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Abstract
A reliable, but cost-effective generation of single-photon states is key for practical quantum communication systems. For real-world deployment, waveguide sources offer optimum compatibility with fiber networks and can be embedded in hybrid integrated modules. Here, we present what we believe to be the first chip-size fully integrated fiber-coupled heralded single photon source (HSPS) module based on a hybrid integration of a nonlinear lithium niobate waveguide into a polymer board. Photon pairs at 810 nm (signal) and 1550 nm (idler) are generated via parametric down-conversion pumped at 532 nm in the LiNbO3 waveguide. The pairs are split in the polymer board and routed to separate output ports. The module has a size of (2 × 1) cm2 and is fully fiber-coupled with one pump input fiber and two output fibers. We measure a heralded second-order correlation function of $g_h^{(2)}=0.05$ with a heralding efficiency of $\eta _h=3.5\, {\%}$ at low pump powers.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Single photons are suitable as information carriers in quantum computation and communication [1,2]. One of the the most important building blocks is an efficient source for the generation of single photons. Different approaches are studied to build a practicable single photon source, such as quantum dots [3–5] or nonlinear photon-pair generation with heralding schemes [6–12]. Efficient plug and play sources have already been demonstrated, being fully integrated with fiber-coupled outputs [13,14]. A major challenge for these sources is an efficient coupling of the generated photons to optical fibers, which is necessary to use these sources practicable. There are commercially available single photon sources based on quantum dot technology, which can be supplied with the associated control electronics and helium cooling [15]. Nevertheless, these sources are very large and expensive. Heralded sources do not need such complex cooling schemes and are thus better suited for further miniaturization. First commercial sources are available as bench-top devices [16], but they are still far away from the ultimate goal of realizing a quantum- system-on-chip (QSoC) providing low cost, small size and robustness, which are the essential features for future commercial exploitation.
To understand the process and required components of a HSPS, a practicable breadboard setup of a HSPS based on a nonlinear crystal and free-space optics is shown in Fig. 1 (top). The pump field is coupled into the nonlinear crystal to generate photon pairs, which are then collected by an out-coupling lens. A filter to suppress the transmitted pump wave and an optical element for separating signal and idler are needed to complete the setup. Due to the probabilistic nature of the nonlinear generation process, a heralding scheme needs to be implemented, which means one photon of the created pair has to be detected to herald the other photon. This gives information on whether there is a single photon in the output or not. The most important parts of a HSPS are therefore the photon-pair generation, pump filtering, signal/idler separation and the detection. Ultimately, in a fully integrated source all of these components must be combined in one module, which has not been demonstrated yet. Sufficient pump filtering is difficult to implement on chip in an integrated device. Various non-integrated approaches to filter out pump light by using fiber-coupled filters placed after the module have been presented [13]. However, for a compact fully integrated source, this filtering must be done on chip. The detection of one of the photons should also be directly integrated in the module. An approach to combine everything in one device is the hybrid integration of multiple materials with different optical properties and fabrication capabilities.
Fig. 1. Comparison of a practicable HSPS breadboard setup based on a nonlinear crystal and freespace optics and the corresponding QSoC.
In this paper, we present a fully integrated chip-size, plug-and-play HSPS module based on lithium niobate and polymer technology. A polymer board (PolyBoard) is used as a chip platform, which enables the fabrication of waveguides and etched slots for the integration of different optical components [17,18]. Filters with various spectral and polarization characteristics can be glued into these etched slots, which open up the possibility for sufficient pump filtering and signal/idler separation. The PolyBoard is therefore a well suited platform for the integration of different optical components on chip. A SPDC process in a titanium-indiffused periodically poled z-cut lithium niobate waveguide ($\mathrm {Ti {:} LiNbO_3}$) is designed to generate photon pairs at $810\, \mathrm {nm}$ (signal) and $1550\, \mathrm {nm}$ (idler). The high second order nonlinearity of $\mathrm {LiNbO_3}$ makes it a favorable choice for an efficient SPDC process [19]. The signal photons are used to herald the telecom photons. The $\mathrm {Ti {:} LiNbO_3}$ waveguide is butt-coupled to the PolyBoard waveguide. The hybrid integration of a $\mathrm {Ti {:} LiNbO_3}$ waveguide into the PolyBoard leads to a fully integrated module, which cannot be realized in one material alone. The signal wavelength of $810\, \mathrm {nm}$ enables the possibility for a future integration of silicon single-photon avalanche diodes (SPADs) to the module and therefore a possible commercially available device with small size, low cost, high robustness and reproducibility.
