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Abstract
We report the polarization preservation of quantum light in the optical systems of the terminals of the world’s first quantum communication satellite, Micius. The main scientific experimental goals and polarization requirements of the satellite and ground station are introduced firstly. Three optical terminals are equipped on Micius to achieve our scientific goals, including a quantum entanglement source (QES), quantum entanglement transmitter (QET) and quantum key distribution transmitter (QKDT), and the function of each optical terminal is described briefly. A polarization-maintaining design for the terminals on Micius is critical for quantum communication, and the optical structure of the QKDT and QET is determined by using three polarization-maintaining methods. The optical configurations of the QKDT and QET are introduced, and the polarization-maintaining methods are described in detail. The final polarization extinction ratios of the QKDT and QET at wavelengths of 850 nm and 810 nm are better than 500:1, which provides critical technical support for realizing the scientific goals of Micius.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Quantum communication, as a new and special type of optical communications, can provide extremely high security due to the fundamental nature of quantum mechanics. A number of successful implementations of quantum communications have been reported and the commercialization is underway. Currently, the maximum distance for practical quantum communication in fiber has reached hundreds of kilometers [1,2], which is almost the limit due to large photon loss in the fiber. Compared with fiber-based quantum communications, satellite-to-ground quantum communications could provide a more appealing solution for secure communications over larger distances [3–6].
The long working distance between the satellite and ground station results in difficulties in practice. To establish effective secret keys between the transmitter and receiver over such a long distance, one should build a steady quantum channel link to maintain the maximum possible channel efficiency and reduce the quantum bit error rate (QBER). Acquisition, tracking and pointing (ATP) system must be designed to establish steady and accurate quantum links. Previously, free-space quantum communication experiments were mostly carried out on the ground [3–6], which does not need real-time polarization basis compensation, and the polarization degradation of both transmitter and receiver could also be compensated by a set of wave plates. Thus, the polarization compensation method on the ground is not suitable for satellite-to-ground quantum communications, in which the polarization basis encounters dynamic change. Moreover, both optical system of transmitter and receiver must maintain polarization state and share the same polarization basis even when the polarization basis keeps changing [7–10].
In Ref. [11], the authors reported a micro-satellite to ground polarization experiment. There are two linearly polarized laser diodes mounted on the micro-satellite, and the linearly polarized lasers are emitted directly without passing through the optical element. However, there are several kinds of dichromatic mirrors and reflectors in our terminals, which are the main factors due to polarization degradation. Hence, the polarization-maintaining of the terminals is the key for completing our experimental goals.
The global quantum communication network took the first step with the success of Micius, and satellite-to-ground quantum communications have been achieved with a working distance of 1200 km [12–14]. All-day quantum communication and miniaturized terminals will be the important research direction in the future. For realizing quantum communication during daylight the suppression of background light would be the major challenge. The miniaturization of terminal is conducive to the establishment of global quantum communication network.
In this paper, we report the optical design and polarization-maintaining design of quantum light in optical systems of the transmitter on Micius. The polarization requirements of the satellite and ground station are introduced in detail. This paper is organized as follows. In Sec. 2, the main scientific experimental goals and optical terminals of Micius are discussed firstly. The optical design and polarization requirements of each terminal are described in detail. In Sec. 3, the optical configuration and the methods for the polarization-maintaining design of QKDT and QET are described in detail. In Sec. 4, polarization measurement methods for QKDT and QET in laboratory are introduced, and the final polarization results for QKDT and QET are described in detail. We draw conclusions in Sec. 5.
2. Polarization requirements
In quantum communication (such as quantum key distribution, quantum entanglement distribution and quantum teleportation), the information is appended to the polarization state of single photon. The transmitted photons are manipulated into four specific polarization directions, such as 0° (H), 90° (V), +45° (D), and –45° (A), and the polarized photon distribution of these polarization directions is decoded by the receiving system. Therefore, the polarization-maintaining of the terminals is the key factor in quantum communication.
