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Broadband biphoton generation and polarization splitting in a monolithic AlGaAs chip

The ability to combine various advanced functionalities on a single chip is a key issue for both classical and quantum photonic-based technologies. On-chip generation and handling of orthogonally polarized photon pairs, one of the most used resource in quantum information protocols, is a central challenge for the development of scalable quantum photonics circuits; in particular, the management of spectrally broadband biphoton states, an asset attracting a growing attention for its capability to convey large-scale quantum information in a single spatial mode, is missing. Here, we demonstrate a monolithic AlGaAs chip including the generation of broadband orthogonally polarized photon pairs and their polarization splitting; 85% of the pairs are deterministically separated by the chip over a 60 nm bandwidth. The quality of the two-photon interference at the chip output is assessed via a Hong-Ou-Mandel experiment displaying a visibility of 75.5 % over the same bandwidth. These results, obtained at room temperature and telecom wavelength, in a platform combining high second-order nonlinearity, electro-optic effect and direct bandgap, confirm the validity of our approach and represent a significant step towards miniaturized and easy-to-handle photonic devices working in the broadband regime for quantum information processing.

The ability to combine various advanced functionalities on a single chip is a key issue for both classical and quantum photonic-based technologies. On-chip generation and handling of orthogonally polarized photon pairs, one of the most used resource in quantum information protocols, is a central challenge for the development of scalable quantum photonics circuits; in particular, the management of spectrally broadband biphoton states, an asset attracting a growing attention for its capability to convey large-scale quantum information in a single spatial mode, is missing. Here, we demonstrate a monolithic AlGaAs chip including the generation of broadband orthogonally polarized photon pairs and their polarization splitting; 85 % of the pairs are deterministically separated by the chip over a 60 nm bandwidth. The quality of the two-photon interference at the chip output is assessed via a Hong-Ou-Mandel experiment displaying a visibility of 75.5 % over the same bandwidth. These results, obtained at room temperature and telecom wavelength, in a platform combining high secondorder nonlinearity, electro-optic effect and direct bandgap, confirm the validity of our approach and represent a significant step towards miniaturized and easy-to-handle photonic devices working in the broadband regime for quantum information processing.

I. INTRODUCTION
Photonic quantum technologies are a valuable approach for quantum information processing including secure communications, quantum computation, simulation and metrology [1,2]. While quantum photonic experiments in bulk optics continue to produce important results demonstrating the advantage of quantum technologies over classical ones in several domains [3][4][5], integration at the chip scale has become essential to scale up these concepts and transform laboratory demonstrators into real-world technologies [6,7]. In the last two decades, significant advances on integrated quantum photonic circuits have enabled the generation and manipulation of quantum states of light at an increasing scale and level of complexity exploiting a variety of optical material platforms. Most of these achievements have been done using glass or χ (3) materials such as silicon nitride, silicon-on-insulator or silica on silicon [8], despite the fact that the use of χ (2) materials leads to more efficient frequency conversion processes. Standing results using this second class of materials have been obtained with lithium niobate-based photonics circuits, having led to the demonstration of an on-chip squeezing experiment [9], a two-channel spectrally degenerate polarization entangled source [10] and a nonlinear integrated quantum electro-optic device [11]. However, in the first work the chip doesn't manage polarization, while in the second and third ones the devices work in a narrow spectral bandwidth regime. On-chip polarization handling of broadband biphoton states would constitute a crucial resource in the toolbox of integrated quantum photonic circuits. Indeed, on the one hand polarization is one of the most used degrees of freedom in quantum information protocols, widely employed both for deterministic separation of photons or to encode entanglement ; on the other hand, broadband frequency states for highdimensional encoding are attracting a growing interest thanks to their capability to convey large-scale quantum information into a single spatial mode [12], an important asset for scalability. Although broadband integrated polarization mode splitters working in the classical regime have been demonstrated in Si-based platforms [13][14][15], polymers [16] and lithium niobate waveguide circuits [17], to date, there exists no device able to combine the generation of broadband biphoton states and their deterministic splitting through polarization. Here, we demonstrate a monolithic AlGaAs waveguide circuit including the generation of broadband orthogonally polarized photon pairs via type II spontaneous parametric down conversion and their polarization splitting through a birefringent directional coupler. We demonstrate that 85 % of the pairs are deterministically spatially separated via their polarization over a bandwidth of 60 nm. The performances of the device as a quantum photonic circuit are assessed by implementing a Hong-Ou-Mandel interferometer at the chip output, one of the fundamental experiments in quantum optics lying at the heart of many nonclassical logic operations; the obtained visibility is 75.5 % for a 60 nm-broad biphoton state. These results, obtained at room temperature and telecom wavelength, in a mate-rial platform combining high second-order nonlinearity (150 pm V −1 at 1550 nm), electro-optics effect [18] and compliant with electrical injection [19], represent a significant step towards real-world quantum photonic integrated circuits working in the broadband regime.

