difference of chip-A and chip-B. The interval times between the three pulses are 800 ps as expected. When the delay time was 11600 ps, the peak of the middle pulse was detected. The location of the middle pulse was independent of the temperature of TEC. To observe interference, the amplitude of the middle pulse was investigated by setting the delay time of the SPD at 11600 ps and scanning the voltage on the TOPM of chip-B. A typical series of experiments was preceded by adjusting the
important functions which influence the performance of the whole system. One is to modulate the power ratio of the two pulses, the other is to modulate the phase difference between the double pulses. In addition, the modulation of power is also important for decoy-state in QKD systems and can be used to prepare different intensities for the light source [14]. The passive method is also useful in decoy-state QKD [15]. In this letter, we propose an AMZI which have the two functions simultaneously. We have demonstrated single-photon interference with high visibility. The interference visibility of the system is dependent on temperature and the polarization of the input light. The devices were fabricated using the silica-based PLC technology. The waveguide core geometry was designed to be 6 × 6 μm, which can optimize coupling loss to single-mode fibers at around 1550 nm. Fig. 1 shows the schematic diagram of the device. The geometric path difference ΔL of the AMZI is 152.51 mm, which can generate 740 ps delay time. The AMZI comprises two parts. The first part is a VOA to adjust the power ratio of the two arms in the second part, which can make the output double pulses have balanced amplitude. The second part not only is to generate double pulses, but also is to modulate the phase difference between the double pulses by the TOPM. The TOPM was used to set the optimum operating point for data decoding using the thermo-optic effect. 2. Experimental results We first measured the insertion loss of the AMZI which is defined as the ratios of the input power into the fiber coupled to the chip and the total output power from the fibers coupled to the two output ports. The insertion loss of chip-A and chip-B are 1.83 dB and 2.24 dB respectively. Then the chips were butt-coupled by fiber arrays with single mode fiber (SMF) pigtails. After the chips were adhered to the printed circuit boards (PCB), the heaters of chips were connected with the PCB by wire-bonding. Fig. 2 shows the packaged chip on the PCB. 2.1. Temperature The experimental setup for investigating the effect of different temperatures of TEC on the performance of AMZI is shown in Fig. 3. Two AMZI chips were connected in series by the SMF to produce a QKD interferometer system. 1550 nm pulses with pulse width 50 ps, pulse
Fig. 2. The packaged AMZI chip. 2
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Fig. 3. The schematic diagram of the QKD interferometer system: the effect of the temperature of TEC.
Fig. 4. The two pulses on the order of single photon transmitted in the quantum channel.
Fig. 6. The single photon interference pattern of the middle pulse at the temperature of 5 °C.
Fig. 5. The three pulses output from chip-B.
temperature of TEC. Single photon counts were acquired as a function of the voltage on the TOPM of chip-B under different temperatures. Note that the dark count background was not subtracted. Fig. 6 shows the single photon interference pattern obtained at the temperature of 5 °C. The interference visibility of 86.03% was calculated from the observed maximum and minimum photon counts. The interference visibility at different temperatures are shown in Fig. 7. The interference visibility reached the maximum of 98.38% and the minimum of 43.03% when the temperature of TEC was 10 °C and 20 °C respectively.
Fig. 7. The interference visibility versus the temperature of TEC.
2.2. Stability In the QKD systems, the stability is an important issue. To demonstrate it, we set the temperature of TEC at 10 °C so that the maximum visibility could be observed. Then we monitored the visibility within four hours and the visibility was measured every 20 min. Fig. 8 shows the measured visibility as a function of time. The visibility varied
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connected like Fig. 3. The transmission process of the pulses was also similar to Fig. 3. The output state of polarization (SOP) of the polarization controller could be tracked to one of the basis SOPs spanning the Stoker space: LP0° (1,0,0), LP45° (0,1,0), LP90° (−1,0,0), LP135° (0,−1,0), RHC (0,0,1), LHC (0,0,−1). The schematic diagram of SOP on the poincare sphere is shown in Fig. 10(b). When the SOP of polarization controller was tracked to LP0°, the temperature of TEC is 5 °C, the voltages on the VOA of chip-A and chipB were 7.4 V and 7.9 V respectively, the three pulses output from chip-B were tested by the SPD. The distribution of the three pulses plotted as a function of delay time is shown in Fig. 11. Because the attenuation of the attenuator was also adjusted to 75 dB, the amplitudes of the first and last pulses were lower than Fig. 5. When the delay time was 11460 ps, the peak of the middle pulse was detected. The curve was moved parallelly because of the addition of polarization controller in the optical path. The location of the middle pulse was independent of the output SOP of polarization controller. Then the amplitude of the middle pulse was investigated by setting the delay time of the SPD at 11460 ps and scanning the voltage on the TOPM of chip-B. A typical series of experiments was preceded by tracking the different SOPs and adjusting the temperature of TEC. The results of the interference visibility are shown in Table 1.