The quantum communication satellite Micius aims to complete three experimental goals: satellite-based entanglement distribution, high-speed satellite-to-ground quantum key distribution and ground-to-satellite quantum teleportation [7–9]. To achieve the above goals, three optical terminals are equipped on Micius, including a quantum entanglement source (QES), quantum entanglement transmitter (QET) and quantum key distribution transmitter (QKDT). The QES is used to generate entangled photon pairs. One photon is sent to ground station A via the QET, and the other photon is sent to ground station B via the QKDT. The entangled photon pairs are separately connected to the QKDT and QET through optical fiber. In particular, the QKDT and QET are capable of simultaneously establishing two independent satellite-to-ground links. Both the QET and QKDT have the ability to perform satellite-to-ground decoy-state quantum key distribution at a wavelength of 850 nm. The QKDT can perform ground-to-satellite quantum teleportation at a wavelength of 780 nm.
All of the experiments need to measure the polarization of the photon, and the polarization degradation of the loads will lead to an increase in the quantum bit error rate. Elliptically polarized light can be expressed as ${\left( {\begin{array}{cc} {{a_x}}&{{a_y}{e^{i\delta }}} \end{array}} \right)^T}$, where δ is the phase delay between the two components. The phase delay δ, basis deviation angle θ, amplitude ratio angle α, and elliptic angle β satisfy the following relations:
The phase delay of elliptically polarized light can be described as the elliptic angle β:
The polarization extinction ratio (PER) can be written as:
The quantum bit error rate (QBER) caused by polarization error can be revised as follows [15,16]:
According to formula 4, there are two main factors in the systematic polarization errors: the phase delay δ and the basis deviation θ. QBER maps with different basis deviations and phase delays are shown in Fig. 1.
Fig. 1. QBER maps with different basis deviations and phase delays: (a) + 45° (D) or - 45° (A) linearly polarized light and (b) 0° (H) or 90° (V) linearly polarized light.
The phase delay is accumulated along with optical element (i.e., faulty film coatings and unsuitable materials will cause serious phase delay), and eventually deteriorates the QBER. Additionally, the basis deviation will cause the polarized signal to diverge from its original orientation and increase the QBER. According to the results in Fig. 1, the phase delay and basis deviation need to be controlled for reduce the QBER in satellite-to-ground quantum communications.
According to the scientific goals of Micius, the polarization requirements for each terminal are listed in Table 1. The last line summarizes the requirements about the polarization extinction ratio of the total link. To ensure the polarization of the total link, we should maintain the polarization of transmitters (QKDT and QET) and receiver (ground station), and share the same polarization basis between them. We assume the average polarization extinction ratios of the total link, the transmitter and receiver as PER, PER1, PER2 respectively, and they should meet the following formula.
In the actual situation, there is a polarization basis deviation between the transmitter and the receiver, which will reduce the polarization extinction ratio of the total link. Let’s assume that the polarization basis deviation be θ, then the final polarization extinction ratio of the total link can be expressed as.
Table 1. The requirements for the polarization extinction ratio.
Considering the feasibility, the bit error rate caused by the polarization basis deviation is assigned to 0.1%, and the corresponding polarization basis deviation is less than 2°. Under the above circumstance, the polarization requirements for the transmitter and receiver are decomposed as Table 1.
3. Polarization-maintaining design for the terminals of Micius
3.1 Optical design for the QKDT and QET
To complete the three experimental goals, we designed a space-borne entangled-photon source (QES) in which the QES emits 5.9 million entangled photon pairs per second with a central wavelength of 810 nm. Meanwhile, we developed two tracking systems in which the tracking optical system and the quantum optical system share the telescope. The entangled photon pairs are separately connected to two high-precision acquisition, tracking, and pointing systems (the QKDT and QET) through optical fiber. The two entangled beams are sent out with a far-field divergence of ∼10 urad by two telescopes with apertures of 300 mm and 180 mm.
Both the QET and QKDT have the ability to establish independent satellite-to-ground links. The QET uses a two-dimensional turntable for large-scale tracking, and the tracking beam is transmitted along the rotation axis. The QKDT uses a two-dimensional pendulum mirror for small-scale tracking, and the satellite's attitude control system assists the QKDT in rough tracking. The optical parameters of the QET and QKDT are shown in Table 2.
