A two-channel, spectrally degenerate polarization entangled source on chip

Integrated optics provides the platform for the experimental implementation of highly complex and compact circuits for quantum information applications. In this context integrated waveguide sources represent a powerful resource for the generation of quantum states of light due to their high brightness and stability. However, the confinement of the light in a single spatial mode limits the realization of multi-channel sources. Due to this challenge one of the most adopted sources in quantum information processes, i.e. a source which generates spectrally indistinguishable polarization entangled photons in two different spatial modes, has not yet been realized in a fully integrated platform. Here we overcome this limitation by suitably engineering two periodically poled waveguides and an integrated polarization splitter in lithium niobate. This source produces polarization entangled states with fidelity of F= 0.973±0.003\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal F} \mathrm{=0.973}\pm 0.003$$\end{document} and a test of Bell’s inequality results in a violation larger than 14 standard deviations. It can work both in pulsed and continuous wave regime. This device represents a new step toward the implementation of fully integrated circuits for quantum information applications. In the context of quantum technology, integrated photonic devices demonstrated great potential to perform quantum tasks stably with ease. Despite the great development of integrated circuits, the generation of quantum states of light remains challenging in an integrated geometry. In particular, one of the most adopted source in quantum information processes, the one firstly proposed by Kwiat et al. (PRL 75, 4337 1995) which provides polarization entangled photons at the same wavelength, was still not available on an integrated platform. Christine Silberhorn and co-workers from the University of Paderborn (Germany), overcome the previous technological issues and realized such a quantum source. With this achievement the Authors provide a device that performs better than the corresponding bulk schemes and is an optimal candidate to be exploited with integrated linear circuit for a full generation and manipulation of polarization encoded qubits in integrated platforms.


INTRODUCTION
In the last decade quantum photonics has played a crucial role in the development of quantum information processes. In particular the transition from bulk to integrated optics has laid the foundation for the implementation of schemes of high complexity, unachievable with previous setups. In the framework of integrated photonic devices, a major development has been carried out in the realization of linear circuits, ranging from the implementation of single building blocks on chip [1][2][3][4][5][6] to the simulation of quantum transport via quantum walks. [7][8][9][10] The integration of up to a hundred optical components on the same chip has made it possible to experimentally implement the recently proposed boson sampling problem [11][12][13][14][15][16][17] opening the way to the experimental investigation of classically hard to solve problems. Although the realization of integrated linear circuits has improved significantly, the conversion toward a fully integrated platform for quantum information requires the development and the combination of sources of quantum light and eventually detectors on chip. Concerning sources on chip, parametric down conversion (PDC) in periodically poled nonlinear waveguides is a promising approach 18-21 due to high brightness and intrinsic stability. However the confinement of light in a single channel makes it challenging to emit single photons into different spatial modes without the need of postselection. This is the case of one of the most adopted sources in quantum information experiments as quantum teleportation, 22,23 quantum key distribution 24,25 and quantum secure direct communication, 26 i.e. a source of spectrally degenerate polarization entangled states. 27,28 While the emission into two different spatial modes is intrinsic in bulk crystals, in integrated waveguides this still remains a challenge and the main reason why a fully on chip source of polarization entangled states was still missing. Indeed nonlinear waveguides have been adopted to realize sources of polarization entangled states, but the entanglement was either generated outside the chip with a probabilistic splitting on different spatial modes, 18,21 or the pairs were split deterministically by frequency, leading to spectrally non-degenerate photons. 19 While for some applications this strategy can be useful, degeneracy over all degrees of freedom is a fundamental requirement when dealing with quantum tasks where completely indistinguishable particles are needed. Recently it has been demonstrated that parametric down conversion in a coupled structure allows for the generation of path entangled states. 29,30 However the adoption of this concept to deterministically address different spatial modes and create entanglement in other degrees of freedom is not straightforward.
Here we overcome these limitations by exploiting the features of titanium indiffused waveguides on lithium niobate (LN) substrates and realize a fully on chip source of polarization entangled states at degenerate wavelengths in the telecom regime. These waveguides can indeed guide both polarizations and present high χ (2) nonlinearity.