II. SAMPLE LAYOUT AND CLASSICAL CHARACTERIZATION
The device, sketched in Fig. 1 (a), combines a parametric source of orthogonally-polarized photon-pairs followed by a broadband polarizing mode splitter fabricated out of an epitaxially-grown multilayer AlGaAs wafer (see Supplementary Material for details). In this design the generation region and the polarization splitter consist of two monolithic waveguides of variable width converging at a central evanescent coupling region through S-Bend waveguides.
Photon pairs in the telecom S+C band are generated into a 5 µm-wide ridge waveguide section which is then tapered down to a narrower width w when approaching the polarization splitting region. In this part of the chip, the waveguides are separated by a gap g and evanescent coupling occurs between the guided modes of the two structures. We design the device by defining w, g as well as the coupling length L such that photons generated in the TM mode, with an electric field along the z-axis, are coupled into the opposite waveguide, while photons generated in the TE mode, with an electric field along the x-axis, exit through the injection waveguide itself. The device was patterned by electron-beam lithography and dry etched by inductively coupled plasma (ICP) leading to a ridge height of 800 nm (see Supplementary Material for details). Scanning electron micrographs of the chip input, output and S-Bends regions, showing high fabrication quality with upright and smooth waveguide sidewalls, are featured in Fig. 1 (b-d).
The generation region is based on a Bragg reflection waveguide emitting photon-pairs through Type II spontaneous parametric downconversion (SPDC) [20,21]. Typical internal pair generation rate and brigthness of a 2 mm-long straight waveguide having the same epitaxial structure are 7 × 10 6 pairs/s and 2 × 10 5 pairs/s/mW/nm (in terms of internal pump power) respectively. Owing to the dispersion properties of the guided modes and the negligible group velocity mismatch between orthogonally polarized photons, this type of source allows for the generation of photon pairs entangled in the frequency and polarization degrees of freedom without the need for off-chip temporal walkoff compensation [21][22][23]. Another key property of the source is its wide spectral bandwidth (60 nm), making it ideal for multi-user entanglement based QKD networks or high-dimensional frequency-based quantum information [22,23]. In this kind of structure, the SPDC phasematching wavelength depends on the effective refractive index of the involved modes and consequently on the waveguide width. As a consequence, by tuning the pump wavelength to the phase-matching wavelength of the generation region (762.5 nm for the 5 µm-wide waveguide), we ensure that pump photons will only trigger the SPDC process in the input waveguide and neither in the polarization splitting region nor in the output arms of the device (where the phase matching wavelength is 770.5 nm).
The polarization splitting region relies on a birefringent directional coupler architecture. We denote by E a , E b the electromagnetic field of the fundamental modes of waveguides a and b, as indicated in Fig. 1 (a). Following the coupled modes theory [24], in the evanescent coupling region the eigenmodes of the structure take the form of symmetric S and anti-symmetric AS supermodes : 2 with associated propagation constants β S and β AS . As a result, light propagating along the y axis in the TE (resp. TM) fundamental mode of waveguide a will hop back an forth between the two evanescently coupled waveguides with a beating length L ). Thanks to the intrinsic modal birefringence of the waveguides, we can find a region in the parameter space (w, g) for which: where p is an integer. In our case, we have chosen p = 3. When this condition is met, we choose a coupling length L = 4L such that incoming TE-polarized light in waveguide a is totally transferred to output port a after hopping four times between the waveguides, while TM-polarized light undergoes three hops before exiting through the opposite output port b.
The figure of merit that we use to quantify the ability of the coupler to spatially separate the two orthogonal polarizations is the splitting ratio. For a coupling length L, it is defined for each polarization as: where P α a , P α b is the output power at port a, b for polarization α = TE, TM. With this definition, a perfect polarization splitting is obtained for s TE = s TM = 1 corresponding to the case where all TE-polarized light exits from arm a and all TM-polarized light exits from arm b. We perform electromagnetic simulations of the guided modes of the structure in the xz plane in the approximation of infinitely long waveguides and solve for the propagation constants β TE S , β TE AS , β TM S , β TM AS . We use these numerically calculated values to find the optimal (w, g) maximizing the splitting ratio over a spectral range matching the 60 nm biphoton bandwidth of the source (see Supplementary Materials for details). We simulate the propagation of light in the fundamental TE and TM modes by solving the Maxwell equations for the electric field using the numerically calculated propagation constants obtained for this set of parameters. The result of this simulation over a xy plane located in the waveg-uide core is shown in Fig. 1 (e). As expected, light in the TE mode exits through port a after two round trips while light in the TM mode exits through port b after one and a half round trip. To validate our design strategy, we fabricated on a single epitaxial wafer 10 devices with fixed values of waveguide width and gap and different values of coupling length L. For all these devices we measured the splitting ratio for the TE and TM fundamental modes and compared them to calculations using Eqs. (2) and (3).
The experimental characterization of the splitting ratio is done by injecting a telecom laser beam into the generation region and recording the transmitted power at the two output ports a and b of the device as a function of the input wavelength λ. In order to access independently the TE and TM splitting ratios, the laser beam is linearly polarized either along the vertical z-axis or the horizontal x-axis (see Fig. 1 (a)). Light is coupled into the waveguide using a microscope objective (NA = 0.95) and collected simultaneously from both output arms a, b of the device using a second microscope objective (NA = 0.65) before being detected with an infrared powermeter. The chip was set at a stable temperature of 20°C using a Peltier element in a PID loop. Fig. 2 (a) reports the experimental results obtained for the device presented in this work, and Fig. 2

