High-quality entangled photon source by symmetric beam displacement design Open Access

Photonic entanglement is a crucial resource for modern quantum science and technology, including quantum key distribution,^1,2 teleportation,^3,4 quantum-enhanced metrology,^5,6 and quantum computing.^7,8 In all these fields, the efficient generation of high quality entangled photon pairs is essential. For instance, the advancement of next-generation projects aimed at establishing a global quantum network, through ground-to-satellite and inter-satellite connections, necessitates the development of compact, robust, and durable sources of entangled photons with high brightness and entanglement fidelity.⁹ 

Entangled states of light can be encoded in many degrees of freedom, such as frequency-bin,¹⁰ energy-time,¹¹ time-bin,¹² orbital angular momentum,¹³ and even in multiple degrees of freedom simultaneously, known as hyper-entanglement.¹⁴ Polarization entanglement, however, has become one of the leading resources for quantum communication applications due to its relative ease of control, scalability, and compatibility with telecom infrastructure.¹⁵ In addition, polarization-encoded quantum states have demonstrated high robustness when propagating through a turbulent atmosphere, making them the preferred choice for free-space and satellite quantum links.^9,16,17

Various technically well-developed physical platforms enable building entangled photon sources (EPSs), both in bulk¹⁸ and integrated photonics.^19–21 Integrated EPSs offer compactness, single mode characteristics, and especially high brightness, on the order of $∼107pairs/s/mW$ pump power in the case of PPLN waveguides.²² However, they currently still face technical challenges that hinder their use in realistic field-deployment, particularly high outcoupling²³ losses from EPS to fiber or free-space link. In contrast, EPSs based on spontaneous parametric downconversion (SPDC) in bulk optics can provide near-ideal heralding efficiencies¹⁸ and broad spectral and spatial multimode characteristics. They also allow access to various degrees of freedom, such as position and momentum, which, in turn, enables manipulation of structured light like OAM and vector vortex modes. These features enable hyper-entanglement capabilities²⁴ and multi-party quantum communications^25,26 while also facilitating higher heralding performance. Therefore, combined with the wide availability and modularity of off-the-shelf components, at present, bulk optics remain the platform of choice for EPS development.

A number of bulk optical geometries have been demonstrated to produce polarization entanglement via SPDC, including the crossed-crystal, Sagnac interferometer, and double-pass (“folded sandwich”) schemes.¹⁸ 

In recent years, EPS designs similar to linear double-path interferometers have emerged. In these designs, a beam displacer (BD) splits the pump into two orthogonally and linearly polarized beams, deviating only one from the input trajectory while maintaining its original k-vector. By passing the pump beam parallel through either one²⁷ or two^28,29 nonlinear crystals, parallel SPDC emission can be achieved and then recombined using a second BD. This solution is easily scalable as all beams propagate in only one direction and experience less walk-off compared to the crossed-crystal scheme.

In this paper, we introduce a compact and robust scheme for polarization entanglement generation, which improves the existing beam displacer EPS designs through the novel combination of half-wave plates and Savart plates, with the latter being a composition of birefringent plates that split a beam into two parallel beams with orthogonal polarization. This innovative scheme intrinsically improves on longitudinal walk-off and compactness compared to previous studies, without compromising on the mechanical sensitivity and on the quality of the generated entanglement. Our device generates entangled photon pairs in the form of N00N states or |Φ^±⟩ Bell states, achieving near-ideal fidelity (F = 0.992 ± 0.001) and high brightness CC = (9.50 ± 0.03) × 10⁴ pairs/(s · mW). It features a modular, miniaturizable architecture, making it suitable for both free-space and fiber-based quantum communication applications.

