Since the first protocol proposed in 1984 [1], quantum key distribution (QKD) has achieved considerable developments in the past few decades [2–4], in both fiber [5–8] and free space [9–15]. Field tests of QKD application in fiber networks have been reported in China [16], Switzerland [17], South Africa [18], and so on. Especially, China has built the world’s longest quantum secure communication backbone network with a fiber distance of 2000 km [19]. Moreover, satellite-to-ground QKD [14] and the satellite-relayed intercontinental quantum network [15] have been successfully realized by the quantum science satellite, Micius.

Polarization encoding is extensively employed in fiber-based QKD [5,6] and free-space QKD [11–15], for which weak coherent pulses are typically encoded into four polarization states of $|H⟩$, $|V⟩$, $|D⟩=\frac{1}{\sqrt{2}}(|H⟩+|V⟩)$, and $|A⟩=\frac{1}{\sqrt{2}}(|H⟩-|V⟩)$. As a simple and effective approach, the multiple-laser scheme is widely used [5,6,11,13–15], where each required polarization state is prepared by an independent laser. However, this method suffers from side-channel information leakage [20]. To guarantee the indistinguishability of pulses emitted by different lasers, the repetition rate is limited to the order of a few hundred megahertz [6,21]. In comparison, an external polarization modulation scheme can reach a much higher repetition rate [22–25] with intrinsic uniformity in other dimensions of photons. The idea of polarization modulation is essentially phase modulation in certain polarization bases. Benefited by the mature development of classical optical communication, a number of off-the-shelf solutions are available for high-speed and high-performance phase modulation.

Thus far, several polarization modulation schemes have been proposed [24–32], the first of which is based on the balanced Mach–Zehnder (MZ) interferometer [24,28]. In this theme, two orthogonal polarization components enter different arms of the interferometer, and a phase shift is applied between them to induce the polarization encoding. Although this method is easy to implement, it is inherently unstable because MZ interferometers are sensitive to external environmental disturbances. Another type of polarization modulation scheme is based on the ${\mathrm{LiNbO}}_3$ modulator with the polarization-maintaining fiber (PMF) input aligned at 45° [25–27]. Because the polarization mode dispersion (PMD) is located between two orthogonal components ($\sim 10\mathrm{ps}$ for common ${\mathrm{LiNbO}}_3$ modulator), a highly birefringent fiber [25] or another phase modulator [26] is usually required for additional compensation. Meanwhile, the stability of this method is also unsatisfactory because the two orthogonal components transmit in different axes of the modulator. The last scheme is based on interferometers that use either Sagnac loops [29,30] or Faraday mirrors [31,32] with single-mode fiber (SMF) for optical input and output. This method exhibits superior stability compared with the previous two methods. However, the drawback of previous implementations is that the calibration procedure is inevitable, which usually involves a polarization controller (PC) to balance the intensity of the $|H⟩$ and $|V⟩$ components.

In this Letter, a new polarization modulation scheme based on an inherently stable Sagnac interferometer is presented. A schematic of this scheme is presented in Fig. 1(a), which is composed mainly of a customized polarization module [Fig. 1(b)] and Sagnac interferometer.

 

Fig. 1. (a) Overview of the presented polarization modulation, which is composed mainly of a customized polarization module and a Sagnac interferometer. (b) Schematic of the customized polarization module. (c) Schematic of the polarization analysis module, which is used to analyze the generated four polarization states for the BB84 protocol. PMF, polarization-maintaining fiber; SMF, single-mode fiber; Pol, polarizer; BS, beam splitter; ATT, attenuator; PC, polarization controller; PBS, polarization beam splitter; SNSPD, superconducting-nanowire single-photon detector.

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The polarization modulation process is as follows:

By changing the value of the additional phase $\phi$, a specific polarization state can be generated. For example, the output polarization state can be written as

 

Fig. 2. (a) Relationships between the generated polarization states and the applied voltages. (b) Typical measured photon distributions of the four detectors ($|A⟩$, $|D⟩$, $|R⟩$, and $|L⟩$). The system frequency is 1.25 GHz, which corresponds to an 800 ps time interval between adjacent two pulses. The horizontal timeline in this figure is omitted for simplicity.

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Because both the clockwise and anticlockwise portions of the optical pulse propagate along the same axis in the phase modulator, the presented polarization modulation is PMD free, which means additional PMD compensation [25,26] is not necessary. Moreover, the typical time scale of the phase noise introduced by the transmission medium [33] is significantly longer than the traveling time (tens of nanoseconds) in the interferometer, which can be well cancelled after transmission through the Sagnac loop. This feature makes the Sagnac polarization modulation scheme inherently stable, showing direct superiority over previous implementations [24–28], even without active polarization stabilization in the experimental setup. Compared with previous Sagnac interferometer methods with SMF input [29,30], the PMF input in this scheme is directly aligned at 45° with respect to the BS in the customized polarization module. The adoption of PMF input rather than SMF input simplifies the use of the PC and circulator, thus enabling the presented polarization modulation to be calibration free and feature improved integration. These features make it an effective solution in many strict environments, such as future CubeSat missions [34] and higher-orbit satellite applications [15].