A model of the QSoC HSPS is shown in Fig. 1 (bottom). In the following we describe the general design and pre-characterization of single components of the module. An analysis of the single photon characteristics follows afterwards.
2. Design and components
We use the PolyBoard technology as the QSoC platform for the HSPS-module. The general design of the module is described in Sec. 2.2. We integrate a periodically poled $\mathrm {Ti {:} LiNbO_3}$ waveguide as nonlinear medium for the SPDC process into the PolyBoard. The design and characterization of the $\mathrm {Ti {:} LiNbO_3}$ is presented in the following.
2.1 Periodically poled $\mathrm {Ti {:} LiNbO_3}$
We use z-cut $\mathrm {LiNbO_3}$ as the nonlinear material for the desired SPDC process, because of its high second order nonlinearity and wide transparency window [19]. Additionally the spontaneous polarization of $\mathrm {LiNbO_3}$ enables a periodic domain inversion of the crystal, which allows for quasi-phase-matched nonlinear processes. We fabricated low loss waveguides (typically $<0.1\, \mathrm { dB/cm}$) by an indiffusion of $5\, {\mathrm{\mu} \mathrm{m}}$ wide, $80\, \mathrm {nm}$ thick titanium-stripes into the substrate for $8.5\, \mathrm {h}$ at $1060\, \mathrm {^\circ C}$. Periodic poling of the waveguides ensures the quasi-phase-matching condition for the designed type-0 SPDC process with a pump wavelength at $532 \, \mathrm {nm}$ and signal and idler at $810 \, \mathrm {nm}$ and $1550 \, \mathrm {nm}$, respectively. We fabricated several waveguides with various poling periods from $6.80 \, {\mathrm{\mu} \mathrm{m}}$ to $7.15 \, {\mathrm{\mu} \mathrm{m}}$ on one sample.
For optimal light coupling between different waveguide structures, the mode field distributions must match as best as possible. The simulated mode field distribution of the $\mathrm {Ti {:} LiNbO_3}$ idler TM-mode is shown in Fig. 2 examplary. The Ti-indiffusion leads to an asymmetric mode distribution in vertical direction [20,21]. At the signal and pump wavelength, the waveguides guide several modes. The corresponding mode field diameters (MFDs, 1/e$^{2}$) of the fundamental modes at different wavelengths are shown in Fig. 2(b).
Fig. 2. Simulated $\mathrm {Ti {:} LiNbO_3}$ mode field distribution of the $1550\, \mathrm {nm}$ idler TM-mode (a); MFDs at different wavelengths $\lambda$ for $\mathrm {Ti {:} LiNbO_3}$ and PolyBoard waveguides (b).
Before the integration of a $\mathrm {Ti {:} LiNbO_3}$ waveguide into the PolyBoard platform, we pre-characterized the waveguides by analyzing the SPDC process to choose the best working one for the integration. We pumped the sample at $532 \, \mathrm {nm}$ (Klastech cw-laser, $100 \, \mathrm {mW}$) and analyzed the SPDC output with a spectrometer at visible wavelengths. We controlled the input polarization and power with a half-wave plate and a linear polarizer and used lenses for the waveguide in- and out-coupling. The measured spectrum for a poling period of $7.05 \, {\mathrm{\mu} \mathrm{m}}$ at two different temperatures is shown in Fig. 3.
Fig. 3. Measured SPDC spectrum of the periodically poled $\mathrm {Ti {:} LiNbO_3}$ for a poling period of $7.05 \, {\mathrm{\mu} \mathrm{m}}$ at different temperatures. Calculated phasematching peak positions for different mode combinations are marked in blue.