Table 2. The main optical design parameters of the QET and QKDT.
As shown in Fig. 2, the entangled photon with a central wavelength of 810 nm is connected to the QET by a single-mode fiber and then collimated by a lens. Two motorized quarter-waveplates (QWPs) and a half-wave plate (HWP) are employed to compensate for the polarization degradation caused by the single-mode fiber, and a BB84 decoding module is employed to analyze the polarization of the entangled photon. We use an improved BB84 module for QKD. The quantum-encoded signal is connected to the system through four optical fibers and then collimated by four couplers (CPLs). The improved BB84 module utilizes quarter-waveplates and a half-wave plate to compensate for the polarization degradation introduced by the BS, while polarization-basis light is sent to the BB84 module through another BS.
Fig. 2. Details of the optical system for the QET. M: mirror. M1-M8: mirror 1-mirror 8.CAM: camera; CAM1 is a fine camera, and CAM2 is a coarse camera. FSM: fast steering mirror with a silver film. DM-P: dichromatic mirror with a polarization-maintaining coating; DM-P1 is designed for reflection at 810 nm and transmission at 850 nm; DM-P2 is designed for reflection at 810∼850 nm and transmission at 532∼671 nm; and DM is designed for reflection at 671 nm and transmission at 532 nm. QWP: quarter-waveplate. HWP: half-waveplate. BL: beacon Laser. BB84: quantum key distribution coding module for 850 nm. PA: polarization analyzer for 810 nm based on the BB84 module.
Compensated entangled beams (810 nm), attenuated laser pulses for QKD (850 nm) and a green laser (532 nm) for tracking and time synchronization are separated by three DMs. Either of the two fast steering mirrors (FSMs) is used for closed-loop fine tracking based on the 671 nm beacon laser images captured by camera 1. To maintain the polarization, the incidence angles of the quantum light on dichromatic mirrors 1, 2, and 3 (DM1, DM2, and DM3) are10°, 35°, and 45° respectively, and two FSMs (FSM1 and FSM2) are arranged in such a way that the incidence planes of the two mirrors are orthogonal.
As shown in Fig. 2, the relay optical systems consist of 6 polarization compensation mirrors (M2, M3, M4, M5, M6, and M7), which are used in 3 pairs. Each pair is arranged in such a way that the incidence planes of the two mirrors are orthogonal. The telescope consists of an 8X beam expander and a polarization-maintaining mirror (M1), and cameras 1 and 2 detect the 671 nm beacon light. The tracking and quantum beam is transmitted along the rotation axis of the QET when the QET performs the coarse tracking process.
As shown in Fig. 3, the entangled photon (810 nm) is sent to QKDT by a single-mode fiber and then collimated by a lens. Two motorized QWPs and an HWP are employed to compensate for the polarization degradation caused by the single-mode fiber, and a BB84 decoding module is employed to analyze the polarization of the entangled photon. We use the same improved BB84 module for QKD in QKDT, which utilizes quarter-waveplates and a half-wave plate to compensate for the polarization degradation introduced by the BS. A motorized QWP and an HWP are employed to change the polarization state of the light (780 nm) being measured for quantum teleportation.
Fig. 3. Details of the optical system for the QKDT. M: mirror. M1-M6: mirror 1-mirror 6; M1-M5 are conventional mirrors, M6 is a polarization-maintaining mirror, and the incidence planes of M1 and M2 are orthogonal, which results in a polarization-maintaining setup. CAM: camera; CAM1 is a fine camera, and CAM2 is a coarse camera. BL: beacon laser. FSM: fast steering mirror with a silver film. DM-P: dichromatic mirror with a polarization-maintaining coating; DM-P1 is designed for reflection at 780-810 nm and transmission at 850 nm; DM-P2 is designed for reflection at 780∼850 nm and transmission at 532∼671 nm; DM-P3 is designed for reflection at 780 nm and transmission at 810 nm; DM-P4 is designed for reflection at 532∼850 nm and transmission at 1064∼1550 nm; DM1 is designed for reflection at 532nm and transmission at 671 nm; and DM2 is designed for reflection at 1550 nm and transmission at 1064 nm. QWP: quarter-wave plate. HWP: half-wave plate. BB84: quantum key distribution coding module for 850 nm. PA: polarization Analyzer for 810 nm based on the BB84 module.
