## Abstract

Interferometers are essential elements in classical and quantum optical systems. The strictly required stability when extracting the phase of photons is vulnerable to polarization variation and phase shift induced by environment disturbance. Here, we implement polarization-insensitive interferometers by combining silica planar light-wave circuit chips and Faraday rotator mirrors. Two asymmetric interferometers with temperature controllers are connected in series to evaluate the single-photon interference. Average interference visibility over 12 h is above 99%, and the variations are less than 0.5%, even with active random polarization disturbance. The experiment results verify that the hybrid chip is available for high-demand applications like quantum key distribution and entanglement measurement.

© 2021 Chinese Laser Press

## 1. INTRODUCTION

Photons are the most critical information carriers and perform high-fidelity operations in up-to-date information-processing systems. The interferometer plays an essential role in various information-processing applications, either in classical or quantum research fields, including metrology and sensing [1], coherent optical communication [2], quantum entanglement measurement [3], quantum communication [4–7], and many other fields [8–12].

Interference visibility and stability are the most concerning issues when designing an interferometer. The former relates to measurement precision, and the latter decides whether the system can operate for a long time effectively. Notably, the recent advancements of the applications like quantum information processing require high-performance interferometers. For example, quantum key distribution (QKD) is one of the most promising quantum information technologies that has been deployed in the laboratory and field. For most of the phase-encoded QKD systems, the intrinsic part of the quantum bit error rate (QBER) induced by the optical components is correlated with the interference visibility $V$ [13], of which the typical value is $(1-V)/2$. According to the decoy-state method [14] for practical BB84 [5] QKD systems, the secure key rate (SKR) will significantly decrease when the QBER increases. Therefore, the interferometer should have high fidelity and keep stable in these applications.

The temperature fluctuation, vibration, and stress variety in the environment will affect the birefringence of the optical components and fibers, which will disturb the polarization of the interfering photons. By monitoring the interference visibility, we can evaluate this disturbance. Since the birefringence in fiber channels is inevitable and uncontrollable, it is a more critical challenge to practical fiber QKD [15]. Many countermeasures have been proposed to overcome polarization disturbance [13,16–20], which can be classified into active and passive categories. Active polarization compensating components have been adopted in practical QKD systems [16–18], which is effective but may increase the complexity, insertion loss, and time-consumption of the system. Birefringence variations can be automatically compensated for in QKD systems using passive schemes, such as the “plug-and-play” system [19], Faraday–Michelson system [13], and Faraday–Sagnac–Michelson system [20]. Although the two-way system like plug-and-play system may suffer from Trojan horse attacks [21], these schemes have been deployed in complex field environments and demonstrated their low QBER and outstanding long-term stability.

For applications like QKD, a pair of asymmetric interferometers is typically placed in different locations. The difference in ambient temperature of the interferometers induces a phase drift that causes the variations of visibility. Generally, we can compensate for the phase shift using phase shifters [22] or eliminate it by isolating the interferometers from complex environments. Although the influence of the temperature variations can be partially resolved using these measures, it is still an engineering challenge to keep long-term stability and high visibility of the interferometers with large arm-length differences for their high sensitivity.

The rapid development of integrated photonics points out a way to solve most of the problems mentioned above [23–25]. Some integrated QKD experiments have been reported recently [26–31], most of which use asymmetric Mach–Zehnder interferometers (AMZIs) for photon phase measurement. The integrated photonic chips (IPCs) make the system stabler in terms of temperature variations and vibrations. However, since most of the waveguides of the IPC platform are polarization-dependent, chip-based QKD systems still suffer from polarization disturbance due to varying birefringence in the channel.