The intensity peak of the generated signal photons at $810\, \mathrm {nm}$ is clearly visible. Smaller peaks at higher wavelengths are due to higher-order mode combinations. We designed the waveguide to guide only a single mode at $1550 \, \mathrm {nm}$, but multiple modes are guided at the other wavelengths. Different mode combinations fullfill the phasematching condition at different wavelengths, which leads to several phasematching peaks in the outptut spectrum. The calculated peak positions for different mode combinations are shown in Fig. 3 (blue). The theoretical position of the peak resulting from only fundamental modes is shifted by an offset so that it matches the measured peak. All other calculated values are shifted by this offset, so the distance between different calculated peaks is unchanged. The offset between calculated and measured values is mainly due to fabrication imperfections. A broad structure in the lower wavelength region next to the PDC signal can be identified as nonlinear Cerenkov radiation [22]. A higher operation temperature of the $\mathrm {Ti {:} LiNbO_3}$ waveguide not only shifts the PDC signal, but leads to a more stable nonlinear process, which is why temperatures above $90\, \mathrm {^\circ C}$ are optimal. The strong photorefractive effect in $\mathrm {LiNbO_3}$ can lead to mode hopping, which can be suppressed by high operation temperatures [23]. Since one $\mathrm {Ti {:} LiNbO_3}$ waveguide is later inserted into a PolyBoard (see Sec. 2.2), a high temperature would lead to misalignment and damage of the assembled module. Tests have shown, that temperatures above $100\, \mathrm {^\circ C}$ can lead to significant misalignment of the assembled module. Therefore, a compromise regarding the operation temperature has to be found. We have chosen a waveguide with a poling period of $7.05 \, {\mathrm{\mu} \mathrm{m}}$ for the integration into the PolyBoard module, because of a desired temperature of around $80\, \mathrm {^\circ C}$. In general, however, a different poling period can be chosen for a future module in order to reduce the working temperature, if necessary. After characterization, we cut and polished the sample to a final length of $15 \, \mathrm {mm}$ and width of $5 \, \mathrm {mm}$. To ensure high transmission between different components, we deposited a dielectric coating consisting of alternating $\mathrm {TiO_2}$ and $\mathrm {SiO_2}$ layers on the endfacets. We designed the output coating to also filter out some of the pump light, since a fully integrated module does not allow for a free-space filtering afterwards. Figure 4 shows the measured spectrum of the input coating with a high transmission at the pump wavelength $T_{in}(532\, \mathrm {nm})=99.8 \, \%$ and the spectrum of the output coating with low transmission for the pump $T_{out}(532\, \mathrm {nm})=0.5 \, \%$ and high transmission for signal $T_{out}(810\, \mathrm {nm})=99.8 \, \%$ and idler $T_{out}(1550\, \mathrm {nm})=99.7 \, \%$. We measured the spectra on a glass substrate and converted them for a transmission between $\mathrm {Ti {:} LiNbO_3}$ and PolyBoard. In addition, we deposited a $200 \, \mathrm {nm}$ protective $\mathrm {SiO_2}$ layer on the top side of the crystal.
Fig. 4. Measured and converted transmission spectra of the $\mathrm {Ti {:} LiNbO_3}$ in- and output coatings.
2.2 PolyBoard
The hybrid integration platform of the HSPS is a perfluorinated acrylate based polymer (ZPU12 series by ChemOptics), which is spin-coated and UV-cured on top of a Si substrate. Square-shaped weakly guiding single mode channel waveguides can be embedded in the PolyBoard. The waveguides are structured by reactive ion etching and the core polymer layers are spin-coated. The square shape ensures a negligible polarization dependence of the waveguides and losses can be $<1\, \mathrm {dB/cm}$ [24]. In addition, U-grooves and slots can be etched for the coupling to optical fibers and the integration of optical elements like thin-film filters (TFFs) into the PolyBoard [24]. The TFFs enable various spectral and polarization filter characteristics and are based on dielectric layer stacks. All this makes the PolyBoard a perfect integration platform for hybrid devices and QSoCs. The biggest challenge of fabricating a fully integrated HSPS is the on-chip pump suppression. The integration of TFFs can solve this problem and is easily expandable.
The HSPS module can be divided in three parts (Fig. 5(a)(bottom)), which are glued together. We achieve optimal positioning by maximizing optical transmission through the complete module. We glued the $\mathrm {Ti {:} LiNbO_3}$ on top of a PolyBoard section to increase stability and coupled the input facet of the $\mathrm {Ti {:} LiNbO_3}$ waveguide to a $532 \, {\mathrm{\mu} \mathrm{m}}$ polarization maintaining (PM) optical fiber, since the SPDC process is designed for a TM input polarization, which can be guaranteed by the PM fiber. We coupled the output facet of the $\mathrm {Ti {:} LiNbO_3}$ waveguide to a second PolyBoard with three integrated channel waveguides and different optical components. The center waveguide in the PolyBoard is coupled to the $\mathrm {Ti {:} LiNbO_3}$ center weaveguide with a poling period of $7.05 \, {\mathrm{\mu} \mathrm{m}}$ (see Sec. 2.1) and the outer ones are only used for alignment. The design of the complete module is shown in Fig. 5(a) (top).