III. ON-CHIP GENERATION AND POLARIZATION SPLITTING OF TELECOM PHOTON PAIRS
We assess the performance of the device in the quantum regime by generating orthogonally polarized photon pairs via SPDC in the generation region and detecting the separated photons at the two output ports of the device. To this end, we pump the input waveguide using a near-infrared CW laser (TOPTICA DL Pro 780) at a wavelength of 762.5 nm using the same input and output coupling microscope objectives. Residual transmitted pump photons are filtered out using freespace long-pass filters while the generated telecom photons are fiber-coupled and detected by two superconducting nanowire single photon detectors (SNSPDs, Quantum Opus). Time-correlations between the photon detection times are recorded using a time-to-digital converter (quTools). The measured number of coincidence counts as a function of the pump power before the input objective and corresponding coincidence-to-accidental ratio (CAR) are displayed in Fig. 2 (c). We observe that the coincidences and CAR display respectively a linear and inversely proportional dependence on the pump power as in the case of a single-waveguide AlGaAs source with off-chip pair separation [20].
To certify the successful polarization splitting of the generated photon pairs, we record the number of coincidences counts in four different experimental configurations (see Fig. 3): case a) with a linear polarizer aligned along x(z) at the output of arm a(b); case b) with arm a blocked and a PBS inserted before the detectors; case c) with arm b blocked and a PBS inserted before the detectors; case d) with a linear polarizer aligned along z(x) at the output of arm a(b). The configuration of case a) selects the events corresponding to the correct functioning of the designed polarization splitter; the configurations b)-d) correspond to unwanted events. The results of time correlation measurements in these four situations are reported in Fig. 3 (a)-(d). We see that the number of events measured in case a) represents 85 % of the total number of emitted pairs, demonstrating the high efficiency of the polarization splitting region design.

