1. Introduction

In future quantum networks photons play an important role as flying qubits [1]. They transmit information encoded in one of their degrees of freedom between stationary quantum nodes, such as trapped ions or atoms [2–5], solid–state quantum systems [6–8] or ensemble–based quantum memories [9–11]. A crucial step in such networks is the generation of the photons in a non–classical photon state, i.e. single photons or entangled photon pairs. Photon pair sources are well–suited due to their capability to create entangled photons with respect to polarization, time–energy or time–bin in a relative simple way. In the case of waveguide–based pair sources, the advantage of large conversion efficiencies compared to sources in bulk material is caused by a large spatial mode overlap as well as a large confinement of the light fields [12–23].

If it is necessary to establish a long distance communication between remote nodes, it is advisable to send the photons via optical fiber links. Thus the photons should either be in the telecom O-band around 1310 nm, which shows the lowest dispersion in standard optical fibers, or in the telecom C-band around 1550 nm, where they experience the lowest absorption. Therefore, a light source which creates photon pairs at telecom wavelengths is required for long–range quantum communication applications as mentioned above.

Another promising application is the calibration and traceability of the detection efficiency of telecom single–photon detectors, which is one of the most important parameters for the characterization of quantum communication systems and networks [24]. A pair source with a well–known heralding efficiency offers the possibility to determine the efficiency of a single–photon detector without the need for a calibrated reference detector [25–28]. Beyond this scheme, a source with a high conversion efficiency enables photon rates high enough to be measured with classically calibrated detectors (traceable e.g. to the cryogenic radiometer or to the synchrotron), but also be able to be used in the calibration of single–photon detectors, e.g. Superconducting Single–Photon Detectors (SSPD) or InGaAs Single–Photon Avalanche Detectors (InGaAs-SPAD) [29,30].

We present here the realization of a pair source based on spontaneous parametric downconversion (SPDC) in a periodically–poled lithium niobate (PPLN) ridge waveguide. We characterized the source with respect to photon pair rates, conversion and heralding efficiencies as well as first– and second–order coherence properties. Finally, the source is pumped with a pulsed laser to demonstrate the generation of pure photons.

2. Device and setup

In our experiment we employ the process of SPDC to convert photons at 712 nm to photon pairs, with one photon located at 1312 nm in the center of the telecom O–band and the other at 1557 nm in the telecom C–band. From now on, the O-band photons are declared as signal photons and the C-band photons as idler photons. The pump light is generated by a cw Ti:Sa ring laser (Matisse, Sirah Lasertechnik GmbH) and guided with a single mode fiber to our device. Passing a polarization control, the light is coupled with an uncoated aspheric lens to a periodically–poled Zn–doped lithium niobate ridge waveguide crystal (NTT Electronics), which has been used in a former quantum frequency conversion experiment [31]. The waveguide chip consists of twelve waveguides with six different poling periods allowing coverage of the whole telecom O– and C–band by changing the poling period. Furthermore, an active temperature control of the chip allows fine–tuning of the signal and idler wavelengths. In this experiment, a waveguide with a poling period of 14.92 µm was operated at a temperature of 30.2 °C. The coupling efficiency of the pump beam to the waveguide is 40%. Behind the waveguide, the signal and idler photons are collimated by an anti–reflection–coated aspheric lens and spatially separated with a dichroic mirror. To eliminate the remaining pump light, two longpass filters are placed in the beams (1312 nm: FEL0750, Thorlabs, transmission: 87%; 1557 nm: FEL0800, Thorlabs, transmission: 89%). After transmission through these filters, the 1312/1557 nm SPDC photons are coupled into the appropriate arms of a 1310/1550 nm single mode wavelength demultiplexer (WDM) and recombined into a single standard telecom fiber. The previous splitting of signal and idler modes is necessary to reach an optimal fiber–coupling of both modes, respectively. The analysis of the photons takes place in another lab connected by a 180 m fiber link. From here, the setup differs depending on the parameter to be measured. In the case of a simple signal–idler–cross–correlation measurement, another WDM is applied to split signal and idler modes again followed by the detection of the photons.

Alternatively we can filter both modes down to a standard telecom channel spacing of 100 GHz before detection. To this end, two completely fiber–based filter systems consisting of fiber–optical circulators and Fiber–Bragg–Gratings (FBG) are available (1312 nm: AOS GmbH, central wavelength: 1312.718 nm, FWHM: 145 GHz; 1557 nm: Teraxion, central wavelength: 1557.00 nm, FWHM: 120 GHz). This setup is shown in Fig. 1(a). For detection, we use two superconducting nanowire single–photon detectors (SSPD, EOS X10 Single Quantum) as well as two InGaAs–SPADs (ID201, IDQuantique).

 

Fig. 1 The experimental setup for the measurement of (a) the temporal correlation, (b) the first order coherence function, (c) the purity. A detailed explanation can be found in the text. Abbreviations: HWP: half–wave plate, PBS: polarizing beam splitter, DM: dichroic mirror, WDM: wavelength demultiplexer, FBG: Fiber–Bragg–Grating, SSPD: Superconducting nanowire single–photon detector.