Fig. 5. Design of the HSPS module (a, top) consisting of $\mathrm {Ti {:} LiNbO_3}$ crystal and PolyBoard with integrated wavguides, long pass filter (LP), dichroic mirror (DM) and side view (a, bottom); assembled and packaged module with PM-input-fiber (purple), two SM-ouput-fibers (yellow) and electrical contacts for temperature control (b).
We implemented square-shaped weakly guided channel waveguides in the PolyBoard with a refractive index change of around $\Delta n=0.011$ between core and cladding material [24] and a square cross-section of $2.9\, {\mathrm{\mu} \mathrm{m}} \times 2.9\, {\mathrm{\mu} \mathrm{m}}$. The simulated modes for a wavelength of $810\, \mathrm {nm}$ ($1550\, \mathrm {nm}$) are shown in Figs. 6(a), (6(b)) and the corresponding MFDs are listed in Fig. (2)b. The PolyBoard waveguide parameters are chosen to have a high mode field overlapp with the $\mathrm {Ti {:} LiNbO_3}$ waveguide to ensure a high coupling efficiency. A comparison of the simulated modes (Figs. 2, 6(a), 6(b)) and the corresponding MFDs (Fig. (2)b), shows a small mismatch between the different waveguide mode distributions, since the $\mathrm {Ti {:} LiNbO_3}$ has a asymmetric mode profile, which leads to a non-perfect coupling. We estimate a theoretical coupling efficiency between PolyBaord and $\mathrm {Ti {:} LiNbO_3}$ waveguides of $95 \, \mathrm {\%} \ @ \ 1550\, \mathrm {nm}$ and $87 \, \mathrm {\%} \ @ \ 810\, \mathrm {nm}$ by calculating the overlap integral of the PolyBoard and $\mathrm {Ti {:} LiNbO_3}$ mode intensity distributions.
Fig. 6. Simulated mode inside a $2.9\, {\mathrm{\mu} \mathrm{m}} \times 2.9\, {\mathrm{\mu} \mathrm{m}}$ PolyBoard waveguide at $810\, \mathrm {nm}$ (a) and $1550\, \mathrm {nm}$ (b) for $\Delta n = 0.011$.
We etched two deep slots for the insertion of the TFFs into the PolyBoard, with the first TFF implemented as a long-pass filter (LP) for pump suppression and the second one as a dichroic mirror (DM) for separation of signal and idler. The TTFs are based on a thin polymer substrate (thickness of $4.6\, {\mathrm{\mu} \mathrm{m}}$) with a dielectric layer stack on top to create the filter characteristics. The overall thickness of the TFFs is around $14\, {\mathrm{\mu} \mathrm{m}}$. The TTFs are inserted by hand into the narrow etched slots and glued afterwards. We determine additional losses due to one TFF insertion of around $1\, \mathrm {dB}$ for both SPDC wavelengths. Passive coupling to single mode fibers (SMF) is done via etched U-grooves with fiber-coupling loss of around $1\, \mathrm {dB} \ @ \ 1550\, \mathrm {nm}$ mainly due to MFD mismatch [24]. We estimate an overall transmission loss through the complete module for perfect coupling and alignment by summing up all single losses of $3.1 \, \mathrm {dB} \ @ \ 1550\, \mathrm {nm}$ and $4.2 \, \mathrm {dB} \ @ \ 810\, \mathrm {nm}$. It should be noted that this value is only a lower limit for the overall losses. To control the temperature, we placed a peltier element and a thermosensor below and above the module respectively. We were able to heat the module up to $100 \, \mathrm {^\circ C}$, which is sufficient for operating the HSPS. Higher temperatures should be possible, but are not tested within this work. Figure 5(b) shows the assembled and packaged HSPS module with PM-input-fiber (purple), two SM-output-fibers (yellow) and electrical contacts for temperature control.
