Entangled photon sources II: PACES
Our team is working actively on entanglement distribution via free-space or optical fiber. Although the wavelengths can be different - for fiber, we prefer something in the telecommunications band (1,550 nm or 1,310 nm) whereas for free-space we currently prefer the Near Infrared (about 800 nm), the design principles for entangled photon pair sources based on Spontaneous Parametric Downconversion (SPDC) are very similar. We also prefer to work in polarization, and to build sources around bulk crystals, because there are many degrees of freedom that can be utilised in a bulk material.
When designing instruments, it certainly helps to have an envelope for Size, Weight and Power (SWAP), and we use this to determine which design choice to optimize. As we like to reduce the footprint of the instrument, we often choose to work on co-linear designs, where all three SPDC fields co-propagate in the same direction.
Parallel Aligned Crystals Entanglement Source - PACES
PACES is the design of the polarization-entangled photon pair source that is implemented on the SpooQy-1 satellite. The papers describing this source were first published in 2018 in Optics Express and Applied Physics Letters. The novelty of PACES stem from the use of two non-linear crystals with parallel-aligned axes and featured also in CQT's Highlights.
We start first by describing the result in the Optics Express paper. The major result of PACES is that it reduces the effects of spatial walk-off allowing easier photon pair collection, which means improved reliability for portable devices. In fact, the brightness of over 100,000 detected pairs per second per mW of pump power, has only been observed by specially engineered crystals in the past, and not in the conventional, single-domain crystals used in PACES. The concept is illustrated in Figure 1.
Fig. 1. Schematic for the source design. (a) Spatial self-compensation of the emitted photon pairs. The BBO optical axes are both pointing upwards as indicated by the black arrow. SPDC light is created along the pump path in both crystals and the red (green) ellipse indicates the shape of the SPDC emission generated in the first (second) BBO crystal. An achromatic half-wave plate (with magnesium fluoride (MgF2) and quartz (Qtz) components) rotates the polarization of the photons born in the first BBO. (b) Theoretically calculated relative phase between |V s V i i and |Hs Hi i with (solid line) and without (dashed line) the phase compensation crystal. For BBO length of 5 mm, a YVO4 length of 3.12 mm can act as the compensator. (c) Overview over the experimental setup, 1: laser diode, 2: fluorescence filter, 3: Glan-Taylor polarizer, 4: half-wave plate, 5: convex lens, 6: concave lens, 7: BBO, 8: achromatic half-wave plate, 9: BBO, 10: dichroic mirror, 11: long-pass filter, 12: phase compensation crystal, 13: position of the analyzer when performing the single polarizer measurement (see Fig. 3(b)), 14: collection lens, 15: single-mode fiber, 16: photon separation via a dichroic mirror followed by coincidence detection.
One of the novel characterization steps we took in this paper was to implement partial tomography with a single polarizer acting on both signal and idler photons in the pair. Unlike a typical physics experiment, where we assume we have no knowledge of the source, in most cases we do know the momentum conservation rules that apply, and we understand the signal we should get. With this prior knowledge we can work towards achieving high fidelity with partial tomography to align the source.
Fig. 2. (a) Theoretical pair rates for both Φ+ and Φ− states when utilizing a single polarizer analyzer. This measurement technique can distinguish between the maximally entangled states Φ+ (zero contrast curve) and Φ− (full contrast curve). (b) Detected photon pair curve using a single polarizer (installed after the temporal compensator, see item 13 in Fig. 1(c)) measurement at a pump power of 0.1 mW. The peak at 0 (90) degree corresponds to horizontal (vertical) polarization. The minimum at -45 (45) degrees corresponds to anti-diagonal (diagonal) polarization. The fidelity calculated from the fit was 99.53 ± 0.22%.
The polarization correlation between photon pairs that we can obtain from the PACES source is very good, and the pair production rate is also best in class for single domain birefringent crystals. In Figure 3 below, you see that the entanglement quality (fidelity to the maximally entangled Bell state) is maintained even when the passively quenched Geiger-mode avalanche photodiodes begin to saturate. However, this rate of observed brightness is NOT the limit. By going to a field-stop, you can get even brighter as shown below.
Fig. 3. (a) Photon pair coincidences obtained using two polarizers. For this measurement, the dichroic mirror was replaced with a 50:50 beam splitter (to avoid wavelength-dependent phase-shifts). Polarization analyzers were placed in both arms after the beam splitter.Single-mode fiber coupling was performed after the polarization analyzer. While fixing the polarization analyzer setting in one arm (A, H, D, V), the polarizer in the other arm was swept and the coincidence events were recorded. (b) Power dependence of the fidelity (blue,left axis) and the detected pair rate (black, right axis) with the polarization analyzer in place.The source saturates the passively-quenched detectors at 2 mW of pump power. The error bars for the experimental rate data points are smaller than the symbols. The solid black line is a guide to the eye indicating the saturation of the coincidence rate. The rate assuming linear power scaling is depicted by the dashed black line.
One of the advantages of PACES is that you have a broad region from which you can collect polarization entangled photon pairs. The results when using a field-stop collection were reported in the Applied Physics Letters article. The design of the collection is shown in Figure 4.
Fig. 4. Sketch of the experimental setup. LD: laser diode, FF: fluorescence filter, HWP: half-wave plate, LP: long-pass filter, and DM: dichroic mirror. An iris is used to control the opening angle of the SPDC light that reaches the detectors. It can be placed either before splitting the signal and idler (Iris 1) or after the dichroic mirror in the signal arm (Iris 2).
Using this field stop approach, we can observe an unprecedented level of brightness for the source, where 400,000 pairs/s/mW were observed with over 95% fidelity to maximally entangled Bell states.
Fig. 5. (a) Observed pair rate (open triangles) and fidelity (filled triangles) as a function of emission angle for a source using 6 mm BBO crystals. The emission angle was calculated from the iris diameter. An error function was fitted to the pair rate data points. The solid line describes the calculated fidelity obtained from the phase map [Fig. 1(d) and is not fitted using a free parameter]. (b) Correlation between fidelity and brightness for multiple crystal lengths. The brightness is controlled by the iris diameter. The dashed line indicates the QBER limit for the Ekert protocol of QBER 15%.
The PACES design is compact, and can produce very high quality entangled photon pairs. For this reason, it was the basis of the SPEQS-2 instrument and flown on SpooQy-1.