In this work, we present a high-performance bulk-optics design for a polarization EPS, named SPaDES (Symmetric Parallel Displacement Entanglement Source). Its configuration, depicted in Fig. 1, draws inspiration from lateral displacement EPSs.^27,28,30

The phase φ represents the optical path difference between the two parallel trajectories through our EPS. The ability to control this phase [φ in Eq. (1)] is crucial for non-locality tests, in the E91 QKD protocol. In fact, the Clauser–Horne–Shimony–Holt (CHSH) inequality can be maximally violated only if φ = 0, π.³² Moreover, for the BBM91 protocol, it is necessary to measure the entangled state with high visibility in both H–V and D–A bases, and this is possible only if φ is fully compensated.^33,34 This phase control is commonly implemented with an additional component, such as an YVO crystal (yttrium orthovanadate) or a quarter-wave plate.¹⁵ In our design, however, we can modify φ simply through a controlled tilting of the second Savart Plate (SP₂) along the yaw axis (indicated by angle θ in Fig. 1). This tilting of SP₂ induces a difference in n_eff between the paths of | + +⟩ and | − −⟩, resulting in a controllable relative phase. Therefore, this enables modulating φ, granting on-demand real-time access to both the Bell states |Φ^±⟩, without the need for any additional external components. A geometrical explanation is given in Sec. III B. Note that Eq. (1) (with φ = 0) represents an N = 2 N00N state if the two photons are not separated into distinct spatial modes. That is, the SPaDES output can be directly used in quantum metrology schemes.³¹ In contrast, here, as described in Sec. II C, we split the photons into two channels to obtain maximally entangled Bell states |Φ^±⟩.

The two SPs (United Crystals) in our EPS are made of calcite and produce a nominal shear S = 1 mm at their respective working wavelengths (λ_p = 405 nm for SP₁; λ_s,i = 810 nm for SP₂). SP₁ and SP₂ lengths are Z_SP1 = 12.27(2) mm and Z_SP2 = 13.28(2) mm, respectively, and both have a 10 × 10 mm cross section.

The sHWPs (CeNing, calcite on the BK7 substrate) have dimensions height × width × length = 5 × 10 × 1 mm³, with fast axes at ± 22.5. The interface between both sections of each sHWP was smaller than 10 μm to minimize blocking the generated beams. However, the implementation of non-collinear generation resulted in part of the SPDC cone being lost.

For the nonlinear medium, we used a type-0 periodically poled potassium titanyl phosphate (ppKTP) crystal (Raicol)^18,35 with dimensions height × width × length = 1 × 2 × 20 [mm³]. The pump laser is continuous-wave, single-frequency, centered at λ_p = 405 nm (Omicron, Bluephoton series), and was focused into the ppKTP crystal using a 200 mm lens positioned before SP₁. This configuration yielded a measured 1/e² beam waist of 2w₀ = 92± 2 μm at the crystal’s center. After the second Savart plate (SP₂ in Fig. 1), the pump light was subtracted via a bandpass and long-pass subsequent filters. Finally, the generated SPDC photon pairs were filtered using a 810 ± 5 nm bandpass filter (see Fig. 2), in order to improve photon indistinguishability and remove background, such as fluorescence, generated in the optical components.

We demonstrated and quantified the source performance in two ways: performing two-photon interference and verifying the experimental violation of CHSH inequality.

First, we measured two-photon interference on our source’s output state in order to certify the Savart plate tilting method. We projected the generated state |Φ⟩ [Eq. (1)] onto the |H⟩ basis using a polarizer while varying φ in Eq. (1) by tilting SP₂. Figure 3 shows the two-photon coincidences measured at the output, demonstrating the successful transition between the states |Φ⁺⟩ and |Φ⁻⟩. Choosing the fitting function to be y = A · cos(ωx + α), with y as the coincidences and x as the motor position, we estimated a period $T=2πω=29.85±$ 0.03 μm. See  Appendix A for details.