IV. HONG-OU-MANDEL INTEFEROMETRY AT THE CHIP OUTPUT
The device operation in the quantum regime is further probed through Hong-Ou-Mandel (HOM) interference. The HOM effect, in addition to being a witness of nonclassicality, represents a cornerstone of quantum information processing [25]. Indeed, this type of two-photon interference is widely used in quantum state engineering [26,27], measurement-device independent quantum key distribution [28] and quantum metrology [29,30]. Lastly, the HOM effect has been proven to be a central tool in time-frequency encoded high-dimensional quantum information with biphoton states [22,31].
The experimental setup used to perform HOM interference at the output of the device is depicted in Fig. 4 (a). Input and output coupling are done with the same microscope objectives used in the previous experiment. After pump filtering and fiber collimation, we apply a temporal delay on arm b using a free-space delay line before recombining the two photons on a fiber 50/50 beam splitter (BS) and detecting them at the output of the BS with SNSPDs. The two fiber polarization controllers (FPC) are used to ensure that the polarization of the two photons is identical in the fiber interferometer.
To probe separately the impact of the properties of the generated quantum state and of the polarization splitting ratio of the device on the two-photon interference, we measure the HOM interferogram in four different settings: first, using the full generated state respectively without and with the addition of polarizers at the chip output; then in the same measurements settings but using the generated quantum state spectrally filtered around degeneracy with a 12 nm-wide filter.
In Fig. 4 (b) we plot the result of a HOM measurement taken directly at the chip output without any spectral filtering nor added polarizers. The measured visibility, given by V = (C ref − C min )/(C ref ), where C ref is the coincidence reference level and C min is the coincidence minimum, is 75.5 % ± 5.4 % exceeding the classical threshold of 50 % thus showing that the integrated source and splitter operate in the quantum regime. The red curve corresponds to the calculated HOM coincidence probability obtained from the simulated quantum state produced in the generation region and the experimentally measured splitting ratios s TE , s TM (see Supplementary Materials for details). We observe that the agreement between our model and the experimental results is excellent.
In Fig. 4 (c) we plot the results obtained by inserting in each optical paths a and b a linear polarizer with transmission axis respectively aligned along the x and z-direction. The obtained visibility in this case is V = 89 % ± 4.6 %, a value which is in agreement with previous experiments on AlGaAs sources consisting of a single straight ridge waveguide followed by an off-chip fiber polarizing beam splitter [21,22], supporting the idea that this measurement gives access to the intrinsic visibility of the generated two-photon state. The limitation to this value comes from waveguide birefringence causing spectral asymmetry with respect to frequency degeneracy between TE and TM-polarized photons. As a result, our measurement shows that a perfect splitting ratio over the whole state bandwidth would allow to reach the maximum value of visibility allowed by the source properties.
We emphasize that both HOM interferograms were obtained with a broadband biphoton state as opposed to previous demonstrations reported in ppLN where offchip filters were used [11] or in Silicon chips generating narrowband degenerate photon pairs [32]. To quantify the effect of spectral filtering on the performances of our device, we repeat the HOM measurement after adding at the chip output a 12 nm filter centered on the biphoton degeneracy frequency. We obtain a value of V = 91.0 % ± 6.6 % without polarizers (Fig. 4 (d)) and V = 91.8 % ± 6.9 % with polarizers ( Fig. 4 (e)). This value is of the same order as in previous state-of-the-art realizations in other platforms, but we notice that in our case the available spectral bandwidth is one order of magnitude higher (1.2 nm in [11]). We stress the relevance of this result by pointing out that spectral filtering is commonly used in many applications such as wavelengthmultiplexed quantum communications [23] or frequencybased quantum information [33] where the emitted photons have to be divided into spectral bins by the use of filters. Hence, in most cases, the spectral asymmetry with respect to frequency degeneracy between the two photons of the pairs causing imperfect HOM visibility is naturally suppressed by the action of filtering.

