Reconfigurable single photon sources based on functional materials

The future of quantum photonic technology depends on the realization of efficient sources of single photons, the ideal carriers of quantum information. Parametric downconversion (PDC) is a promising route to create highly coherent, spectrally pure single photons for quantum photonics using versatile group-velocity matching (GVM) and tailored nonlinearities. However, the functionality to actively control the poling period of nonlinear crystals used in PDC is currently missing, yet would enable to dynamically modify the wavelength of single photons produced in the PDC process. Here a detailed GVM study is presented for functional PMN-0.38PT material which can be dynamically repolled at ambient conditions with fields as low as 0.4 kV/mm. Our study reveals phase-matching conditions for spectrally pure single photon creation at 5-6 microns. Further, a practical approach is proposed for on-flight wavelength switching of the created single photons. The reported reconfigurable functionality benefits a wide range of emerging quantum-enhanced applications in the mid-IR spectral region where the choice of single photon sources is currently limited.


Introduction
In recent years quantum technology has shown immense progress in demonstrating a variety of photonic platforms allowing coherent quantum control using pure single photon PDC sources [1,2] , quantum dots [3,4] and diamond NV centers [5,6] . Harnessing single photons for quantum information encoding stands out as a promising direction, which on one hand benefits from superior coherence robustness of the photons at ambient temperatures, and on the other from the maturity of field of photonics in general, allowing numerous ways for the single photons to be generated, manipulated and detected. Single photon sources, therefore, constitute a crucial part of today's quantum photonics agenda. It has been shown that despite probabilistic operation, PDC sources can produce highly pure single photons approaching on-demand operation in multiplexed schemes [7] . There has been a surge of interest in single photon sources from a nonlinear parametric processes operated in wider spectral regions [8] and in mid-IR in particular [9][10][11] . The applications for mid-IR single photon sources primarily concern quantum sensing and metrology [12][13][14] , stealth ranging and quantum LIDARs [15][16][17] , quantum enhanced medical imaging [18][19][20] , as well as for free-space secure communication in the atmospheric window, in light of recent demonstration of entanglement distribution using satellite-to-ground downlinks [21] .
In the nonlinear PDC process, one pump photon is decomposed into the two photons (signal and idler) satisfying energy and momentum conservation. While there is little problem with preserving the energy conservation, it proves to be harder to satisfy the momentum conservation due to the natural dispersion of the nonlinear crystal. Techniques such as quasiphase matching via periodic poling of ferroelectric nonlinear crystals allow to compensate the wave vector mismatch by adding additional wave vector kg= 2π/Λ of the poling grating, where Λ is a poling period. All current periodically poled ferro-electric crystals used for PDC photon sources, primarily LiNbO3 [22] and KTiOPO4 [23][24][25] , lack tunability of the poling period once fabricated, making the spectral characteristics of the created photons inaccessible for an active reconfigurability. Tailoring the poling period enables the option to change the wavelengths with a single crystal, switch the PDC generation on and off, or to reshape wavepackets of the subsequent photons. In conventional materials it requires large coercive fields and high temperatures to modify the crystal domain structure (see Table 1). In this letter we introduce a material that on one hand can be dynamically polled, and on the other suitable for the generation of spectrally pure single photons. We find this unique combination in the ferroelectric lead magnesium niobate-lead titanate, (1-x)Pb(Mg1/3Nb2/3)O3 -xPbTiO3) or short PMN-PT and show it is possible to obtain both pure single photon and wavelength-switching operation in the first atmospheric window, where there is currently a scarcity of single photon sources [9] .
Unlocking dynamic access to the poling period allows active shaping of the spectral and temporal properties of the single photons [1] , for example to apply or remove apodization on demand, to optimize single photon purity, or to manipulate the single photon wave-packet at a particular wavelength. Reconfigurable switching functionality, in particular, is very promising for free-space quantum secure communication as it permits to change the frequency band of the communication channel, which has not been shown previously with the PDC sources.
We focus on the x=38% composition (PMN-0.38PT), which exhibits a wide transparency region [26] , high refractive index, low coercive field, and low Curie temperature Tc of just 180 C, enabling functional poling domain switching at ambient temperatures using <1 kV/mm fields [27] , which is not possible with other conventional nonlinear media used for PDC. We provide a comparison of some key material properties in Table 1.