The compensated entangled photon (810 nm), attenuated laser pulses for QKD (850 nm), laser pulses of quantum teleportation (780 nm), synchronization light (1550 nm) for the downlink and synchronization light (1064 nm) for the downlink are separated by 5 DMs. Either of the two fast steering mirrors (one for a backup) is used for closed-loop fine tracking based on the 671-nm beacon laser images captured by a fine camera (CAM1).
To maintain the polarization, the incident angles of the quantum light on DM-P1, DM-P2 and DM-P3 are 10°, 35° and 22.5°, respectively, and two fast steering mirrors and two DMs (DM-P4) are arranged in such a way that the incident planes of the two mirrors are orthogonal. The telescope consists of a 12X beam expander, a camera (CAM2) detecting the 671-nm light, a small mirror and a two-dimensional rotating mirror with an aperture of 300 mm. The incident planes of the small mirror and the two-dimensional rotating mirror are orthogonal for polarization compensation.
3.2 Polarization-maintaining methods
In practice, the phase delay δ and basis deviation θ are the main factors that lead to an increase in the bit error rate. Some papers have performed studies on the basis deviation [12], and the phase delay is mainly considered in this paper. The phase delay is caused by problems in the optical elements (i.e., faulty film coatings and unsuitable materials will cause serious phase delay), and three polarization-maintaining methods are used. The details of these methods are as follows.
3.2.1 Polarization-maintaining coating
The optical elements that quantum light passes through all require polarization-maintaining thin-film coatings, including DM-P1, DM-P2, the reflectors (FSMs and mirrors in the relay optical systems and telescope) in the QET, DM-P1, DM-P2, DM-P3, DM-P4, and the reflectors in QKDT. DM-P1, DM-P2 and the reflectors are adopted to transmit quantum light in both QET and QKDT. The design of polarization-maintaining coating systems are as shown in Table 3, and the results of the design of the polarization-maintaining coating or various optical elements are shown in Fig. 4.
Table 3. The design of the coating systems.
DM-P1 is used to separate the quantum light at 780∼810 nm and 850 nm, with a transition band of only 40 nm. In such a narrow band, the phase difference between 810 nm and 850 nm needs to be regulated while the spectral separation is completed. To reduce the requirement of the coatings, the incidence angle is set to 10°.
DM-P2 is used to separate the quantum light at 780∼850 nm and the beacon 532∼671 nm light with an incidence angle of 35°, and the phase difference at 780∼850 nm needs to be regulated while the spectral separation is completed. The structure of the membrane system adopts the irregular matched layers of a back cut-off membrane system with polarization control.
DM-P3 is used to separate quantum light at 780 nm and 810 nm, with a transition band of only 30 nm and an incidence angle of 22.5°. In such a narrow band, the phase difference between 780 nm and 810 nm needs to be regulated while the spectral separation is completed.
DM-P4 is used to separate quantum light at 780∼850 nm and 1064∼1550 nm, with an incidence angle of 45°. The phase difference at 780∼850 nm needs to be regulated while the spectral separation is completed.
A mirror is used to change the direction of the light (wavelength range of 532∼1550 nm), where the wavelengths of the polarization-maintaining light are 810 nm and 850 nm. Ni-Cr and Cu are selected as the pre-coating layer materials to improve the adhesion between the substrate and Ag, the addition of Al2O3 to the Ag film can improve the adhesion between Ag and the dielectric layer, and the polarization phase can be regulated by the coatings of 5 layers.
