Silicon core fibers: A new platform for quantum light generation

Silicon core fibers (SCFs) are emerging as a platform for various applications, from electro-optic devices to infrared modulators and power delivery fibers.¹ The continuous reduction of propagation losses, now in the range of 0.2 dB/cm in the telecom band,^2,3 makes SCFs suitable for efficient nonlinear optical processes.⁴ In this context, while many studies focused on classical nonlinear effects, no one, to the best of our knowledge, has explored their quantum counterparts. Quantum applications need sources with high brightness, low losses, low footprint, and high scalability.⁵ At present, sources based on silica fibers and silicon photonic integrated circuits (PICs) do not meet all these requirements at once. In this paper, we present a photon pair source based on spontaneous four wave mixing (SFWM) in a SCF that potentially combines the low loss and cost of the fiber platform with the high nonlinearity and compactness of silicon PICs. Given the central role of losses in quantum applications, we also present a method to characterize the coupling and propagation losses of a probabilistic photon pair source. This method directly estimates the losses of the source itself, without the need of auxiliary fibers/waveguides or the use of destructive methods, e.g., cutback method. The setup used for the quantum source demonstration is shown in Fig. 1(a). We used a SCF with a nominal core diameter of 1 μm [Fig. 1(b)]. It was fabricated with a laser based molten core method:³ a high purity silicon rod (electrical resistivity $>3$ kΩ cm, float zone method, University Wafer) was sleeved with a fused silica tube (Heraeus F300), then tapered, and re-sleeved to achieve the targeted core–cladding ratio. The 6 mm diameter of the final preform was subsequently drawn directly to 125 μm diameter using a carbon-monoxide laser, operating at 5.5 μm, as a heat source.³ Fibers drawn using this technique typically have a single-crystal core, avoiding the need for laser post-processing,⁶ with propagation losses of the order of 0.1–0.5 dB/cm. The length of the sample used in the experiment is about 58 mm, chosen because of its lower loss compared to similar samples prepared for the experiment. A continuous wave (CW) pump laser at $∼1551$ nm was coupled into the SCF with an aspherical lens with a focal length of 2 mm. Its power was adjusted with a variable optical attenuator (VOA) and measured with a photodiode [not shown in Fig. 1(a)] before coupling. Inside the fiber, idler and signal photons were generated through SFWM and extracted with a lensed fiber with a mode field diameter of 2 μm (OZ Optics). After the SCF, a cascade of fiberized bandpass and notch filters (Opneti) created a filtering system that split the idler and signal photons into two telecom channels at $∼1543$ and $∼1559$ nm (bandwidth of 1.15 and 1.4 nm, respectively). The filtering system was composed of a first notch filter for the pump wave and two additional bandpass filters per channel to reach a total pump rejection of more than 120 dB. Subsequently, an additional broadband filter around 1550 nm (Thorlabs) was used to remove the residual noise spectrally far from the C-band. The transmission coefficients of the filtering system were 0.40 and 0.42 for the idler and signal photons, respectively. The output idler and signal channels were measured by two superconducting nanowire single photon detectors (SNSPDs) (Quantum Opus). Both had a nominal dead time of 30 ns and a dark count rate of d = 100 Hz. The idler and signal detection efficiencies were 0.93 and 0.91, respectively. A time tagger (Swabian Instruments) allowed tracking idler, signal, and coincidence rates with a 10 ps time resolution. The coincidence time window used in the analysis was τ = 100 ps. During the experiment, the fiber-coupled pump power was $<2$ mW, to avoid nonlinear absorption.

Figure 3(a) shows the performance of the source—idler, signal, and coincidence rates—while Fig. 3(b) shows the performance of the CAR. Raman scattering in the silicon core dominates the singles counts. Its contribution, i.e., $Ri(s)R$ in Eq. (2a), was estimated from the linear component of a quadratic fit of the idler and signal rates vs fiber-coupled pump power. The error on this estimation results in an uncertainty in the simulated rates and CAR indicated by the shaded areas in Figs. 3(a) and 3(b), respectively. The coincidence rate [the inset of Fig. 3(a)] grows quadratically and is not affected by Raman counts, since detection in coincidence filters away most of the uncorrelated noise counts.¹¹ The maximum measured CAR is 133 ± 2 at a fiber-coupled pump power of 134 μW. The simulation shows that this value approaches the maximum reachable CAR, which, in our source, is limited by Raman scattering.

