Entanglement demonstration on board a nano-satellite

Global quantum networks for secure communication can be realised using large fleets of satellites distributing entangled photon-pairs between ground-based nodes. Because the cost of a satellite depends on its size, the smallest satellites will be most cost-effective. This paper describes a miniaturised, polarization entangled, photon-pair source operating on board a nano-satellite. The source violates Bell's inequality with a CHSH parameter of 2.6 $\pm$ 0.06. This source can be combined with optical link technologies to enable future quantum communication nano-satellite missions.

milestone towards realizing space-to-ground entanglement distribution from a CubeSat 23 .

II. METHODS
The in-orbit experiment occupies approximately 2U of volume in the 3U CubeSat, SpooQy-1 (Fig. 1, designed and built at the Centre for Quantum Technologies, National University of Singapore). The remaining 1U houses the spacecraft avionics. The experiment is composed of a source of entangled photon-pairs coupled to a detector module (see Fig. 2(a)) all controlled by an integrated electronics sub-system. A micro-controller on the experiment interfaces to the satellite's on-board computer to receive commands and to return science data to ground control.
The polarization entangled photon-pair source is based on collinear, non-degenerate type-I SPDC with critically phase-matched non-linear crystals. The source design ( Fig. 2(b)) uses a parallel-crystal configuration 24,25 . The beam overlap found in this design provides the source with better alignment stability in contrast to other two-crystal designs 26 .
A collimated laser diode (central wavelength λ = 405 nm, spectral linewidth ∆ν=160 MHz) with a beam full-width half-maximum of 800 µm×400 µm is used as a continuous-wave pump for the SPDC process. The pump produces horizontally polarized photon-pairs in two β-Barium Borate (BBO-1 and BBO-2) crystals (cut angle: 28.8°, length: 6 mm). Between the two BBO crystals, an achromatic half-wave plate (HWP) induces a 90°rotation in the polarization of the SPDC photons from BBO-1, while the pump polarization remains unaffected.
The photon-pair source produces the state |φ = 1 √ 2 |H s H i + e i∆ϕ |V s V i , where s (i) denotes the signal (idler) photon wavelength, and ∆ϕ is the relative phase-difference between photon-pairs born in BBO-1 and BBO-2. Excess pump light is removed by a dichroic mirror to a detector that tracks power and pointing. An a-cut yttrium orthovanadate (YVO 4 ) crystal compensates for the birefringent dispersion of the SPDC photons (related to ∆ϕ 24 ). The tilt angle of BBO-1 is adjusted such that the final phase difference ∆ϕ becomes π generating the maximally entangled Bell state |Φ − .
The relative angle of the pump beam and the optical axis of the BBO crystals must be kept within 100 µrad in order to control the phase of the generated photon-pairs (see Fig. A.1 in Appendix A). This can be achieved without active alignment using titanium flexure stages. To reduce misalignments resulting from a mismatch in the thermal expansion of different materials the rest of the optical bench is also made of titanium.
The SPDC photon-pairs are separated by a dichroic mirror, and signal and idler photons have their polarization state analysed separately. Each polarization analyser is composed of a liquid-crystal polarization rotator (LCPR) followed by a polarizer 27 . Photon detection is performed using un-cooled, passively-quenched, Geiger-mode avalanche photodiodes (GM-APDs, with detection efficiencies of 45% at 800 nm) with active areas of 500 µm located 10 cm away from the centre of the source. Detection events are identified as correlations if they occur within a time window of 4.84 ± 0.06 ns.
To simplify the optical assembly, collection optics were not used. This collection condition, described in Fig To investigate the polarization correlation of the photon-pairs, one arm is analysed with fixed polarization (either H: horizontal, V: vertical, D: diagonal, or A: anti-diagonal) while the other arm is swept through different polarization states. In principle, the LCPR devices can achieve almost 2π of phase shift, but towards the end of the range the performance of the devices lack precision. To improve performance reliability, the LCPR devices were restricted to a phase shift of approximately 150 degrees.
The visibility (contrast) of the polarization correlation curves can be used to assess the quality of the entangled state. Additionally, it is possible to extract 16 data points from these correlation curves. Each curve can provide four data points that are separated by 45°(see Fig. 3). These data points are used to obtain a measure of entanglement known as the Clauser-Horne-Shimony-Holt (CHSH) 29 parameter, S.
After assembly of the satellite, the on-ground detected pair rate (combined for both polarization bases) is 1400 pairs/s at approximately 17 mW of pump power (≈ 590 000 singles/s for signal and idler). The visibilities (corrected for accidentals) recorded in the two bases (H/V and D/A) were: .84 ± 0.05 and V A =0.90 ± 0.05. From these curves, a CHSH parameter of 2.63 ± 0.07 was extracted (see The typical in-orbit detected pair rate (combined for both polarization bases) was 2200 pairs/s (≈ 700 000 singles/s for signal and idler). The highest recorded visibilities were: .88 ± 0.06. These visibilities yielded a CHSH parameter of V H =2.60 ± 0.06 ( Fig. 3(b)). This value is a slight underestimate of the actual CHSH parameter because the LCPR settings for the diagonal and anti-diagonal polarization states had a systematic error. This can be seen from Fig. 3(b) where the extrema of the correlation curves in the diagonal/anti-diagonal settings do not occur exactly at the D/A (45°/135°) basis setting. Nevertheless, this causes only a slight degradation in the CHSH value compared to the on-ground baseline value.
Entangled photon-pair production was observed over a temperature range from 16°C to 21.5°C (Fig. 3(c)). The experiment experienced relatively high temperatures when the satellite entered an orbital condition of continuous solar illumination (no data was collected during this period). Data collection resumed after exiting continuous illumination and pre-illumination performance was observed (see red data points in Fig. 3(c)).