Fig. 8. The stability of the PLC-based AMZI.
between 95.69% and 99.45% within four hours, the variation was less than 3.76%. The phase could keep basically stable within four hours. So the PLC-based AMZI has sufficient visibility and time-stability performance. In addition, the above experiments were carried out through an attenuator. In order to emulate the operation of a real system, we measured the performance of the PLC-based AMZIs over 20 km singlemode fiber G.652 with transmission loss 3.8 dB@1550 nm. The three pulses transmitted were shown in Fig. 9(a). The curve was broaden compared with Fig. 5 due to the dispersion of the fiber. The tested visibility was 97.95%. In order to emulate different lengths of fiber, a variable attenuator was inserted after the 20 km fiber. This can emulate the transmission of dispersion-shifted fiber G.653 with very low dispertion. The visibility was measured with increasing the attenuator 1.9 dB (that is, increasing 10 km fiber) every time. The results are shown in Fig. 9(b). The visibility decreased to 89.7% when the emulated fiber length increased to 50 km, as shown in black curve. It should be noted that the dark count background was not subtracted and the dark count background of SPD was about 150. The visibility with background subtraction was shown in red curve in Fig. 9(b). The visibility varied between 93.9% and 99.3% within 80 km. So the PLC-based AMZIs could keep a high visibility within 80 km.
2.4. Different phase points of the middle pulse In the real QKD system, it is not essential to set all phase points on the interference curve. Generally, we only need to acquire four phase points, such as, 0, π/2, π and 3π/2. In the experiments of section A, the interference visibility reached the maximum of 98.38% when the temperature of TEC is 10 °C. When the voltages on the TOPM of chip-B were 5.4 V, 6.8 V, 8.6 V and 10.2 V respectively, the interference curve reached the minimum, the average of the maximum minus the minimum, the maximum, again the average of the maximum minus the minimum. And these four voltages corresponded to the phase difference between chip-A and chip-B of π, 3π/2, 2π, 5π/2. An example with typical pulse shapes is shown in Fig. 12. 3. Discussion The perfect interference occurs when two interfering pulses recombine at the output coupler with the same polarization [16]. The photon counts in the middle pulse is
2.3. Polarization
N = N1TE + N2TE + 2 N1TE N2TE cos(ΔϕTE ) + N1TM + N2TM
In the experiments of section A, we found the polarization of the input light affected the amplitude of the middle pulse significantly. So we implemented the setup in Fig. 10(a) to investigate the effect of the polarization of the input light. The input pulses were first polarization controlled before input to the chip-A. The other apparatuses were
+ 2 N1TM N2TM cos(ΔϕTM ) N1TE = N1TM = N1/2 N2TE = N2TM = N2/2
Fig. 9. (a) The three pulses output from chip-B over a real fiber of 20 km (b) The visibility versus the emulated fiber distance. 4
(1)
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Fig. 10. (a) Schematic diagram of the QKD interferometer system: the effect of the polarization of the input light (b) The schematic diagram of SOP on the poincare sphere.
where N1 and N2 are the photon counts of the two interference pulses, N1TE and N1TM are the photon counts of one of the two interference pulses for TE and TM modes, N2TE and N2TM are the photon counts of the other one interference pulse for TE and TM modes, ΔϕTE is the relative phase delay between the two arms of AMZI in the TE polarization mode and ΔϕTE = 2πnTEΔL/λ0, ΔϕTM is the relative phase delay between the two arms of AMZI in the TM polarization mode and ΔϕTM = 2πnTMΔL/ λ0. The difference of the modal phase mismatch between TE and TM Δϕ = ΔϕTE − ΔϕTM = 2πΔnΔL/λ0. polarization modes is TE TM Δn = n − n is the modal birefringence. nTE and nTM are the modal refractive index for TE and TM modes in the silica waveguides, Ls and Ll are the geometrical path length of the short and long arm of AMZI (s:short and l:long), ΔL = Ll − Ls is the geometrical path-length difference of the AMZI. λ0 is the wavelength in vacuum. ΔϕTM can be expressed as Fig. 11. The three pulses output from chip-B when the SOP was tracked to LP0°.