In Table I, we compare the performance of our device with state-of-the-art for photon pair quantum sources in fibers and silicon PICs. The comparison is limited to sources with characteristics similar to our device: χ⁽³⁾ process-based, without resonant optical structures and with at least one of the generated photons in the C-band. The intrinsic brightness, propagation losses, CAR, and device length are considered and reported.⁷ For fair comparison, in the case of pulsed operation, brightness is normalized as described in the caption of Table I. We also report both the temperature at which the experiments were carried out and either the pump pulse width or the coincidence time window, being parameters that affect dramatically the CAR value.¹² The lower the temperature and the pulse width/time window, the higher the CAR. The propagation losses of SCFs are lower than those of silicon PICs, which are typically larger than 0.5 dB/cm.¹³ Therefore, given the same coincidence rate, a lower pump power is required, resulting in a higher brightness. At the same time, the high nonlinearity of silicon makes our SCF a very bright, if not the brightest, fiber-based source per unit length. This remains valid even when extending the comparison to fiber sources generating shorter wavelengths that, usually, offer a higher performance.^14,15 Moreover, according to our model, by optimizing the length of our fiber, which occurs when L = 1/α ∼ 14 cm, it is possible to further increase the brightness by a factor ∼1.8.⁷ The maximum CAR value would not be affected significantly by a longer fiber. Similarly to other optical fibers, fabrication is cost effective and SCFs can be drawn reliably in spools of hundreds of meters at a speed of ∼cm/sec³. The geometry of the cross section and of the optical modes is circular, making standard fibers naturally more compatible with SCFs than silicon PICs. The main limiting factor to CAR is Raman scattering, as it is also the case for all other sources of Table I. Various techniques to mitigate Raman noise can be implemented: source cooling, which, unfortunately, increases the complexity of the setup;¹² dispersion engineering to generate the photon pairs in regions with low Raman scattering at the expense of using non-standard fibers;¹⁵ and intermodal phase matching in polarization maintaining fibers, which has shown improved CARs too, but, mainly, in the visible range.¹⁶ In the recent years, new approaches have been explored, such as using short standard fibers to broaden the generated spectrum¹⁷ and intermodal phase matching using transverse modes.^18,19 In both cases, photons can be generated in spectral regions with low Raman scattering, hence decreasing the noise. All these methods are compatible with the SCF platform. In addition, the material of the fiber plays an important role on CAR. Recent studies have shown gas filled hollow core fibers as a promising platform for noise free parametric sources,²⁰ and with this paper, we explored silicon. In our case, we can estimate the improvement in terms of CAR of SCFs over silica-based fibers by calculating the ratio, r, between the nonlinear parameter, γ, and the Raman gain of the material. There is an increase of almost two orders of magnitude between r ∼ 0.6 for silica⁸ and r ∼ 56 for silicon (from our data). Thanks to this improvement, it was possible to build a bright photon source with a high CAR without the need of any complicated setup and using only the fundamental mode of the fiber. Further optimizations will be possible in the future, especially overcoming the high losses of SCFs. Propagation losses can be improved by reducing the content of impurities in the silicon core and further optimizing the draw parameters.²¹ We note that surface scattering, typically high in PICs, is negligible in SCFs, thanks to the atomically flat core–cladding interface.^1,21 Regarding coupling losses, various approaches to improve the coupling to standard fibers have been studied, but further research is needed to reduce them below 2 dB per facet.^22,23 Fabrication of many identical sources represents another significant future challenge, being of great importance for the majority of quantum applications.²⁴ In this context, the laser based molten core approach is promising as a single draw can yield several hundreds of meters of low loss fiber from the same preform.

In conclusion, to the best of our knowledge, we performed the first demonstration of a photon pair source based on a SCF and we described a practical method for characterizing the losses of a quantum source. The loss characterization method is a powerful tool that can be easily generalized to any source based on SFWM or SPDC but also, to any device, quantum or not, provided that the output has a nonlinear dependence on the coupling losses. By characterizing the brightness and propagation losses of the photon pair source, we showed how SCFs can fill the technology and application gaps between compact PICs and low-loss fibers. Further developments are still needed to reduce the losses and improve the scalability of the platform so that one can reach the full potential of SCFs in practical quantum applications.

This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 956419. This work was funded by the Swedish Foundation for Strategic Research (Grant No. RMA15-0135), the Horizon 2020 Framework Program (Grant Nos. 820466 and 820405), and the European Union (Grant Nos. QSNP 101114043 and ONAIR 101065309). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union, European Commission-EU or European Research Executive Agency (REA). Neither the European Union nor the granting authority can be held responsible for them. This project is funded by the Departament de Recerca i Universitats de la Generalitat de Catalunya (2021 SGR 01458). This work was partially funded by CEX2019-000910-S (MCIN/AEI/10.13039/501100011033), Fundació Cellex, Fundació Mir-Puig, and Generalitat de Catalunya through CERCA. This study was supported by MCIN with funding from European Union NextGenerationEU(PRTR-C17.I1) and by Generalitat de Catalunya.

We thank Alessia Mezzadrelli and Vittoria Finazzi for their technical support and Nicolás Linale for his help in the initial study of the system.