Second, we quantified the generated entanglement via violation of the CHSH inequality.^32,36 As shown in Fig. 4, our CHSH characterization setup separates the entangled photon pairs, sending them to two independent measurement stations, Alice (A) and Bob (B). We used a deterministic spitting method, in which a knife-edge mirror (keM) is placed in the SPDC Fourier plane of a 200 mm lens. The momentum anti-correlation of the SPDC photon pairs here corresponds to opposite positions in the transverse plane,¹⁸ allowing us to divide the ring-shape emission into left and right halves, which are directed to Alice and Bob, respectively. We measure coincidences between A and B, using the liquid crystal retarders (LC_A and LC_B in Fig. 4) and polarization projection setups [HWPs and polarizers (P) in Fig. 4] to obtain the Bell curves shown in Fig. 5. See  Appendix B for details.

We detected a total coincidence rate CC = (2.470 ± 0.005) × 10⁵ pairs/s and singles rate SC = 2.058 ± 0.003 × 10⁶ counts/s, at a pump power P = 2.6 mW, corresponding to a brightness of (9.50 ± 0.03) × 10⁴ pairs/(s · mW) and heralding efficiency η = 12%. We therefore estimated the emitted brightness to be $CCη2≈7×106pairs/(s⋅mW)$⁠. The average fringe visibility of the fitting Bell curves (coincidences with accidentals subtracted) is V > 0.99 ± 0.01. The final CHSH parameter was computed similarly to Ref. 36, obtaining S_exp = 2.82 ± 0.04, giving a violation of the Bell inequality by 20σ.

A brief overview of the source performance is displayed in Table I.

The state-of-the-art for polarization-entangled photon sources is represented by the Sagnac architecture, which many papers have reported to deliver excellent results.^15,18,38 The Sagnac EPS offers a phase-stable platform, however, at the expense of wavelength-dependent performance (polarization extinction, polarization rotation, reflectivity, etc.) due to the necessity for dual-wavelength components. In addition, the experimentally challenging alignment and the high precision required when positioning the crystal at the center of the loop drastically hinder the scalability of this design for field applications. Moreover, slight misalignment of the crystal position can modify differently the counter-propagating SPDC generations, thus increasing both longitudinal and lateral crosstalk between photons.³⁹ 

Linear beam displacer based sources^27,28,30 propose to solve these problems, with simple, robust, and compact architectures. SPaDES represents an evolution of these schemes, aiming to further simplify the design and improve mechanical sensitivity and miniaturizability. Compared to Ref. 28, our design uses only a single nonlinear crystal, rather than two. Thereby, SPaDES avoids potential related issues stemming from the use of two distinct crystals, such as phase-matching temperature differences and spectral distinguishability of the two SPDC generations. SPaDES also replaces the BD pairs with monolithic Savart plates, which improves stability and compactness and enables facile accurate modulation of φ in Eq. (1) (see  Appendix A). Compared to single BD schemes,^27,30 our design completely removes longitudinal walk-off between the two polarization paths at all points in the source. This enables implementations with arbitrarily short nonlinear crystals and in the strong pump focusing regime. See Sec. IV for further details.

The SPaDES design eliminates all walk-off, i.e., the two SPDC generation modes focus in the exact same longitudinal position in the nonlinear crystal. In order to demonstrate the impact of single beam displacers, beam displacer sources design the generation, superposition, and collection of entangled photons; we reproduced the case in which a focused beam passes through a BD element, as displayed in Fig. 6(a). We measured the relative longitudinal locations of the two beam waists after the BD. We performed the measurement at λ = 405 nm for a BD with a lateral shear S_BD = 1.010 ± 0.001 mm and for a Savart plate with S_SP = 0.972 ± 0.001 mm. The light source was initially collimated to a diameter D = 1.4 mm and focused down to 2w₀ ∼20 μm using a f₁ = 150 mm lens.

The beam displacer and Savart plate were placed in the middle point between the f₁ lens and w₀, simulating the EPS configuration. We detected the beam profile using a CMOS camera, which was longitudinally translated along the optical z axis by means of a motorized stage, in order to capture the different focusing planes. The measured beam waists in each z position are reported in Fig. 6(b) for both the single beam displacer and the Savart plate.

