Quantum-correlation-based free-space optical link with an active reflector

Broadband multi-mode laser diode (LD) at 405 nm ($\Delta\lambda\sim 0.5$ nm) was used as the pump laser. Degenerate photon-pairs with a center wavelength of 810 nm are collinearly generated via a type-0 ($e\to e+e$) SPDC process using a 30 mm-long periodically-poled potassium titanyl phosphate (ppKTP, Racol) crystal with a 3.425 $\mu$m poling period (Fig. 2(a)). The SPDC process generally has the highest conversion efficiency when the pump, signal, and idler modes satisfy energy conservation and phase-matching conditions:

where $\omega_{j=p,s,i}$ and $k_{j=p,s,i}$ are the angular frequency and wavenumber of the pump, signal, and idler modes, respectively. Figure 2(b) shows the temperature dependence of the phase-matching curve calculated using Eq. 1 OE12Steinlechner ; JOSAB14Steinlechner . The phase-matching curve shows an increased non-degeneracy of the signal and idler photons as the temperature increases. The pump beam was collimated to a diameter of 700 $\mu$m at FWHM. A plano-convex lens of focal length, $f=300$ mm is then used to focus the pump beam to have the waist $\it{w}_{o}$ at $\sim$ 44 $\mu$m at the center of the crystal PRA05Ljunggren ; PRA10Bennink . At the set temperature of 25.3 ^∘C, degenerate photon-pairs are produced with a waist size of $\sim$ 33 $\mu$m and propagate collinearly with the pump beam, blocked by a dichroic mirror (DM). The signal and idler photons are separated using the BS and coupled to the SMFs. The idler photons are directly sent to an SPCM to herald the signal photons sent to the target mirror through the telescope. The number of photon-pairs is aproximatedly 3.0$\times$10⁵ Hz/mW in the coincidence counts. Figure 2(c) shows the normalized cross-correlation function $g^{(2)}(\tau)$ as a function of the delay time $\tau$.

FSO links involve absorption and scattering depending on atmospheric conditions and transmission. Therefore, one of the major challenges facing FSO systems is compensating for the effects of turbulence-induced photon fluctuations on system performance. Atmospheric turbulence results from both the spatial and temporal fluctuations of the refractive index due to temperature, pressure, and wind variations along the optical path IEEE02Zhu ; IEEE06Uysal ; IEEE06Djordjevic . Our system utilizes an 810 nm wavelength for the quantum channel and a 660 nm wavelength for monitoring the beam deflections and correcting the quantum channel deflections. To characterize the behavior of the beam wander caused by atmospheric turbulence depending on the wavelength, we measure the instantaneous x- and y-positions of two aligned laser beams at 810 nm and 660 nm, respectively, which were subjected to the same atmospheric conditions (Fig. 3(a)). The two beams travel through the same optical path and enter the receiver telescope. After reflcetion using an FSM (PI, S-330.4SL) with an angle resolution of 0.25 $\mu$rad and resonance frequency of 1.6 kHz, the beams split into PSD1 and PSD2. The inset in Fig. 3(a) shows the active area of the pin-cushion-type PSD (Hamamatsu, C10443-03) PSD . The PSD sensor consists of a common cathode and four anodes, the optical signal on the PSD surface generating a photocurrent proportional to the light energy. The photocurrent is split into the four anodes via a resistive layer, and the optical spot position $(x,y)$ on the PSD surface is extracted using the following expressions:

where $L_{x}$ and $L_{y}$ are the sensor dimensions (14$\times$14 mm²), and $V_{j}$ is the voltage obtained from the anode current through the amplifiers. Figure 3(b) presents the sample results for the beam-wander effects of the two beams over a period of 10 s, both signals following the same movements.

In addition to the wavelength dependence of the beam wander, we examined the beam-path drift owing to the outdoor temperature. As shown in Fig. 1, because the active reflector is set up on an outdoor hill, the optical beam path along the free-space channel can be affected by the atmosphere’s change in refractive index change and thermal expansions of the optical components due to changes in the outdoor temperature. Figure 4 shows the influence of the outdoor temperature on the temporal beam drifts over a period of 400 min. The measurements were performed on a bright sunny day from 11:00 to 17:40 on 27 April 2022 (Korea Standard Time, KST). The temperature ranged from 12 ^∘C to 20 ^∘C. For more clear observation of the outdoor temperature effect, a sunny day with a relatively big change in the temperature was chosen. The long-term drift depends on the temperature variation. During the night when the temperature doesn’t change much, the long-term drift reduced significantly. Therefore, as the sunlight becomes stronger, the temporal drift of the beam centroid position or radial distance increases, finally moving beyond the bounds of the telescope. In this work, the long-term beam drift due to changes in the outdoor temperature is corrected by a coarse alignment using a wireless link between PSD1 and the hexapod supporting the target mirror in the outdoor active reflector, as shown in Fig. 5(a).