RESULTS
Working principle and device design In order to achieve polarization entanglement, we implemented a scheme as shown in Fig. 1. Here, two periodically poled nonlinear waveguides designed to generate orthogonally polarized photons via type II parametric down conversion are connected to a zerogap directional coupler acting as a polarizing beam splitter (PBS). When a pair is generated in waveguide 1 (wg1) the output state is |H A , V B 〉, where H i (V i ) represents a horizontal (vertical) polarized photon in the output mode i = A,B; while when the pair is generated in waveguide 2 (wg2) the resulting state is |V A , H B 〉. By enabling PDC in both waveguides the superposition of these two contributions yields to the desired entangled The phase ϕ is now defined by the phase between the two pump beams.
We can describe the action of our device through the transformation from input to output modes of the integrated PBS as a function of transmissivity and reflectivity: Here a y k;J is a creation operator acting on a photon in mode k with polarization J and T J = 1−R J are the transmissivity and reflectivity of a photon with polarization J in either modes. The state generated in the two periodically poled waveguides when both are pumped is ψ in j i ¼ 1 ffiffi 2 p ½a y 1;H a y 1;V þ e iϕ a y 2;H a y 2;V 0 j i. The creation operators evolve according to transformations (1) and then the output state will read In the ideal case R V = T H = 1 and the device produces the expected entangled state ψ j i ent ¼ 1 ffiffi 2 p ½a y A;H a y B;V À e iϕ a y B;H a y A;V 0 j i: Deviations from these ideal values lead to a non vanishing probability of having two photons in the same output (for a detailed description see Supplementary Information).
This design has two main challenges: the fabrication of two identical periodically poled waveguides such that the PDC light produced in both of them has the same spectral properties and the realization of an integrated PBS with polarization dependent splitting ratios as close as possible to the ideal ones.
Periodically poled titanium indiffused waveguides on lithium niobate substrates are the optimal candidate to realize this design with the required quality: they guide both polarizations, present very low losses and high χ (2) nonlinearity. Moreover, we have achieved a control over the fabrication technique such that our source has excellent performances and higher brightness compared to bulk sources 28 due to the combination of high χ (2) nonlinearity of lithium niobate and waveguide confinement.
A fundamental requirement is that the photons have no temporal distinguishability, otherwise it will reduce the entanglement. 27 Lithium niobate is a birefringent material, thus horizontal and vertical polarized photons experience different group velocities when traveling through the waveguides. We can consider that the photons are generated at the center of the poled region of length L p , this yields a delay between H and V photons which is proportional to an effective crystal length where n gJ is the group refractive index for J = H,V polarization in LN and c the speed of light in vacuum. In order to compensate for this temporal walk off we adopt polarization maintaining fibers (PMFs) and let the fast polarized photon travel through the slow axis of the fiber and vice versa. The length of the fibers L f is chosen such that the delay between H and V in the fiber is B being the birefringence of the PMF. In our experiment the length of our chip is L = 49 mm and the periodic poled waveguides occupy L p = 24 mm of it (see Methods for detailed description of the circuit design). The effective length is then L eff = L − L p /2 = 37 mm, which introduces a delay Δτ = 9.31 ps. The length of polarization maintaining fibers is chosen accordingly to be L f = 6.95 m. Let us note that the PMFs can be directly glued to our chip and be considered part of the integrated source itself. However, for some applications, such a temporal compensation can be applied after the total evolution of the two-photon states through a linear network; in this case the PMFs can be considered part of the detection scheme, implying that the presence of the PMFs does not prevent the possibility of directly interfacing this LN chip with other integrated circuits.
A second source of distinguishability that we should prevent or compensate is a possible non-perfect overlap between the PDC spectra of H and V photons. This is directly related to symmetry of the joint spectral amplitude (JSA) of the PDC light produced in each waveguide (see Supplementary Material for more details). For a type II process, where orthogonally polarized pairs are emitted, this condition is true only when the pump bandwidth is small enough to ensure a JSA oriented at −45°in the plane of signal and idler wavelengths. This case correspond to a process driven by continuous wave (CW) pump light. On the contrary the use of pulses results in an asymmetry of the JSA and a consequent difference in the bandwidths of the spectra for H and V photons. In this case spectral filters have to be introduced. We pumped our source with both CW and picosecond pulses. In the case of pulsed light we adopted fiber Bragg grating (FBG) filters which, as in the case of PMFs, can be considered part of the source or of the detection scheme.

