Spontaneous Parametric Down-Conversion from GaAs Nanowires at Telecom Wavelength

. We report on the generation of photon pairs at 1550 nm from free-standing epitaxially grown self-assisted micrometre long GaAs nanowires. The efficiency of the spontaneous parametric down-conversion process has a rate of 320 GHz/Wm normalized to the transmission of the setup, the pump intensity, and the volume of the nanostructure. GaAs is a high index dielectric that can support electromagnetic Mie modes, therefore we model how shorter nanowires could improve the second-harmonic signal and we found that sub-micro long nanowires (600 nm length and 250 nm diameter) can support quality factors up to 15 at the pump wavelength (780 nm). We anticipate that the near field enhancement compared to micrometre long nanowires will boost the second-harmonic generation and, correspondingly, the biphoton rate efficiency.


Introduction
Photon pair sources are needed for applications in quantum cryptography [1], quantum imaging [2] or quantum metrology [3].Spontaneous parametric downconversion (SPDC), first demonstrated in 1970 by Burnham and Weinberg [4], is one method to generate photon pairs at room temperature with high spatial and temporal coherence.In the last years, increasingly smaller sources have been developed.Centimetre-sized nonlinear crystal [5] and periodically poled waveguides [6], requiring temperature and wavelength control, have given way to thin films [7], metasurfaces [8] and nanoantennas [9,10].The lower photon pair rate that is inherent to miniaturizing the source is compensated by an increased generation efficiency (Hz/Wm).The overall photon pair rate can be improved when several sources, pumped by the same laser, are integrated next to each other.Furthermore, the typically stringent energy and momentum requirements for SPDC are relaxed for smaller structures, leading to a broad emission spectrum.
III-V materials such as GaAs have valuable properties for nonlinear applications such as a direct band gap and a non-centrosymmetric crystal structure.Additionally, compared to LiNbO3 or beta-BaB2O4 (BBO) crystals, the bulk quadratic χ (2) nonlinearities of GaAs are very high with a value for d36 of 370 pm/V [11].

III-V Nanowires for SPDC
We demonstrate photon pair generation from epitaxially grown III-V GaAs nanowires and present a pathway to increase the generation efficiency by slicing a nanowire to a pre-determined size using focused ion beam milling [12].With this technique, we can shape high-quality nanoantennas, combining also lattice-mismatched materials, different refractive indices and crystal phases that are not available in bulk III-V materials [13].For instance, a strong tuning of the SHG efficiency was recently demonstrated by simply tuning the GaAs NW crystal phase [14].Mie-resonant nanostructures can be engineered to localize the electromagnetic field inside the nanostructure and therefore increase efficiencies of nonlinear processes [15,16].
A schematic of the SPDC process is shown in Figure 1a).A GaAs nanowire is pumped at 780 nm and the photon pairs (signal and idler) are collected in transmission.The goal is to compare the SPDC generation efficiencies of a long and a sliced nanowire (see Figure 1b) such that it shows a strong Mie-type resonance at the pump (780 nm) and conversion wavelengths (1560 nm).To determine this size, several spectra of secondharmonic generation (SHG), which is the reverse process of degenerate SPDC, were calculated for nanowires with different diameters and lengths.Figure 1c) shows a simulation using a finite element method (COMSOL Multiphysics) for a nanowire with a 250 nm diameter and sliced to a length of 600 nm.The resonances are located around 780 and 1560 nm as set for the experiment, with a dominant electric dipole emission profile.The quality factor Q at the pump wavelength of 780 nm is 15, indicating a field intensity enhancement inside the nanostructure, enabling an increase in the biphoton conversion efficiency.

Experimental Results
Figure 2 shows the coincidence counts for a long nanowire measured in the Hanbury Brown-Twiss configuration [7].This was achieved by integrating over 1 hour and pumping with a cw laser at 780 nm with 4 mW incident power.The signal to noise ratio (SNR) was above 2, indicating photon pair emission from the nanowire.After taking into account the 0.4% transmission of photon pairs in the setup and after normalizing to the pump intensity (0.05 mW/μm 2 ), we obtain an SPDC conversion efficiency of 320 GHz/Wm.This value is in comparison as high as in periodically poled waveguides (photon rate of 10 7 Hz with L0 ∼ 50 mm, Pin ∼ 1 mW) [6,17] or two orders of magnitude higher than similar GaAs nanoantennas [9].
In conclusion, we have shown that GaAs nanowires are efficient compact sources of biphotons.The advantage of nanowires is that they can be easily deposited on any substrate, allowing the use of their full length to slice several nanoantennas, for example to form a cavity structure or a phase array where all emit in phase.

Figure 1 .
Figure 1.a) Schematic of the SPDC process for a GaAs nanowire pumped at 780 nm.b) Electron microscopy image of a nanowire before and after being sliced by focused ion beam milling.c) Simulation spectrum of second-harmonic generation (SHG), the reverse process of degenerate SPDC, for a sliced nanowire with a 600 nm length and a 250 nm diameter.The resonances are located around 780 and 1560 nm as set for the experiment, with a dominant electric dipole emission profile.

Figure 2 .
Figure 2. Coincidence counts of a long nanowire integrated over 1 hour and pumping with a cw pump laser at 780 nm with 4 mW incident power.The signal to noise ratio (SNR) is greater than 2 indicating photon pair emission from the nanowire.