The atmosphere in a free-space optical channel can lead to various detrimental effects$-$such as beam wander and slow temporal beam drift$-$which reduce the SNR and increase the QBER. To compensate for atmospheric effects and to achieve stable SMF coupling for the quantum channel, we used coarse alignment followed by fine alignment using a closed-loop feedback system in which an FSM is placed before the quantum and tracking channels IEEE18Fernandez . This allows for the correction of the beam variations using the FSM, making it possible to monitor the beam correction in real-time. The overall feedback system includes a control PC, FSM, PSD, and field programmable gate array (FPGA)-based board for data processing as shown in Fig. 5(a). The 810 and 660 nm signals are received and divided using the DM and directed to the SMF and PSD1, respectively. Here, the distance of the SMF and PSD1 to the FSM must be equal to guarantee efficient beam correction for the quantum channel. The FPGA board receives voltage information (V₁, V₂, V₃, and V₄) from PSD1, calculates the current beam position, and proviodes V_x and V_y output voltages (0$-$10 V), corresponding to the beam offsets from the center of PSD1 to the FSM. The control PC monitors the FPGA output signals and controlls the PID values at a sampling speed of 20 Hz using LabView. Coarse alignment (or slow feedback) is based on the use of a wireless bridge (TP-Link, CPE510) connecting PSD1 to the hexapod stage (PI, H-810.D2) in the outdoor active reflector. A long-term beam drift due to the outdoor temperature is relatively slow compared to the beam wander, which can be as fast as 100$-$200 Hz MOTL16Casado . From the beam position value averaged over 10 s, a coarse alignment controlled the beam position to the center of the PSD1 every minute. Immediately after the coarse alignment, a fine alignment (or fast feedback) is implemented at approximately 200 Hz using the FSM, driven by PID control through the FPGA. Figure 5(b) shows the beam centroid positions of the 660 nm tracking laser with a 250 m FSO link. The beam-wander range was reduced by the rapid feedback (or fine alignment). The inset presents the corresponding normalized histograms, and the Gaussian fit curves for the data are shown in Fig. 5(c). Consequently, the FWHM of the beam wander range was reduced from 350 to 24 $\mu$m. To improve the fiber-coupling performance in the quantum channel, we can consider the chromatic aberration of the receiving telescope. In the system, two laser beams with different wavelengths are received through a commercial Galilean telescope with $\times$20 magnification, which results in axial and lateral chromatic aberrations. If we use a Cassegrain telescope as a receiver, it would eliminate these chromatic effects.

A quantum-correlation-based free-space optical link over 250 m was constructed based on a closed-loop feedback configuration, as shown in Fig. 5. To monitor the coupling efficiency into the SMF for the laser power immediately after the receiving telescope, a weak 810 nm laser ($\sim$ 10 mW) was used for measurements instead of the signal photons since it’s impossible to measure the single photon counts directly in front of the SMF coupler. We achieved an average coupling efficiency of 19 $\%$ as shown in Fig. 6(a). The inset shows the SMF coupling efficiency as the function of time. Here, it shows the relatively large standard deviation ($\sim$ 520 $\mu$W) of the coupling efficiency. This is due to the chromatic abberation effects. The large wavelength difference between the signal and the guiding laser and the use of the refractive receiving telescope cause axial and lateral chromatic abberations which lead to the misalignment of 810 nm and 660 nm wavelengths. If we use a Cassegrain-type telescope as a receiver, these chromatic effects would be suppressed. Figure 6(b) shows the cross-correlation function between the idler and signal photons transmitted in a 250 m FSO channel. The normalized cross-correlation function is defined as

where indices $s$ and $i$ represent the signal and idler photons, respectively. $g^{(2)}_{si}(\tau)$ determines the rate of coincidence detection between modes $s$ and $i$ at a time delay $\tau$, and is useful for charaterizing light sources.

The blue $g^{(2)}_{si}(\tau)$ peak in Fig. 6(b) represents the cross-correlation between the idler and signal photons immediately before the transmitted telescope. The red data indicate the $g^{(2)}_{si}(\tau)$ function between the idler and received signal photons which were reflected from the outdoor active reflector. The fiber-coupled signal photon counts was about 1$\times$10⁶ counts/s immediately after the SPDC source, and the signal photon counts at the receiver site after the 250 m free-space propagation was about 5.5$\times$10⁴ counts/s. The background noise data are subtracted from the original $g^{(2)}_{si}(\tau)$ data. The total system loss ($>$ 90 $\%$) includes the free-space channel loss ($\sim$16 $\%$), the SMF coupling loss ($\sim$81 $\%$) in the quantum channel, and the tranceiver optical stage loss ($\sim$45 $\%$). The reduction in the $g^{(2)}_{si}(\tau)$ peak value is due to the total loss of the signal photons and daylight background noise (10 times larger than the number of signal photons). For large daylight background noise, if we use a single-mode pump laser, linearly polarized signal photons and a black shielding box, the background noise would be further reduced using a narrower optical filter and filtering randomly polarized noise photons.