For the BD element with d_o = 8.73 mm, the expected walk-off is Δz_BD = 0.542 mm (see  Appendix C). The experimental result, extrapolated from the fitting functions in Fig. 6(b), is $Δz̄BD=0.52±0.03mm$⁠. For the Savart plate, we obtained a walk-off $Δz̄SP=0.06±0.03mm$⁠. We see that $Δz¯BD$ is at least one order of magnitude higher than standard crystal periodicities, making the BD an unsuitable component when utilizing chirped poling periods. This also limits the minimum length of the crystal one can employ: for $∼1$ mm long crystals, by placing the waist of one polarization in the center of it, we already would find the waist of the orthogonal component outside the crystal. The Savart plate walk-off did not appear to be perfectly null due to experimental error. In addition, some minor astigmatism typical of these components could have affected the accuracy of this measurement.

The estimated brightness of our source was CC = (9.50 ± 0.03) × 10⁴ pairs/(s · mW), which is sufficient for achieving optimal secure key rates in realistic free-space or fiber entanglement-based QKD applications.⁴⁰ Our source brightness (Table I) is, however, lower than the maximum reported values in the literature.¹⁵ We attribute this mainly to the choice of an SPDC working-point in the non-collinear phase-matching regime, which induces a lower spectral brightness compared to the collinear case.⁴¹ Nonetheless, the advantage of the non-collinear regime is that it enables deterministically splitting the generated photon pairs, without relying on non-degenerate spectral correlations, as would be required when using a sharp dichroic mirror or wavelength-division multiplexing devices.

Optical losses in our EPS are attributed to the optical components’ transmissivities (78%) and fiber coupling. In particular, sHWP₂, at the interface between the two segmented-HWP segments (see the inset of Fig. 1), partially absorbs a portion of each SPDC far-field ring $(∼10%)$⁠. Moreover, the knife-edge mirror (keM in Fig. 4), due to fabrication limits, induces some diffraction and scattering effects that cause additional losses $(∼15%)$ to light in proximity of the edge.

As mentioned in Sec. III A, the SPaDES design presents some advantages compared to other linear beam displacer sources in the literature.^27,28,30 For example, our source is more suitable for wave-division multiplexing (WDM) and quantum communication applications, such as increasing network capacity²⁵ or boosting the secure key-rate.⁴² This is because WDM-based schemes require entangled photon emission across a broad wavelength range, with high spectral indistinguishability across the entire range between the two SPDC generations. This broad indistinguishability requirement is challenging to meet for any double crystal EPS,²⁸ as, in general, two distinct nonlinear crystals will have non-identical emission spectra.⁴³ In contrast, the single-crystal SPaDES intrinsically avoids this issue. Compared to Refs. 27 and 30, the SPaDES’ zero longitudinal walk-off allows, first, using shorter nonlinear crystals that yield a broader spectrum, and second, tighter pump focusing, which maximizes fiber-coupled pair rates across a wide wavelength range.³³ As another application example, its compatibility with short crystals allows SPaDES to generate entangled photons with strong spatial correlations, which are a requirement in many quantum imaging schemes.^31,44 Finally, superior mechanical characteristics of SPaDES will enable its use in harsh environments, such as for satellite-based use cases. Compared to Ref. 28, monolithic Savart plates provide better stability and avoid potential issues of refraction, back-reflection, and astigmatism caused by the gap between separate BDs. Moreover, the use of a single nonlinear crystal allows greater miniaturization in the transverse plane, due to the lack of physical interface between the two SPDC generation zones. Due to this, the separation can be lowered; hence, the SP can be shortened. At the same time, by eliminating the walk-off, the crystal can also be shortened in the longitudinal plane, provided appropriate focusing. A tight focus will then allow for lower separation between the beams and reinforce the advantage of a zero-walk-off fully-symmetric design. We emphasize that SPaDES miniaturization involves trade-offs, such as in the generation spectrum and efficiency. Therefore, systematic design choices are required to optimize parameters for a given use case.