3.2.2 Polarization compensation between optical components
The phase addition of optical elements results in a degradation of linearly polarized light into elliptically polarized light, which is the direct factor that leading to an increase in bit error rate. In practice, phase compensation can be achieved by a specific arrangement of the optical elements. For example, assume that $r_y^2$ and $r_y^2$ are the reflectivity of the x and y components, respectively, and is the phase delay of two identical mirrors.
As shown in Fig. 5(a), the incidence planes of the two mirrors are the same, and the transmission matrix of the system is:
As shown in Fig. 5(b), the incidence planes of the two mirrors are orthogonal, and the transmission matrix of the system is:
Fig. 5. Polarized light is reflected by two mirrors arranged in different ways. (a) The incidence planes of the two mirrors are the same, which leads to phase addition and polarization degradation. (b) The incidence planes of the two mirrors are orthogonal, which results in phase cancellation and polarization preservation.
In the second case, the transmission matrix reduces to the identity matrix, which does not change the polarization. In the optical design of the QET, many pairs of mirrors are arranged in such a way that the incidence planes of the two mirrors are orthogonal, e.g., the two fast steering mirrors (FSMs) and 3 pairs of mirrors of the relay optical systems in Fig. 2.
Generally, the polarization extinction ratio of 45° linearly polarized light is approximately 2000:1∼3000:1 after it is reflected on a polarization-maintaining mirror, while the PER can be reached to 10000:1 after passing through two mirrors with orthogonal incidence planes. As shown in Fig. 2, the PER of the relay optical system (6 mirrors) at 810 nm and 850 nm reaches nearly 10000:1, while the PER of each mirror is approximately 2000:1∼3000:1.
3.2.3 Polarization compensation by waveplates
As shown in Fig. 6, the entangled photon pairs (810 nm) are separately connected to QKDT and QET through optical fiber, which changes the polarization of the light. Therefore, two motorized QWPs and an HWP are employed to compensate the polarization degradation caused by the single-mode fiber, and a BB84 decoding module is employed to analyze the polarization of the entangled photon. After compensation, the polarization extinction ratio of the linearly polarized light [0 ° (H), 90 ° (V), +45 ° (D), and -45 ° (A)] passing through the fiber can be obtained and maintained at approximately 1000:1 for a long time. The basic principle of the polarization compensation is as follows.
Fig. 6. Compensation for the polarization degradation caused by the single-mode fiber with two motorized QWPs and an HWP.
The effect of the optical fiber on the polarization of the light is a unitary transformation, so one can use three wave plates (2 QWPs and 1 HWP) to realize the unitary transformation U, which returns H, D, and R back to their original positions on the Poincare sphere. The unitary transformation compensates for the influence of the optical fiber on the polarization of the light. Therefore, any polarized light can maintain its original polarization state after passing through the combination of the optical fiber and three wave plates [17].
Polarization compensation is accomplished through four steps. First, the polarization state is measured by the BB84 module when the right circularly polarized (RCP) photon passes through the optical fiber. Generally, the output state is elliptical when an RCP photon passes through a certain length of single-mode fiber. Second, the elliptical photon is transformed into linearly polarized light by a QWP. At this time, a horizontally polarized photon is generally converted to an elliptical photon. Thirdly, the elliptical photon, which is converted from horizontally polarized light passing through the fiber and a 1/4-wave plate, is converted to linear polarization by another 1/4-wave plate. At this time, the RCP photon returns to its original position on the Poincare sphere. Finally, a half-wave plate is used to convert the horizontally polarized light to its original position, and a photon of any polarization returns to its original position on the Poincare sphere.
As shown in Fig. 7, we use an improved BB84 module for QKD [18–20]. The improved BB84 module consists of four couplers(CPLs) and polarizers(POLs), two polarizing beam splitters (PBSs), beam splitters (BSs), a half-wave plate (HWP) and a quarter-wave plate (QWP), and polarization-basis light is combined with the improved BB84 module by another BS. The CPLs, POLs and PBSs are used to produce collimated polarized light with a high extinction ratio (approximately 100000:1). When 45° linearly polarized light passes through the BS, the polarization extinction ratio decreases to 100:1, so the HWP and QWP are employed to compensate for the polarization degradation caused by the BSs. The horizontally polarized light is converted into 45° polarized light through the QWP and HWP, and the additional phase generated by the BS is compensated. The basic principle of the polarization compensation is as follows.