We perfomed a first characterization of the assembled module by pumping it with a cw-laser at $532\, \mathrm {nm}$ (Klastech) and analyzing the outputs with a spectrometer at visible wavelengths. We controlled the input power and polarization with a half-wave plate and a linear polarizer and coupled the light into the input PM-fiber of the HSPS module. The output fibers were directly connected to a spectrometer. Figure 7 shows the measured spectrum of the signal output port at three different temperatures measured with the integrated thermosensor. A comparison with the measured spectrum of the pure $\mathrm {Ti {:} LiNbO_3}$ waveguide (Fig. 3) indicates a working module with temperature wavelength tunability. The intensity drop for high temperatures can be explained by a small misalignment in the module due to different expansions of the components. Peaks from higher-order modes and Cerenkov radiation are clearly visible. We observe a perfect separation of signal and idler, since the spectrum of the idler output port shows no intensity counts at around $810\, \mathrm {nm}$ (see Fig. 7, green). Nevertheless, a small amount of pump photons is visible in both output ports, which indicates a insufficient pump filtering within the module. We measured a pump suppression of around $\alpha _{532\mathrm {nm}}=66\, \mathrm {dB}$ in the complete module. Thus we found that an additional filter is needed. We implemented this by fabricating a external fiber-coupled filter for the signal output port. Since the module is already assembled, the integration of a additional TFF is not feasible, but will be noted as an improvement for future modules.
Fig. 7. Measured HSPS module output spectra of the signal and idler photons at different temperatures. No counts at around $810\, \mathrm {nm}$ in the idler output indicate a perfect separation of signal and idler photons
2.3 Fiber-coupled narrow band filter
For filtering the signal output port, we deposited a dielectric coating on a SM-fiber tip. We cutted the fiber near the fiber plug for insertion in the coating machine. We designed a dielectric coating consisting of $23$ alternating $\mathrm {TiO_2}$ and $\mathrm {SiO_2}$ layers. In order to ensure high quality, the layer thicknesses are measured optically in situ and the design is adjusted automatically if necessary.
The transmission of a test glass coated simultaneously for a transmission measurement is shown in Fig. 9(a) (black). We designed the coating to have a narrow band transmission at $810\, \mathrm {nm}$ not only for pump suppression but also for additional filtering of the Cerenkov radiation and possible luminescence of the used glue. We spliced the coated fiber tip to the original fiber and connected a second SM-fiber (see Fig. 8). The connected fiber tips are glued to the fiber mating sleeve for protection of the coating. The measured transmission through the assembled fiber-filter is shown in Fig. 9(a) (red), with a transmission peak of $42\, \mathrm {\%}$ ($3.8 \, \mathrm {dB}$ losses) at $809.5\, \mathrm {nm}$. The spectrum of the HSPS module signal output port with connected fiber-filter is shown in Fig. 9(b). A comparison with the unfiltered module (Fig. 7) indicates the narrow band-pass filtering of the coated fiber.
Fig. 8. Sketch of the deposited coating between to SM-fiber tips for filtering the signal output port.
Fig. 9. Transmission of the deposited coating, measured on a glass substrate (a, black) and after assembly of the fiber-filter (b, red); filtered spectrum of the HSPS module signal output port (b).
3. Results and discussion
After we analyzed the spectral characteristic and temperature dependency of the module, we then investigated the single photon characteristics of the module by performing conditioned measurements with superconducting nanowire single-photon detectors. The experimental setup is shown in Fig. 10. We used a frequency-doubled pulsed pump source (Katana-05, Onefive GmbH Zürich) with a center wavelength of $532 \, \mathrm {nm}$ and a spectral width of $0.19 \, \mathrm {nm}$ to operate the modul. The Gaussian shaped pulses have a repetition rate of $10 \, \mathrm {MHz}$ with pulses of $43 \, \mathrm {ps}$. To filter out background light, we used a blazed-grating after the laser. We adjusted the intensity and polarization by neutral density filters (NDF) and a combination of a half-wave plate (HWP) and a linear polarizer (Pol). The light was then coupled into a PM-fiber, which is connected to the input fiber of the module. We connected the filtered output of the signal to a SNSPD (Cryospot 4, Photon Spot California) with a detection efficiency of around $\eta _{Det,s}=65 \, \mathrm {\%}$ @ $810 \, \mathrm {nm}$ for click-detection (rate $R_s$). The output of the idler was coupled to a 50/50 fiber beamsplitter (FBS) and the photon rates ($R_{i1}$ and $R_{i1}$) are detected by two SNSPDs (detection efficiency of $\eta _{Det,i}=85 \, \mathrm {\%}$ @ $1550 \, \mathrm {nm}$). By splitting one of the outputs and detecting both rates individually, the generation of more than one photon pair can be measured. The threefold coincidence between all detectors indicates the generation of at least two photon pairs.