IV. DISCUSSION AND CONCLUSION
The operation of a polarization entangled photon-pair source on board a CubeSat in LEO has been reported.
This shows that entanglement technology can be deployed with minimal resources in novel operating environments, providing valuable 'space heritage' for different components and assembling techniques.

A. ANGULAR TOLERANCE OF THE SPDC CRYSTALS
The phase-matching conditions for the BBO crystals used in the source are achieved by angle tuning. With this technique, the relative angle between the pump beam and the optical axis of the crystal is crucial. This angle must be maintained within ±100 µrad to maintain source performance (e.g. photon-pair phase). This is depicted in Fig. A.1, where the visibility in the D/A basis is measured while introducing an angular detuning in one of the two BBO crystals.

B. IN-ORBIT HEATER OPERATION
The safe operating temperature range for the experiment was defined as between 15°C to 28°C; this was driven by the requirements of the pump laser diode. Most of the time, the experimental apparatus does not experience this temperature. Instead, the temperature fluctuates between −5°C and 10°C (Fig. B.2(a)). These fluctuations depend on the satellite's position and orientation during orbit. Furthermore, during the lifetime of the satellite, the solar illumination condition varies as depicted in Fig. B.2(b). Due to the specific inclination of the orbit 38 , in some cases the satellite does not spend time in eclipse for several days (note the pronounced valleys in Fig. B.2(b)). During these non-eclipse periods, the satellite could heat up, potentially damaging the experimental apparatus with excess heat.
In order to restrict heat conduction between the experimental apparatus and the satellite bus, and also maintain passive optical stability across varying temperatures, an isostatic mount was fabricated. This mount is made out of three 0.4 mm thick stainless steel blades (manuscript under preparation). The blades serve to absorb any thermal expansion mismatch between the experiment and the satellite structure. To achieve the necessary operating temperature a 2.5 W heater is activated until the required condition is achieved (see Fig. B.2(c)). operated. There is a 120 second gap in between heating cycles for the on-board electronics to perform system checks.

C. SURVEY OF PUMP MODES THAT PRODUCE HIGH-QUALITY ENTANGLEMENT
The pump wavelength is a function of temperature and current 39 . Changes in wavelength (mode-hops) are accompanied by changes in phase ∆ϕ. This phase change can degrade the entanglement quality produced by the source.
Mode-hops are common in orbit due to the fluctuating temperature. To recover the entanglement quality, an optimal laser current can be used. A survey of the in-orbit pump laser was performed at different temperatures to identify laser currents that supported the production of high-quality entanglement. The resulting heatmap (see Fig. C.3(a)) was used as a reference when operating the experiment in space. Additionally, it is worth noting that the output power of the laser diode does not always scale proportionally with the laser current, as shown in Fig. C.3(b).

D. SATELLITE BUS AND GROUND CONTROL
The SpooQy-1 satellite (with NORAD catalogue number: 44332) is based on a 3U Gom-X platform from GomSpace ApS. The SpooQy-1 satellite bus includes: a half-duplex UHF transceiver combined with deployable canted turnstile UHF antennas used for both uplink and downlink; a 32-bit AVR computer with a 64 MByte flash storage used as the onboard computer (OBC) for housekeeping and data handling; an attitude determination system (embedded in the OBC) with 3 magnetorquers for 3-axis detumbling; and a 38 Whr battery pack (four lithium-ion 18650 cells, 7.7 Whr maximum depth of discharge) with the electrical power management system.
The peak system power consumption is rated at 3.85 W, while the peak power consumption of the experiment is rated at 2.5 W. As photon detection is performed on board the satellite, no optical ground station is needed and only UHF ground stations are used for telemetry and satellite command. To increase the link budget two ground stations were used; one located at the National University of Singapore (NUS) campus in Singapore, and another one at the University of Applied Sciences Northwestern Switzerland (FHNW) campus in Switzerland. Both ground stations are equipped with two WiMo X-Quad antennas (amplification gain of 15 dBi). The rotor for the tracking mount is controlled by a Linux-based server computer (NanoCom MS100). The ground station radio (NanoCom GS100) is the ground counterpart (with a 25 W power amplifier) to the NanoCom AX100 radio on board SpooQy-1, designed to work together using the CubeSat Space Protocol.
The decision to forego the use of collection lenses in the experiment leads to an optical configuration in which the geometrical loss dominates the overall performance of the experiment. This is illustrated in Fig. E.4. As the laser beam ( Fig. E.4(a)) triggers SPDC along the nonlinear crystals, entangled photon-pairs are emitted and directed towards the Geiger-mode avalanche photodiodes (GM-APD). Depending on both the position within the crystal at which the photon-pair is generated and its emission opening angle (up to 0.3°), the percentage of photon-pairs successfully detected can be estimated via ray tracing techniques. We use the intensity distribution of the pump beam in one crystal (BBO-2) to randomly generate rays of downconverted photon-pairs. Signal and idler wavelengths and opening angles are chosen randomly distributed based on phase-matching considerations. We propagate the individual rays (considering the refraction at the crystal-air interface) towards the single photon detectors (Fig. E.4(b)). The rays are discarded if none of the photons hits its corresponding detector. The ray tracing results are shown in Fig. E.4(c). It can be seen how only a small percentage