ΔϕTE = ΔϕTM + Δϕ Then
Table 1 The interference visibility under different temperatures and input SOPs. Temperature/°C
N = N1 + N2 + 2 N1 N2 cos
Polarization
= N1 + N2 + 2 N1 N2 LP0°
LP45°
LP90°
LP135°
RHC
LHC
92.87% 92.01% 82.23% 97.40% 94.96% 31.71% 97.58% 90.46% 86.68%
96.99% 91.12% 52.46% 37.39% 51.89% 71.47% 75.95% 52.57% 83.56%
91.76% 88.84% 66.01% 96.46% 92.14% 37.26% 97.44% 84.56% 86.73%
97.28% 90.89% 74.88% 28.42% 48.25% 67.10% 66.53% 46.40% 74.96%
91.54% 72.77% 96.94% 42.32% 53.45% 81.86% 63.31% 43.12% 79.06%
92.88% 68.41% 96.94% 48.44% 57.73% 76.11% 71.10% 41.48% 73.64%
(2)
(
ΔϕTE + ΔϕTM 2
cos(ΔϕTM
) cos (
ΔϕTE − ΔϕTM 2
+ Δϕ/2) cos(Δϕ/2)
) (3)
The interference visibility is 5 7.5 10 12.5 15 17.5 20 22.5 25
V=
N1 N2 Nmax − Nmin cos(Δϕ/2) =2 Nmax + Nmin N1 + N2
(4)
It is obvious that the visibility depends on N1, N2 and Δϕ . It depends only on Δϕ when N1 = N2. The interference visibility reached the maximum whenΔϕ = 2mπ and the interference visibility reached the minimum when Δϕ =(2 m + 1)π, where m is an integer. ΔϕTM changes with the voltage on the TOPM. The silica waveguides have the birefringence and the thermo-optic effect, so the modal birefringence Δn is temperature dependent. Hence the interference visibility is temperature-dependent. According to the formula (4) and the interference visibility was 86.03% when the temperature of TEC was 5 °C, Δϕ could be got as 0.34π. And ΔϕTM changes linearly with the square of the voltage. N1 = 6339 and N2 = 6381 could be get from Fig. 5. Then the fitting curve of Fig. 6 is shown in Fig. 13 through setting the appropriate coefficient for ΔϕTM and the square of the voltage. In addition to the maximum value of the fitted curve, the curve fitted well with the test data. According to the data in Table 1, we calculated the mean square deviation of the interference visibility between the different input SOPs. The mean square deviation achieved the minimum value when the temperature was 5 °C. In other words, the input SOPs have less impact on the interference visibility at the temperature of 5 °C. Corresponding to each input SOP, the interference visibility reached the maximum at a special temperature. For example, the interference visibility reached the maximum of 97% at the temperature of 20 °C for the input SOP of
Fig. 12. The typical pulse shape for different phase difference between chip-A and chip-B.
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Fig. 13. The fitting curve of the single photon counts of the middle pulse at the temperature of 5 °C.
doi.org/10.1016/j.optlastec.2019.105837.
LP0° and LP90°. The interference visibility reached the maximum of 97% at the temperature of 5 °C for the input SOP of LP45° and LP135°. The interference visibility reached the maximum of 96.9% at the temperature of 10 °C for the input SOP of RHC and LHC. The test interference visibility may not reach the best because the temperature step was 2.5 °C in the experiment. It should be noted that there was a sudden drop for every input SOP at a specific temperature range. For example, the visibility dropped from 94.96% to 31.71% for LP0° when the temperature increased just 2.5 °C. Similarly, the visibility dropped from 91.12% to 52.46% for LP45°. I think the reasons for this phenomenon were as follows. Because no polarization maintaining fiber was used between the polarization controller and the AMZI chip, for any of the six basis SOPs, it can be split into two polarization modes (TE and TM modes) corresponding to the polarization direction of the waveguide. Then there will be a similar curve like Fig. 7 for any of the six basis SOPs. The curve had steep and flat areas. In steep areas, the visibility changed significantly within a small temperature change.
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4. Conclusion In summary, we have demonstrated an AMZI integrated chip that has the potential to form the basis of the passive decoder in the future quantum cryptography systems. This AMZI can modulate the power ratio and the phase difference between the double pulses. The influence factors of single photon interference visibility were investigated, such as temperature, the polarization of the input light. In order to guarantee the stable temperature for the chips, it is necessary to use the TEC platform. And the whole systems should be placed in aluminum box with the heat preservation cotton. These results were useful to improve the long-term stability of the practical fiber-based QKD system. Acknowledgement This work was supported by National Key R&D Program of China (2018YFA0306403), National Nature Science Foundation of China (61805232, 61435013) and K.C. Wong Education Foundation. Appendix A. Supplementary material Supplementary data to this article can be found online at https://
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