Nambu *et al*. [26] and Li *et al*. [32] have studied the silica planar light-wave circuit (PLC) platform and proposed solutions to overcome this inherent challenge of dependency on polarization. The existing schemes need to control the PLC at a specific temperature with an accuracy of better than 0.05°C. The appropriate temperature working points are the birefringence of the chip, which comes from residual stress during fabrication, and is difficult to control accurately. As a result of this uncertainty, each sample should be tested separately. When the proper working points are far away from the room temperature, the energy consumption will increase. The control modules should also have a wider dynamic range and better precision control. In a complex environment, the trade-off between large dynamic range and high accuracy may decrease system performance.

We implement and evaluate a hybrid integrated design for asymmetric Faraday–Michelson interferometers (AFMIs) by combining a silica-on-silicon PLC chip and Faraday rotator mirrors (FMs). We cascade two AFMIs and evaluate their interference visibility at the single-photon level. Experimental results show that these interferometers can achieve an average interference visibility of above 99% over 12 h, and the visibility variations are less than 0.5% with an active random polarization perturbation. We verify that the polarization-independent high visibility can be obtained over a wide temperature range from 10°C to 35°C. We also propose a method to calculate the delay difference between two AFMIs using the single-photon interference results, which is essential for QKD systems.

## 2. DESIGN OF THE AFMI AND EXPERIMENTAL SETUPS

The scheme of the hybrid integrated AFMI is illustrated in Fig. 1(a). The PLC chip contains a directional coupler (DC) with a splitting ratio of 50:50 and two asymmetric waveguides acting as the two arms of the interferometer. Two FMs [19] are coupled and glued to the edge of two waveguides and reflect the photons back to the entrance coupled with a fiber array (FA).

The silica PLC platform is used to implement the structure, taking advantage of its relatively low transmission and coupling loss, which are essential for QKD decoders to get a higher SKR. The refractive index difference of the PLC chip for the waveguide core and cladding is 0.75%, and the geometry of the core is $6\text{\hspace{0.17em}}\mathrm{\mu m}\times 6\text{\hspace{0.17em}}\mathrm{\mu m}$, which is optimized to minimize the propagation loss and the coupling loss to single-mode fibers at around 1550 nm. It is worth mentioning that the chip size can be drastically reduced if we adopt the silica with a higher refractive index difference like 2.0% in the future. The fabrication flow of the PLC chip can be briefly described as follows. First, a 16 μm-thick down cladding layer is formed by thermal oxidation on a silicon substrate. A 6 μm-thick ${\mathrm{GeO}}_{2}\text{\u2212}{\mathrm{SiO}}_{2}$ core layer is formed using plasma-enhanced chemical vapor deposition (PECVD), and then patterned using photolithography and inductively coupled plasma (ICP) etching. PECVD is employed to deposit a 20 μm thick boro-phospho-silicate glass (BPSG) upper cladding layer. Finally, the chip is annealed and packaged with two off-the-shelf Faraday mirrors to make up the AFMI structure. The optical group delay between the two arms after the DC is 200 ps, and thus the round-trip delay of the AMFI is 400 ps, which is appropriate for the phase-encoding QKD system with a pulse repetition rate of 1.25 GHz. A photograph of the hybrid integrated AFMI is shown in Fig. 1(b). A copper heat sink with a thermoelectric cooler (TEC) and a thermistor is packaged with the PLC chip as the temperature control unit, which can be used to stabilize and modulate the relative phase of the two arms of the AFMI at an accuracy of 0.01°C.

The effect of the FM is to transform an arbitrary input polarization state of the photons into its orthogonal polarization state. If we define the Jones vector of an input state as ${J}_{\mathrm{in}}$, the function can be described as [33]

Suppose the Jones matrix of a waveguide is $T$, which is an arbitrary two-by-two matrix describing the wavelength-dependent polarization rotations and the polarization-dependent loss. The photon state behind the DC is represented as ${J}_{\mathrm{in}}^{\prime}$. The overall forward and backward transmission process through the waveguide and reflected by the FMs can be written as

This result indicates that the hybrid integrated AFMI can provide perfect interference with arbitrary input polarization states in principle, which means that the structure can compensate for the polarization perturbance in the chip and the fiber channel.