In addition to integrating the above listed advantages, the SPaDES design has mechanical phase stability at least equal to single-BD designs,^27,30 as confirmed by our measurements (see the supplementary material 1), similar to Refs. 45 and 46.

We note that, when seeking compactness and high scalability, it is natural to mention integrated platforms, which offer some advantages over traditional bulk sources. In particular, waveguide-based sources excel in brightness due to their intense light confinement. These can be specifically engineered to produce light with desirable single-mode characteristics (spatially and spectrally).^19,47 Photonic Integrated Circuits (PICs) mark a significant advancement for vertically integrating quantum technologies,^21,48 given their scalable manufacturing processes. However, at present, the versatility and modularity of such PIC systems are limited, as they cannot harness multi-modal characteristics such as position, momentum, and orbital angular momentum correlations. In addition, integration is feasible only for narrowband, single-mode systems, and efficiently outcoupling from PIC EPSs to free-space or fiber remains challenging.¹⁸ Finally, a promising candidate for the next generation of quantum technologies is semiconductor-based quantum dots that provide on-demand entangled photon pairs with narrow linewidth and negligible multiphoton events.^20,49 However, quantum dot sources have not yet attained the performance levels of their bulk EPS counterparts, both in terms of brightness and in state fidelity,^20,50,51 and typically require cryogenic temperatures that limit field deployment and scalability.

In this work, we have shown a SPDC-based polarization entangled photon pair source (EPS) design, based on the evolution of previous linear beam-displacer architectures. This design is based on laterally displacing the | + ⟩ and | − ⟩ components of a vertically polarized pump beam and sending these parallel modes through the nonlinear crystal. The two generated SPDC modes are then recombined to obtain the Bell state $|Φ〉=|++〉+eiφ|−−〉2$⁠. The parallel splitting of the pump and recombination of the SPDC modes are performed by a pair of Savart plates, which symmetrically displace each polarization mode. This evolution serves the purpose to completely remove the longitudinal walk-off from inside the crystal.

Our EPS generates polarization entangled photons in the form of N00N states or Bell states, easily tunable between the |Φ⁺⟩ and |Φ⁻⟩ states through motorized tilting of the second Savart plates. Characterizing the entanglement generated by our source, we measured a CHSH parameter S = 2.82 ± 0.04 (⁠$∼20σ$ violation of the CHSH inequality), which implies a near-ideal fidelity F = 0.992 ± 0.001, from Ref. 37. The brightness of our EPS was measured to be CC = (9.50 ± 0.03) × 10⁴ pairs/(s · mW), which gives an estimated entangled photon pair emission rate CC_em = 105 × 10⁶ pairs/(s · mW) when taking into account system losses. We also studied the mechanical robustness and longitudinal walk-off of our EPS. In comparison with existing standard BD designs, we found that our source drastically reduces longitudinal walk-off while maintaining near-identical mechanical stability.

Our design combines a series of unique ideas, whose implementation offers high performance either for (i) scalability: all components can be easily miniaturized both in the longitudinal and transverse dimensions, thanks to the virtually null walk-off and the use of a single nonlinear crystal, or for (ii) harsh environments: bulk optics offers one of the best generation stabilities under thermal/pressure fluctuations, making our EPS an ideal candidate for space quantum communications.

Future upgrades will include superior segmented half-wave plates in order to improve the heralding efficiency, as well as development of an engineering model to further miniaturize the setup and enable real-environment qualification, such as space qualification.

The supplementary material evaluates the mechanical robustness of the SPaDES design compared to beam displacers (BDs). It analyzes phase response sensitivity to tilting misalignments by measuring interference patterns shifts as a function of SP and BD tilt angles.31 The results confirm that SPaDES maintains alignment robustness comparable to BD-based designs, supporting its feasibility for quantum applications.