Nonlinear characterization
We first tested the nonlinear properties of the two periodically poled waveguides via second harmonic generation (SHG) in order to find the correct wavelength for a spectrally degenerate process. A CW bright field at telecom wavelength has been injected in each waveguide singularly and photons at half of the wavelength have been detected with a PIN-diode. By varying the wavelength of the bright field the curves in Fig. 2 are recorded. The full width at half maximum (FWHM) of the two curves are Δλ wg1 = (0.306 ± 0.009)nm and Δλ wg2 = (0.359 ± 0.008)nm for waveguide 1 and 2 respectively The slight difference in the FWHMs is due to a slightly different effective poling length of the waveguide, arising from fabrication imperfections. Nevertheless the overlap between the two curves is O % 0:97, i.e. the two poled waveguides present almost the same nonlinear properties, which is essential for the correct functioning of the device. The peak wavelength of the SHG curve also tells us the wavelength combination to phase match the corresponding degenerate PDC process. It corresponds to λ p = 777.22 nm → λ s = λ i = 1554.44 nm (subscripts p, s, i stay for pump, signal and idler respectively). This is the process we will exploit to produce spectrally degenerate polarization entangled states.

Quantum characterization
The second step is to characterize the quantum performances of our device. The setup for quantum measurements is described in the Materials and Methods section. We first connect the output of our source directly to superconducting nanowire detectors (SNSPD). By measuring single counts and coincidences between the two SNSPDs we evaluated the high brightness of our source to be B ¼ ð4:8 ± 0:2Þ Á 10 6 pairs s nm mW . The Klyshko efficiency for signal and idler calculated as ratio between measured coincidences and singles are respectively η Ks ¼ 0:120 ± 0:001 and η Ki ¼ 0:095 ± 0:001 which are mainly due to detection efficiency, coupling efficiencies into single mode fibers and losses from optical components. In order to fully characterize our quantum state, we performed a quantum state tomography 31 to reconstruct the density matrix describing the produced light. We set the pump wavelength at 777.22 nm to ensure spectral degeneracy and measured all the possible polarization states projections. Real and imaginary parts of the experimental density matrix are reported in Figs. 3a,b for pulsed and in Figs. 3c,d for CW pump light. For pulsed pump light the fidelity (overlap) between the measured state and the singlet state of the Bell basis is F ps ¼ 0:973 ± 0:003 and the concurrence 32 is C ps = 0.965 ± 0.003, confirming a high degree of entanglement. These values are mainly affected by the imperfect splitting ratio of the PBS on chip, residual temporal mismatch and possible slight mismatch of the central peak of the adopted FBGs.
We then performed a Bell test according to the scheme of Clause, Horne, Shimony and Holt (CHSH) 33 and obtained a value of the S-parameter of S ps = 2.694 ± 0.046 corresponding to a violation of more than 14 standard deviations. We performed the same measurements with a CW pump and no filters and obtained a fidelity of F CW ¼ 0:941 ± 0:002, a concurrence of C CW = 0.823 ± 0.003 and S-parameter S CW = 2.597 ± 0.027. This fidelity is lower compared to the pulsed pump case because of slightly different properties between the two poled waveguides (shown already in the SHG measurements). However this can be improved in the fabrication process.

DISCUSSION
We have demonstrated the realization of a completely integrated source of spectrally degenerate polarization entangled photons emitted into different spatial modes. These results show that our fully integrated source of polarization entangled states has high quality performances. In this device the high brightness, low losses and the ability of guiding both polarizations, in combination with a smart waveguide design allow us to achieve a considerable step forward in the realization of integrated multi-channel sources. On one hand the high brightness and stability make this device the optimal candidate for replacing bulk sources commonly adopted in quantum information setups. On the other hand, its integrated geometry will have great potential when combined with integrated linear photonic devices as waveguide arrays for quantum walks, 8,34 on-chip manipulation of quantum states, 35 boson sampling, [12][13][14][15] making it possible to build up a fully integrated platform for generation and manipulation of quantum states.