Figure 2 shows the experimental setup to evaluate the polarization independence and the stability of the hybrid integrated AFMI. We cascade two AFMIs, which act as the optical encoder and decoder module in phase-encoding QKD systems. The insertion loss of the AFMI1 and AFMI2 is 3.99 and 3.31 dB, respectively. The light source is a gain-switch semiconductor laser (Qasky WT-LD200-D) with a pulse width of 50 ps and a central wavelength at 1550 nm. A controllable attenuator and a polarization controller (PC) are placed between the two AFMIs to control the light pulses’ intensity and polarization. The intensity of the light pulses is attenuated to about 0.1 photons per pulse when entering the single-photon detectors (SPDs) to simulate the single-photon interference in QKD systems. The PC is used to simulation the polarization disturbance in the long-haul fiber channel. A circulator (Cir) is placed before the AFMI2 to collect one of the two light beams after interference. Therefore, we can measure both the constructive and destructive ports of the interferometer simultaneously. We adopt two SPDs (Qasky QCRP-SPD-01) with a repetition rate of 1.25 GHz to detect the photon of the interfering peak.

The temperature variation of the chips will change the phase of the two arms and affect $\mathrm{\Delta}\theta $ in Eq. (3). When using an SPD to monitor one port of the interferometer, $I$ in Eq. (4) should be replaced with the counting rate $C$ of the SPD, and $V$ can be calculated using $V=({C}_{\mathrm{max}}-{C}_{\mathrm{min}})/({C}_{\mathrm{max}}+{C}_{\mathrm{min}})$, where ${C}_{\mathrm{max}}$ and ${C}_{\mathrm{min}}$ represent the maximum and minimum counting rate of the SPD (dark counts have been subtracted), respectively.

## 3. RESULTS

We first measure the temperature manipulation parameters of the PLC-based AFMIs without any disturbance. We maintain the temperature of one AFMI (AFMI1 in Fig. 2) at 24°C and adjust the TEC to regulate AFMI2’s temperature. The normalized counting rate is shown in Fig. 3, from which we can see that the $\pi $ phase modulation temperature is about 0.91°C.

To examine whether this PLC-based AFMI is immune to the polarization disturbance, we next use a PC (Keysight N7788B) to modulate the polarization state of the light input to the AFMI2. The PC can act as a polarization scrambler or set the photons to specific polarization states. We first track the states to one of the six basis states among the Stokes space [34], including linearly polarized, $\mathrm{LP}0\xb0$ (1,0,0), $\mathrm{LP}45\xb0$ (0,1,0), $\mathrm{LP}90\xb0$ (−1,0,0), $\mathrm{LP}135\xb0$ (0,−1,0), right-handed circularly polarized, RHC(0,0,1), and left-handed circularly polarized, LHC(0,0,−1). We fix the temperature of AFMI1 at 24°C and scan the AFMI2’s temperature with a step of approximately 5°C. The visibility obtained at each temperature working point is shown in Fig. 4. The minimum and maximum visibilities are 98.75% and 99.25%, respectively. The slight fluctuations of the visibilities may be due to the imperfections of the FM devices.

We also evaluate the interference stability of the AFMIs with random polarization scrambling. We first adjust the interferometers to their maximum interfering point by tuning the temperature of AFMI1 and AFMI2 to 24°C and 24.66°C, respectively. Since the light intensities from the two ports are anticorrelated in principle, the counting rates of SPD1 and SPD2 should reach their maximum and minimum at the same time. We detect single-photon signals from the two ports of the interferometer simultaneously and collect the counting rate every second, which are denoted as ${C}_{\mathrm{SPD}1\mathrm{max}}$ and ${C}_{\mathrm{SPD}2\mathrm{min}}$, respectively. We evaluate the visibility and the variation of $\mathrm{\Delta}\theta $ using $({C}_{\mathrm{SPD}1\mathrm{max}}-{C}_{\mathrm{SPD}2\mathrm{min}})/({C}_{\mathrm{SPD}1\mathrm{max}}+{C}_{\mathrm{SPD}2\mathrm{min}})$ in the following experiments.