In our experimental setup, we employ a self-developed pulse generator (PG) board to drive a 1550 nm distributed feedback (DFB) laser diode (LD) at a system frequency of 1.25 GHz. This LD is gain-switched by consecutive electrical pulses to generate short optical pulses of $\sim 50\mathrm{ps}$, which are directly fed into the presented polarization modulation. The PG board can generate 200-ps pseudo-random electrical pulses with four different voltages (0, $V_{\pi }/2$, $V_{\pi }$, $3V_{\pi }/2$, where $V_{\pi }$ is the half-wave voltage of the phase modulator). The generated pseudo-random electrical pulses have a repeated 1024-bit pattern at a system frequency of 1.25 GHz. Meanwhile, the phase modulator in the Sagnac interferometer is driven using the electrical pulses to prepare the target polarization states ($|A⟩$, $|R⟩$, $|D⟩$, $|L⟩$) for the BB84 protocol.

The generated polarization states are first attenuated to the single-photon level and then analyzed using the polarization analysis module, as shown in Fig. 1(c). The PC is used to compensate for the unitary transformation introduced by the SMF and convert the generated states into the target polarization states of the customized BB84 decoder, which consists of a BS and two polarizing BSs. After that, the optical pulses finally get detected by four superconducting-nanowire single-photon detectors (SNSPDs), labeled as $|A⟩$, $|D⟩$, $|R⟩$, and $|L⟩$ respectively. The detected signals of the four SNSPDs are fed into a time-correlated single-photon-counting (TCSPC) device (PicoQuant, HydraHarp 400) to analyze the measured results. Another synchronous electrical signal generated from the PG board is used for time synchronization. The time bin width of the TCSPC device is set as 32 ps.

Every photon detection event given by the four SNSPDs is correlated with the synchronous electrical signal. After count accumulation of 5 s, the TCSPC device gives out the measured photon distributions. Typical photon distributions from the four SNSPDs ($|A⟩$, $|D⟩$, $|R⟩$, $|L⟩$) are displayed in Fig. 2(b). To demonstrate the feasibility and stability of the presented high-speed polarization modulation, a long-term polarization modulation test is conducted. The whole experimental setup is placed on an indoor optical platform, with no additional temperature control other than the laboratory’s general air conditioner. The corresponding measurement results of the measured average quantum bit-error rates (QBERs) are given in Fig. 3. The measured QBERs of the four polarization states indicate some correlation with the applied electrical signals. Due to the voltage fluctuations of electrical pulses, the introduced additional phases have inevitable fluctuations as well. This will cause the deviation of the generated polarization states and eventually results in the deterioration of measured QBERs. When the zero voltage (zero for polarization state $|A⟩$) is applied, the electrical signals are very stable, and the polarization state of $|A⟩$ demonstrates the lowest QBER of $0.05\pm 0.01\%$. When the applied voltages ($V_{\pi }/2$, $V_{\pi }$, and $3V_{\pi }/2$ for polarization states $|R⟩$, $|D⟩$, and $|L⟩$, respectively) increase, the voltage fluctuations of the applied pseudo-random electrical pulses become larger, and more phase noise is introduced, eventually resulting in a larger QBER. As depicted in Fig. 3, the other three polarization states of $|R⟩$, $|D⟩$, and $|L⟩$ have respective QBERs of $0.25\pm 0.01\%$, $0.37\pm 0.02\%$, and $0.47\pm 0.03\%$. The measured average QBER of the four polarization states is $0.27\pm 0.01\%$ for 80 consecutive minutes without any adjustment to the setup.

 

Fig. 3. Measured QBERs of the four polarization states ($|A⟩$, $|D⟩$, $|R⟩$, and $|L⟩$), which demonstrate long-term stability.

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The repetition frequency of polarization modulation in this work is pushed up to 1.25 GHz compared with prior Sagnac implementations [29,30]. One issue that must be noted is that the length of the waveguide in the phase modulator limits the performance of the polarization modulation. Considering the typical length of 7 cm, the transmission time of the optical signals in the waveguide is about 500 ps. Due to this non-negligible transmission time, the modulating electrical pulses inevitably interact with the anticlockwise optical pulses when the repetition frequency exceeds 1 GHz. Thus, a lower phase difference is applied between the clockwise and anticlockwise pulses at the same electrical signals. This results in a slightly higher half-wave voltage of the phase modulator, but does not cause performance degradation of polarization modulation. The absolute maximum repetition frequency of random polarization modulation is limited to about 2 GHz, in order to avoid the pattern interaction between the modulating electrical pulses and adjacent two counterclockwise optical pulses. This repetition frequency bottleneck can be mitigated by using much smaller phase modulators [35,36] and does not affect the applications of the presented polarization modulation in practical QKD systems.

More importantly, an intrinsically stable QKD optical source can be realized by combining the presented polarization modulation and patterning-effect mitigating intensity modulation [37]. Such an intrinsically stable QKD optical source can get wide applications in future CubeSat missions [34] and higher-orbit satellite applications [15].

To summarize, a new polarization modulation scheme based on an inherently stable Sagnac interferometer is presented. The presented scheme is PMD free, calibration free, and insensitive to environmental influences. The feasibility and stability of the presented scheme have been demonstrated directly via experiments conducted at a repetition frequency of 1.25 GHz. The measured average QBERs of the four polarization states are as low as 0.27% for consecutive 80-min tests without any adjustment to the experimental setup. The presented high-speed intrinsically stable polarization modulation is widely applicable in polarization-encoding QKD experiments.