Fig. 10. Experimental setup for conditioned measurements. NDF: neutral density filters; HWP: half-wave plate; Pol: linear polarizer; PMF: Polarization-maintaining fiber; SMF: single-mode fiber; FF: custom fiber-filter; FBS: fiber beamsplitter 50/50; FPC: fiber polarization controller; SNSPDs: superconducting nanowire single-photon detectors; TT: time-tagger
We determined the single count rates and coincidences between the three used SNSPDs by a time-tagger (TT). To determine the single photon and heralding performance of the module, we evaluated the heralding-efficiency [6]
where $R_{s \wedge i1}$ and $R_{s \wedge i2}$ describe the coincidences between signal and idler 1/idler 2 with a coincidence window of $5 \, \mathrm {ns}$. The heralding-efficiency $\eta _h$ describes the probability of a single photon in the idler output upon the detection event in the signal output. The power dependent heralding efficiency of the filtered module is shown in Fig. 11. The heralding efficiency increases with higher pump powers, due to an increase of higher order photon components, which is caused by the high brightness of SPDC waveguide sources. For low pump powers, we can obtain a constant heralding efficiency of around $\eta _h=3.5 \, \mathrm {\%}$, which is low compared to other works [25]. It is important to mention that our module is a hybrid integration, which is not the case with the comparable sources.Fig. 11. Heralding efficiency $\eta _h$ vs. pump power of the filtered HSPS module. For low pump powers the heralding efficiency approaches a vlaue of $\eta _h=3.5 \, \mathrm {\%}$.
Non-optimal coupling between the two material systems leads to additional losses that reduce the heralding efficiency. To estimate the total losses within the assembled module, we performed count rate measurements with different additional filter combinations. We measured the output count-rates of the module without any filters and after the insertion of the built fiber-coupled narrow band filter in the signal port and another narrow band filter in the idler port. Count-rates drop by around $90 \, \mathrm {\%}$ in both outputs after insertion of the filters. This indicates a background in the unfiltered module of around $90 \, \mathrm {\%}$, which should be mainly due to residual pump light. As described in Sec. 2.3 the background can be completly reduced by inserting the narrow band filter. We estimate the transmission efficiency through the module for the signal path ($\eta _s$) and idler path ($\eta _i$) by using the measured countrates $R_s$, $R_i$ and $R_{s \wedge i}$ and the following equations
To evaluate the simultaneous generation of multiple photon pairs in the generated SPDC , we make use of the heralded second-order auto-correlation function $g^2_h(0)$, which is given by [6]
for the given measurement scheme. $R_{s \wedge i1 \wedge i2}$ is the threefold coincidence between signal, idler 1 and idler 2, which is only present if multiple photon pairs are generated. For a perfect SPDC prozess, the $g^2_h(0)$ should therefore vanish. Figure 12(a) shows the measured $g^2_h(0)$ of the filtered module for different pump powers. For low pump powers $<1 \, \mathrm {\mu W}$ the second-order auto-correlation function reaches values of $g^2_h(0)<0.005$, which indicates an excellent single photon character and is comparable to a previous HSPS based on $\mathrm {Ti {:} LiNbO_3}$, developed and fabricated in our group [6]. For a further investigation of two photon pair generation and an analysis of possible photoluminescence within the module, we calculate a coincidence-to-accidental ratio $CAR_{rep}(m)$. The CAR is the ratio between coincidences of photons in the signal and idler outputs for one input pulse $R_{s \wedge i}(\Delta \tau =0)$ and for coincidences with neighbouring pulses $R_{s \wedge i}(\Delta \tau =m\tau _{rep})$. We shift the relative time delay between signal and idler such that a pulse overlaps with a neighbouring pulse. $\tau _{rep}$ is the repetition time of the pulsed laser and $m$ is a natural number, which gives the number of skipped pulses. $CAR_{rep}(m)$ is given by [6]Fig. 12. Heralded second-order auto-correlation function $g^2_h(0)$ vs. pump power (a). An increase for higher pump powers indicates the generation of higher-order photon components; time shifted coincidence-to-accidental ratio $CAR_{rep}(m)$ vs. pump power for time shifts of one and two pulse repetition times (b).