Fig. 7. Improved BB84 module for QKD. LD: laser diode. CPL: coupler. RLD: reference laser diode. HWP: half-wave plate. QWP: quarter-wave plate. POL: polarizer. PBS: polarizing beam splitter. BS: beam splitter. ATT: attenuation.
Assuming that the angles of the QWP and HWP are ${\alpha _1}$ and ${\alpha _2}$, the phase delay generated by the BS is $\delta$, The transmission matrix of the QWP, HWP and BS is expressed as follows:
According to $\delta$, there are 4 solutions to ${\alpha _1}$ and ${\alpha _2}$:
Theoretically, the phase of BSs can be compensated perfectly. In fact, the polarization extinction ratio of 45° linear polarization emitted by the BB84 module is approximately 2000:1.
4. Laboratory performance of the QKDT and QET
The QET and QKDT are slightly different in terms of polarization design. The polarization basis barely changes when the QKDT completes rough coarse tracking. Therefore, it can be considered that the polarization basis remains unchanged and that polarization compensation can be carried out for the entire optical system. The QET can be divided into quantum and tracking optical systems, relay optical systems and a telescope. The tracking and quantum beam is transmitted along the rotation axis of the QET when the QET performs the coarse tracking process. The rotation of the turntable will cause a change in the polarization basis of the quantum light. The phase of the quantum light will be superimposed on a different polarization basis, which will change the direction and the polarization state of the polarized light. To ensure that the polarization of the quantum light does not degrade under the condition of dynamic tracking, a polarization-maintaining design is required for each part of the relative motion optical systems.
The polarization characteristics of QKDT and QET are guaranteed by using the above three polarization-maintaining methods. In laboratory, a single parabolic mirror is used to test the polarization of the terminals, and the specific polarization test optical system is shown in Fig. 8. On the focal surface of the parabolic mirror, two optical fibers are located on both sides of the beam splitter. One fiber is used to receive the quantum light, and one fiber is used to produce the parallel beacon light. The polarizer for the polarization testing is located in front of the BS, and the narrow-band filter is located between the fiber and the beam splitter.
The beacon light guides the tracking of the terminal, which sends the quantum light into the optical fiber at the focal surface of the paraboloidal mirror and is eventually detected by a single-photon detector. The number of photons detected by the single-photon detector will change when the polarizer is rotated. The ratio of the maximum number of photons to the minimum number of photons is the extinction ratio of the quantum light. Finally, the polarizations of QKDT and QET are shown in Table 4.
Table 4. The results of the polarization for the QET and QKET in the laboratory.
5. Conclusion
In summary, we reported the optical design and polarization preservation of quantum light in the optical systems of the transmitters on Micius. The main scientific experimental goals and polarization requirements of the satellite and ground station are introduced, and three optical terminals are equipped on Micius to achieve our scientific goals, including a quantum entanglement source (QES), quantum entanglement transmitter (QET) and quantum key distribution transmitter (QKDT). A polarization-maintaining design for the QET and QKET on Micius is critical for achieving our scientific goals. The optical configurations of the QKDT and QET are introduced, and three polarization-maintaining methods are described in detail. Finally, the polarization measurement system and methods of the terminals in the laboratory are introduced, and the final polarization extinction ratios of the QKDT and QET at wavelengths of 850 nm and 810 nm are better than 500:1, which provides critical technical support for realizing the scientific goals of Micius.
Funding
Strategic Pioneer Research Projects of Defense Science and Technology; National High-tech Research and Development Program (2017YFA0303900); National Natural Science Foundation of China (U1738204).
Acknowledgments
We thank many colleagues at the University of Science and Technology of China, Shanghai Engineering Center for Microsatellites, and the National Space Science Center.
Disclosures
The authors declare no conflicts of interest.
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