The visibilities with and without random polarization scrambling are shown in Fig. 5(a), which are in the first and the second hour, respectively. In the first hour, the visibilities fluctuate slightly due to the practical control precision of the TEC and the counting fluctuations of the SPDs. When adding the random polarization scrambling, the average interference visibility drops slightly from 99.13% to 98.93%. The fluctuations relatively increase with the range less than 1%, which may also be due to the imperfections of FM devices.

Then we fix the temperature of AFMI1 at 24°C and modify AFMI2’s temperature from 10°C to 35°C to evaluate the impact of temperature variations on the visibilities. The average value and the standard deviation (SD) of the visibility are calculated using the data collected every 10 min. The visibilities with and without polarization scrambling are shown in Fig. 5(b), in which the average fringe visibility is about $99.10\%\pm 0.04\%$ and $98.93\%\pm 0.18\%$ with fixed polarization states and random polarization scrambling, respectively.

Besides the polarization of photons, phase stability is also an essential factor affecting the interference results in practical scenarios. We initialize the temperatures of the two chips at their maximum interference working points, keep the temperature steady, and then perform a free-running measurement over 12 h. The average visibilities are calculated every 10 min, as shown in Fig. 6. It can be seen that visibilities with and without polarization scrambling are $99.14\%\pm 0.07\%$ and $98.89\%\pm 0.20\%$, respectively.

The above results indicate that this hybrid integrated AFMI scheme can keep high and stable interference visibilities with arbitrary polarization states over a wide temperature range, which is beneficial for highly demanding applications like QKD. Furthermore, to implement high interfering visibilities between multiple interferometers is a fundamental requirement to support multiuser applications like a QKD network. How to fabricate uniform interferometers is a technical challenge. We derive the method to calculate the arm length or the optical delay difference between the two AFMIs using the interference results. We consider two pulses generated by a gain-switched distributed feedback (DFB) laser and pass through a pair of AFMIs with 50:50 DCs, which is a typical setup in QKD systems up to date. The two pulses can be represented by [35]

From Eq. (7), the visibility is affected by the mismatch of the time ($\mathrm{\Delta}t$) and amplitude ($\mathrm{\Delta}A$), as shown in Fig. 7(a).

As shown in Fig. 7(b), the peak-to-peak ratio between the two peaks passing through the two AFMIs is 0.969 and 0.942, respectively. Then the corresponding $\mathrm{\Delta}A$ is equal to 1.0287. The average visibility we obtained in the experiment is 99.25%. Therefore, we can calculate that the delay difference between the two AFMIs $\mathrm{\Delta}t$ is about 120 fs, according to Eq. (7). The mismatch can be attributed to errors in fabrication, such as the differences in coupling loss and distance between the PLC chips and FMs. However, according to this method, we can finely adjust the coupling in real time based on the single-photon detecting results and the visibility calculated.

## 4. CONCLUSION

In conclusion, we implement a hybrid integrated AFMI structure by combining a PLC chip with Faraday mirrors. We experimentally demonstrate that the chips have high interference visibilities and can tolerate the polarization disturbance over a wide temperature range. This characteristic makes the chips more robust to the environment and can reduce energy consumption. The delay difference of the interferometers can be precisely measured online using interference results and the model proposed in the text, which will benefit mass production and high-requirement applications in the future.

## Funding

National Natural Science Foundation of China (61627820, 61622506, 61822115); National Key Research and Development Program of China (2018YFA0306400); Anhui Initiative in Quantum Information Technologies (AHY030000).

## Acknowledgment

We would like to acknowledge Chang Ling Zou for useful discussions. This work was partially carried out at the USTC Center for Micro and Nanoscale Research and Fabrication, and we thank Wen Liu for helpful discussions on manufacturing and packaging.

## Disclosures

The authors declare no conflicts of interest.

## Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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