MATERIALS AND METHODS
A detailed scheme of our device is shown in Fig. 4. The waveguide circuit is realized on lithium niobate through lithographic techniques. Titanium diffusion is carried out for about 9 h at 1060°C in oxygen environment. The waveguide width is W = 7 μm and the height 85 nm. The input waveguide separation is 80 μm while the output one is 127 μm which matches the separation of fibers in standard waveguide arrays. The input waveguides present periodic poling with period Λ = 9.08 μm for a length of L p = 24 mm. These waveguides merge in the structure of a zero-gap directional coupler used as polarization splitter. Its basic design is shown in the inset of Fig. 4. It consists of a central section with length L c in which the two waveguide branches merge into a single waveguide with width W c = 2W which is twice the width of the single waveguides. A linear branching is performed to separate the two waveguides, i.e. the single waveguides are inclined by an angle Θ. To avoid problems with the lithography in the range in which the waveguide separation is smaller than 2 μm a single tapered waveguide with increasing width is chosen (L e region in the drawing). In our design W = 7 μm, L c = 480 μm and Θ = 0.6°. Spectrally degenerate pairs at 1554.44 nm are generated when the sample is at a temperature of T = 50°C via type II PDC. We optimized the design of the polarization dependent coupler to achieve optimal splitting ratios for horizontal and vertical polarized light and achieved transmission for H and reflectivity for V of respectively T H = 0.996 ± 0.002 and R V = 0.968 ± 0.003. This corresponds to a probability of generating the singlet state of P ψ À j i ¼ 0:942 (See Supplementary for detailed calculations). The total length of our chip is L = 49 mm. The output facet is coated to highly reflect the pump wavelength around 775 nm and to highly transmit the PDC pairs at telecom wavelengths. We achieve a suppression of ≈22 dB for the pump and a transmissivity ≥98% for PDC light. Our device presents very low losses, as expected for LN, the average value being 0.03 dB/cm.
The setup for quantum measurements is shown in Fig. 5: it can be divided in three sections: the pump preparation setup, the source itself and the analysis setup. The pump preparation setup consists of a loop: here a diagonally polarized beam is split on a bulk PBS and fed into a Sagnac loop. The two beams are recombined on the PBS, however, no interference occurs because a displacement between them is introduced by tilting one mirror (M) of the loop. This displacement is imaged to the separation between the two input waveguides of the chip through a set of lenses (not shown in the picture). Such a configuration ensures a common path geometry for the two pump beams such that their relative phase remains constant in time. The desired phase ϕ between them is then set via a liquid crystal device (LCD). After the loop a half waveplate and another PBS are used to set the polarization state of both beams (horizontal). Let us note that by properly rotating the waveplates before and after the Sagnac loop we are able to pump only waveguide 1 or waveguide 2 and generate separable states, or both at the same time and generate polarization entanglement. The second part of the setup is the source itself: the LN chip which generates the polarization entangled state. The last part is the analysis setup: PMFs are used for temporal delay Fig. 2 SHG measurements: purple squares correspond to SHG process in wg1 and blue dots to SHG in wg2. Continuous lines are fits. It is clear that the two processes overlap. Error bars are smaller than the size of the markers compensation. In our scheme we chose to use a free space coupling but it is also possible to directly interface a fiber array of PMFs to the output of the chip, as the waveguide separation at the output matches the standard separation between fibers in fiber arrays (s = 127 μm). In the case of pulsed pump beams FBG filters with bandwidth Δλ = 0.25 nm are inserted to apply spectral filtering. Standard polarization analysis components and superconducting nanowires single photon detectors (SNSPD, Quantum Opus) are used to characterize the state. Coincidence counts between the two outputs are recorded.