The unique ferroelectric switching mechanism in PMN-PT is realized thanks to the ultrarich phase diagram where different thermodynamically equivalent crystalline phases manifest metastable coexistence in close to morphologic phase boundary region [28] . This is ideal for external domain poling control, where 180̊ polarization switching can be realized by weak electric fields [27] . Despite being known as highly nonlinear material [29,30] with strong electrooptical coefficients [31][32][33] the reports on nonlinear optical properties remain limited to just second harmonic generation [34] . To the best of our knowledge, the periodic poling has not been demonstrated for nonlinear PDC in bulk PMN-PT materials. However, a microscale periodically poled PMN-PT with precise domain structure down to 5 microns has been demonstrated by electron beam patterning technique [30] and also 200 nm pitch size by backswitch poling using nanopatterned composite electrodes [35] . The main issues with PMN-PT periodic poling has been the formations of cracks but very recently, there has been an important progress made in achieving high optical quality monodomain state in PMN-PT by using pre-poling thermal annealing [29] to prevent cracking which is an important step for nonlinear optical applications of PMN-PT material family. We report the first study which describes, evaluates and proposes a practical scheme of dynamic poling of nonlinear crystal by using a single electrode mask and show a variety of PDC types which are possible to achieve for PMN-0.38PT.

Parametric down conversion and group velocity matching
The material composition of PMN-0.38PT is an ideal candidate for mid-IR GVM because it offers a wide optical transparency window extending up until 6 microns. Normally GVM [36] is employed to maximize heralded-photon purity by minimizing spectral correlations of the firstorder PDC bi-photon state: where f(ωs,ωi) denotes the joint spectral amplitude (JSA) which is determined both by spectral bandwidth of the pump photon and the nonlinear profile of the crystal, and ωs,i denotes the signal and idler photon frequencies respectively. In this letter we consider both degenerate and nondegenerate cases where signal and idler are of the same and different wavelengths respectively. The refractive index Sellmeier coefficients were taken from He et al. [36] using the Wemple-DiDomenico single oscillator dispersion model [37] for mid-IR wavelength range dispersion approximation, along with thermal expansion data from [38] .
Pure single photon source engineering via GVM lies in selecting conditions under which the pump envelope function (PEF) ( , , % ) and nonlinear crystal phase-matching function (PMF) Φ( , , % , ) can form close-to-separable JSA of the bi-photon state: On the other hand, an optimal GVM condition can be estimated when the dispersion parameter where GD represent group delays of the three interacting photons pump, signal, and idler respectively. The dispersion parameter allows the evaluation of the tilt of the phase-matching function, θ = tan -1 (D), in the signal-idler wavelength space, with respect to the x-axis [1,39] .
In principle the best single photon purity can be obtained when the PMF tilt angle θ is anywhere between 0 and 90 degrees. High signal-idler indistinguishability can be achieved when θ = 45, a condition known as symmetric group velocity matching, when PEF and PMF are aligned orthogonally thus forming a symmetric JSA profile. Moreover, photon purity can be optimized by apodizing the poling structure of the crystal to reduce the spectral correlations between the PDC photons [1] .
To the best of our knowledge, PMN-0.38PT has not been studied previously for PDC, therefore respectively [36] .
In our code we also account for thermal expansion of the poling period with the coefficient of 3.8×10 -6 C -1 extrapolated for the 38% PMN-PT from ref [38] . Based on the abovementioned parameters and the crystal temperature of 35 C we obtain the quasi-phase-matching under which the wavevector mismatch is made to vanish: Δk= k(λp) -k(λs) -k(λi) -2π/Λ = 0, where Λ is the crystal poling period.
We first consider the type-0 case with the two options e → e+e, o → o+o, further in text denoting pump conversion into signal and idler photons, where e and o indicate photon polarization along extra-ordinary and ordinary crystal axes respectively. We obtain phasematching results with Λ of 0.493 mm and 0.510 mm for o → o+o and e → e+e cases respectively. The key observation from Figure 1 is that the PMF is inclined at the same angle as PEF in Figure 1(a-b), which is not useful for pure photon generation [1] . From the numerical estimation of the value of θ, the tilt of the phase-matching function, we also find no useful type-0 PDC condition for the wider span of the pump wavelengths ranging from 0.6 -9 µm.