V. CONCLUSION AND OUTLOOK
In summary, we have demonstrated a monolithic nonlinear AlGaAs waveguide circuit integrating the generation of spectrally broadband photon pairs in the telecom range and their polarization splitting with a birefringent directional coupler. 85 % of the pairs are deterministically separated by the chip over a 60 nm bandwidth. Its performances in the quantum regime have been assessed via a Hong-Ou-Mandel interference experiment displaying a visibility of 75.5 % (91 %) for a 60 nm (12 nm) broad biphoton state. We notice that a maximal visibility of the HOM dip requires that the splitting ratio curves for the TE and TM modes are superposed and symmetric with respect to the frequency degeneracy for the down-conversion process; a possible way to improve the performances of the present device is to adjust the waveguide width of the generation region to shift the frequency degererancy of the generated state at the optimal wavelength. Further progress on the device performances is possible following two main directions: on one hand the design of the epitaxial structure could be optimized in order to reduce the modal birefringence thus increasing the HOM visibility [34]. On the other hand, the design of the polarization splitting region could be refined by using adiabatic couplers which, in LiNbO3 waveguides without an on-chip photon pair source, have been shown to exhibit a flat spectral profile with splitting ratios above 98 % over a spectral range of more than 100 nm [17]. The device presented in this work can already be used as a source of broadband frequency anticorrelated photon pairs separated in two different spatial modes, directly employable for information processing protocols based on high-dimensional quantum states [35,36]. Using both input arms of the splitting region to generate orthogonally polarized photon pairs would also allow to obtain a source of polarization entangled photon pairs directly separated in two spatial modes, as reported in PPLN [10] , albeit with a narrow bandwidth (0.25 nm) in the latter work. Using AlGaAs would not only allow a miniaturization of the device of around one order of magnitude, but also to take benefit of the low modal birefringence to avoid temporal walk-off post-compensation in frequency channel-based quantum networks. By taking a step further the device could be upgraded by adding an electro-optic delay line [18], a polarization rotator [37] and a 50/50 mode splitter [38]. In this configuration the photons, after being generated in a waveguide, would be deterministically separated at the polarizing mode splitter and time-shifted by the electrooptic delay line; one of them could be polarization rotated and finally the to photons would be recombined on the 50/50 mode splitter. Such nonlinear integrated quantum electro-optic circuit would enable a full flexible control over single-qubit operations [11] as well as an onchip generation of polarization-frequency hyperentangled states [39] over a wide spectral range, opening promising perspectives for its utilization in quantum communication networks [40].

Disclosures
The authors declare no conflicts of interest.

Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request. and coupling length L sim and infer the TE and TM splitting ratio as shown in in Fig. 1 (a-b).
At a wavelenth of 1525 nm, for L sim = 864 µm, we observe that the dotted lines denoting the regions where s TE and s TM are equal to 1 can be almost perfectly superimposed. As a consequence, in this design, we can achieve simultaneously perfect TE and TM polarization splitting. The optimal working point, corresponding to the region where the two TE and  Exp. Exp. Sim.
Sim. length L correspond to a device with w = 1.29 µm and g = 1.51 µm.

BILITY
To model Hong-Ou-Mandel (HOM) effect in our integrated device, we use the physical picture sketched in Fig. 3 (a). The photon pairs emitted by the source are incident on a frequency-dependent polarizing beam splitter, which models the polarization splitting region of our device. We assume that the two photons are initially in the same arm a of the PBS.
Then, after they exit the PBS, a delay is applied to arm c and the polarization in this arm is rotated with a half-wave plate such that the two photons end up with identical polarization.
As in a usual HOM interferometer, the photons are recombined on a 50/50 beam splitter.
The first term P c,sep defines the envelope of the HOM interferogram while the the second term P c,bunch is a rapidly oscillating term resulting from Franson-type interference between the two paths of the interferometer. In Fig. 3 (b-d), we display the simulated coincidence probability for different values of the TE and TM (H and V ) splitting ratios. We observe that in all three cases the general shape of the interferogram follows a typical HOM dip with a background oscillating at a temporal period of 3 fs, which cannot be resolved by our free-space delay line. Hence when measuring the experimental HOM coincidence probability P c,exp , these oscillations reduce to a constant background given by the average value of the oscillating term over a temporal window of 30 fs defined by the resolution of our free-space delay line : P c,exp =P c,bunch + P c,sep . The simulated value for P c,exp is shown in Fig. 3 (b-d) as a solid red line. We note that, in agreement with experimental results, the visibility drops from V = 89 % to V = 80 % when going from s H = s V = 1 (Fig. 3 (d)) to the experimental values s H (ω), s V (ω) of the splitting ratios ( Fig. 3 (c)). As can be seen from our model this decrease can be attributed to the imperfect polarization splitting which gives a non-zero contribution to P c,bunch subsequently lowering the HOM visibility.