Regardless of the number of skipped pulses $m$, $CAR_{rep}(m)$ should be constant. Figure 12(b) shows the power dependent $CAR_{rep}(m)$ for shifts of one and two pulses. The absolute values are again comparable to other works [6]. As can be seen, a larger pulse shift does not changes the $CAR_{rep}(m)$ significantly, which underlines the excellent single photon character. A decrease for higher pump powers indicates contributions of non-correlated photons. Therefore, the HSPS has to be operated at pump powers $<1\, \mathrm {\mu W}$, which however leads to a low heralding efficiency due to the excess losses in the module discussed above.
An important property of a single photon source is its brightness. To analyse the brightness, we calculate the mean number of generated photons per pulse $<n_{pulse}>$ by dividing the signal count rate $R_s$ by the detector efficiency and the laser repetition rate of $10 \, \mathrm {MHz}$. The power dependent $<n_{pulse}>$ is shown in Fig. 13. To gain information about the mean photon number per pulse of the $\mathrm {Ti {:} LiNbO_3}$ crystal itself, we also calculated $<n_{pulse}>$, excluding the module transmission. The low module transmission leads to a strong difference in the mean photon number of the complete module and the $\mathrm {Ti {:} LiNbO_3}$ itself. The mean photon number, exlcuding the module losses, is comparable to previous reportet values [6], which indicates a efficient SPDC process in the $\mathrm {Ti {:} LiNbO_3}$.
Fig. 13. Mean photon number per pulse vs. pump power of the filtered HSPS module with included and excluded module losses.
In summary, the different components of the module, like the $\mathrm {Ti {:} LiNbO_3}$ waveguide or the TFF, show excellent characteristics. The total transmission losses drastically reduce the module performance and therefore need to be reduced in a future module.
4. Conclusion and outlook
We demonstrated the first chip-size ($(2 \times 1)\, \mathrm {cm^2}$) fully integrated fiber-coupled Heralded Single Photon Source module based on a hybrid integration of a $\mathrm {Ti {:} LiNbO_3}$ waveguide into a polymer board with integrated optical components. The module can be pumped at $532\, \mathrm {nm}$ via a input PM-fiber. A SPDC process in a low-loss periodically poled $\mathrm {Ti {:} LiNbO_3}$ waveguide creates signal and idler photons at $810\, \mathrm {nm}$ and $1550\, \mathrm {nm}$. The nonlinear crystal is coupled to a PolyBoard with integrated waveguides and filters for pump suppression and dichroic photon separation. A characterization showed an operating module with temperature tunability. Nevertheless, measurements of the output spectra showed residual pump light in the outputs.
Therefore, we fabricated a fiber-coupled narrow band pass filter, with a high transmission at $810 \, \mathrm {nm}$ by depositing a $23$ layer dielectric coating onto a SM-fiber tip. We measured a heralding efficiency of $\eta _h=4.5\, \mathrm {\%}$ for the filtered module at low pulsed pump powers, which is low compared to a reported heralding efficiency of around $\eta _h=60\, \mathrm {\%}$ in free space setups [6,13] and can be explained by low coupling efficiencies within the module. Significantly improving the coupling in the module could greatly lower losses, which should result in a higher heralding efficiency. Calculations of a pulse dependent coincidence-to-accidental ratio and a heralded second-order correlation function of $g_h^{(2)}=0.05$ show a excellent single photon character.
In addition, the hybrid integration of $\mathrm {Ti {:} LiNbO_3}$ into a PolyBoard opens up the opportunity for a future multi-channel source and a direct integration of silicon SPAD arrays for the detection of the signal photons on chip. The realization of a quantum- system-on-chip (QSoC) providing low cost, small size and robustness is therefore conceivable with a hybrid integration approach.
Funding
European Union’s Horizon 2020 Framework Programme Research and Innovation Programme through Quantum-Flagship Project UNIQORN, (820474).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this work may be obtained from the authors upon reasonable request.
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