In the type I case, the two configurations e → o+o and o → e+e, yield phasematching with Λ = 0.297 mm and 0.136 mm respectively. In Figure 2 the GVM plots for the e → o+o configuration reveals a distinct feature with a large crossover in the PMF. Such spectrally broad PMF forms a JSA of a bi-photon spreading between 4.8 and 6 microns (Figure 2 (b)).
The behavior of the singularity observed in PMF can be further investigated at different pump wavelengths by looking into the GVM mismatch angle results presented in Figure 2  is important to note that that it is possible to obtain high purities at any PMF angle between 0 and 90 degrees by transforming the PMF from Sinc into a Gaussian profile by using domain engineering techniques [40] . The results in Figure 3 (c) show that when including the nongenerated cases it is possibility of generating pure bi-photon states at much larger spectral window spanning from 1 to 6 microns (limited by the crystal transmission edge).
Another degenerate PDC case is also available for the symmetric type II e → e+o case in  Figure 5 (a)). By applying a pre-fabricated electrode mask with a linear gradient elongation starting from the first electrode length and moving further along the waveguide, one can effectively shrink the poling period by then applying the poling voltage as shown in Figure 5 (c) therefore achieving the desired period. The effect of the domain boundary regions is negligible in our calculations due to their atomically thin volume fraction [41] in respect to the domain sizes which are of a millimeter order.
The switching process can be explained as follows. We start from the crystal in the Figure 5 Moreover, single photon purity produced in PMN-PT can be further increased by either use of narrowband filtering if the tilt of the PMF is not ideal, or by the domain apodisation techniques [1] where the advantage of switching functionality of PMN-PT makes them ideal candidates for dynamic control of single photon spectral purity or even creation of frequency encoded photons for hyperentangled state generation for quantum information processing.

Outlook and conclusion
Given the fact that most quantum photonic applications strive for device miniaturization and compactness, where smaller devices usually deliver faster operation speeds and lower power consumption -here we discuss the potential impact where PMN-PT can have in the field of integrated quantum photonics. The combination of the high refractive index of PMN-0.38PT and the technological readiness of thin-film pulsed laser deposition [43] make such materials highly desirable for integrated photonic circuits constructed of dielectric/PMN-PT/dielectric stacks where photolithographically defined waveguides written into a PMN-PT slab core can achieve higher integration density, and ultimately high intensity optical field confinement for stronger nonlinear optical interaction. Furthermore, implantation of rareearth ions, like Er 3+ into PMN-PT waveguides will allow for on-chip integration of NIR pump lasers for on chip PDC and circuit operation even at ambient temperatures [44] . The important electro-optical (EO) and electro-mechanical functionality of PMN-0.38PT makes it superior to widely used LiNbO3 [31] , with the figure of merit half-wave voltage Vp factor of 3 better, allowing lower operating voltages and therefore more efficient, compact and faster EO phase controlled on-chip Mach-Zehnder interferometers as well as Pockels cells [45,46] . It is important to mention that PMN-0.35PT has almost twice stronger rc of 81 pm/V which reduces the Vp to just 452 V [31] [47] in comparison to 2800 V typically found in LiNbO3 [48] . These characteristics   [50] 16.9 [51] LiNbO3 0.4 -5 20 1145 2.29 2.6 20.1 27.5 [52] a) Due to the absence of experimental values the 2 nd order nonlinear coefficient for PMN-0.38PT can be estimated using method of F. Wang [52] ; which gives a factor of 2 bound approximation. For the birefringence input parameters for PMN-0.38PT [36] , KTiOPO4 [53,54] and LiNbO3 [55] it gives d 2ω 33 of 12.6, 29 and 27.7 pm/V for these materials respectively.    Figure 1(a), and (c) shows spectral positions for the optimal PMF inclination angles, also including non-degenerate cases.  Figure 1(a), and (c) shows spectral dependence for the all PMF inclination angles, also including non-degenerate cases.