This study was supported by MCIN with funding from the European Union Next Generation EU (Grant No. PRTR-C17.I1) and by the Generalitat de Catalunya. This project has received funding from the European Union’s Horizon Europe research and innovation program under the project “Quantum Security Networks Partnership” (QSNP, Grant Agreement No 101114043). This work was partially funded by Grant No. CEX2019-000910-S [MCIN/AEI/10.13039/501100011033], Fundació Cellex, Fundació Mir-Puig, and Generalitat de Catalunya through CERCA. G.P. acknowledges funding from the European Union’s Horizon Europe research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 101081441. A.C. work was funded by Grant No. CEX2019-000910-S [MCIN/AEI/10.13039/501100011033], Fundació Cellex, Fundació Mir-Puig, and Generalitat de Catalunya through CERCA. R.C. acknowledges funding from the European Union’s Horizon Europe research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 713729 (ICFOstepstone 2) and from the European Union’s Horizon Europe research and innovation program under Grant Agreement No. 101082596 (QUDICE). A.D. acknowledges support of the ICFO CELLEX PhD-fellowship.

A.C., R.C., A.D., and V.P. are co-inventors of a patent application related to the content of this paper.

G. Paganini: Conceptualization (supporting); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (equal); Software (lead); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). A. Cuevas: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Project administration (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). R. Camphausen: Conceptualization (equal); Methodology (equal); Project administration (equal); Supervision (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). A. Demuth: Conceptualization (equal); Methodology (equal); Project administration (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). V. Pruneri: Conceptualization (equal); Funding acquisition (lead); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

SP₂ tilting is implemented using a stepper motor pushing one side of SP₂ along the z axis. The motor is mounted on the side of the Savart plate holder to control its tilt angle θ in the yaw direction (see Fig. 1), where motor position p ∝ sin θ and sin θ ≈ θ for θ ≈ 0. Yaw angle θ is proportional to the phase between the | + ⟩ and | − ⟩ polarization modes.⁴⁵ Therefore, the stepper motor position is directly proportional to φ in Eq. (1). By fitting a cosine function to the two-photon interference curve (Fig. 3), we extract the motor position values corresponding to desired phases φ = 0, π, in order to switch between |Φ^±⟩ states.

The coincidence interference visibilities with and without accidentals subtraction were $VSP=1.000±0.010$ and $Ṽsp=0.840±0.008$⁠, respectively. This result also shows that SMF-coupling remains unaffected by the Savart plate tilting.

As shown in Fig. 4, Alice (Bob) side contains a liquid crystal LC_A (LC_B) placed at 45° rotation to implement φ_A (φ_B) phase between vertical and horizontal polarizations. Note that, before the beam splitting via the knife-edge mirror, the state in Eq. (1) is rotated with a HWP to $|HH〉+eiφ|VV〉2$⁠.

The half-wave plates (HWP_A and HWP_B) and polarizers (P_A and P_B) in each arm enable the projection into vertical and horizontal polarizations. By alternating between these polarization states, we can measure coincidences across various polarization combinations without needing the four detectors typically required in Aspect-type experiments.³⁶ This is achieved by simply rotating the polarization of the state. The light in A and B is coupled into SMFs and sent to SPADs for coincidence detection (1 ns window), with accidentals removed. The optimal Bell angles for Bob are $π2$ apart.⁵² Therefore, the liquid crystal LC_B in Fig. 4 was fixed to $δB=0,π2$⁠, while LC_A was scanned over an entire period, in order to find the δ_A values that maximize the inequality. For each Bob phase setting $(δB=0,π2)$⁠, we obtained four coincidence curves for four combinations of the four channels Alice 1,2 and Bob 1,2. Here, Alice 1(2) and Bob 1(2) correspond to horizontal(vertical) detected polarization. These results are shown in Fig. 5.