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3. Experimental results

3.1. Temporal correlations

In this chapter the measurement of the temporal correlation of both filtered and unfiltered photons is presented. In the following, only the curves of the filtered photons are shown as the curves of the unfiltered photons look identical only revealing different slopes. The correlation between the two SSPD channels delivers the signal–idler–correlation function $g_{si}^{(2)}$. The inset in Fig. 2(a) shows this function at a pump power of 200 nW with a clear peak indicating the temporal correlation. As the photons have coherence times below 1 ps (s. section 3.2), the width of the correlation peak is only determined by the detection jitter of the SSPDs around 50 ps. Important figures of merit of our source are the signal and the accidental pair rate. These are extracted from the $g_{si}^{(2)}$–function by integrating the coincidences inside the correlation peak. The interval with a width of 240 ps is marked in the inset of Fig. 2(a) by the dashed red lines. Inside this interval, the signal pair rate is determined by the coincidences above the background level and the accidental rate by the coincidences at this level, respectively. These rates are plotted in Fig. 2(a) for different pump powers. As expected from theory, the signal pair rate (red data points) increases linearly with pump power, which is confirmed by a slope of one in the double–logarithmic scale. On a linear scale we get a slope of 1456 ± 10 pairs/s·µW (unfiltered: 58620 ± 133 pairs/s·µW) for this rate. The accidental correlations should increase quadratically with pump power resulting·in a slope of two. The quotient of these two rates is defined as Signal–to–Background ratio (SBR), which is depicted in Fig. 2(b). The slope of minus one is related to the hyperbolic dependance on the pump power. At low pump powers, high SBRs up to 260000 can be observed. Even at high pump powers with pair rates around 10⁶/s (unfiltered: 10⁷/s) reasonable SBRs of 7.5 (4) are accessible. The low background is a typical property of a waveguide source, as one can benefit from a high photon–to–photon conversion efficiency. In comparison to bulk sources, this allows much lower pump powers to get large pair rates and consequently a reduced background. We can determine the photon–to–photon conversion efficiency inside the waveguide crystal to (3.95 ± 0.1) × 10⁻⁶. Another important figure of merit is the Klyshko–efficiency, which is a measure for the losses behind the waveguide. It is defined as the quotient of the signal pair rate and the count rate of the herald photons (in this case the idler photons). In this case, the heralds are the idler photons at 1557 nm. We calculate the Klyshko–efficiency to be 9.9 ± 1.1% (unfiltered: 16.1 ± 0.5%). To obtain only the losses between the waveguide and the detector, the heralding efficiency defined as quotient of the Klyshko efficiency and the detection efficiency of the signal photons at 1312 nm can be calculated. In our setup, this efficiency is limited by the transmittance of the bandpass filters, the fiber–coupling behind the waveguide, the fiber–fiber couplers and in the filtered case by transmission losses of the FBG. With a detection efficiency of 25% we get heralding efficiencies of 39.9 ± 4.5% (unfiltered: 64.1 ± 2.1%).

 

Fig. 2 (a) The signal (red dots) and accidental (black dots) pair rate as function of the pump power. The solid lines are linear fits to the data. The slope of the accidental rate is twice as the signal rate’s slope caused by a quadratic dependency on the pump power. Inset: The temporal correlation peak at a pump power of 300 nW. The red lines determine the interval, which has been taken into account for the coincidence rate. (b) The Signal–to–Background ratio (SBR) for different pump powers. The negative slope indicates the hyperbolic dependency on the pump power.

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3.2. Coherence properties

In the next step, the first and second order coherence properties have been measured. For the first order coherence function g⁽¹⁾(τ) a free–space Michelson interferometer is applied, which is shown in Fig. 1(b). Both input and output ports of the interferometer are coupled to single mode fibers. In one arm we have a mirror mounted on a piezo translator for fine tuning of the phase. The mirror in the second arm is fixed on a translation stage for coarse tuning with a maximal path length difference of 1.45 ns. Since several components suffer from birefringence (e.g. the solid uncoated retro–reflecting prisms located at the end of the two arms), it is possible that each arm alters the polarization in a different manner, which lowers the visibility. To avoid this, the polarization of the input light is adjusted with a fiber paddle polarization controller until an identical polarization of the two beams at the beam splitter is achieved.

As we want to measure the g⁽¹⁾–function for signal and idler modes at the same time, the interferometer is inserted in the setup before the second WDM. In Fig. 3, the visibility of the interference fringes depending on the path length difference (the envelope of the g⁽¹⁾–function) for the unfiltered photons is shown. We observe a coherence time in the order of one picosecond with a maximal visibility of one in the signal mode (black dots). The reduced maximal visibility of the idler photons (red dots) originates from a non–optimal polarization state, because the polarization was optimized for the signal photons. The spectrum of the photons is given by the phase–matching curve, i.e. in the ideal case a sinc² function. Therefore, we expect a triangular function for the envelope of the g⁽¹⁾–function. In our case, the spectra which have been measured with a grating spectrometer equipped with a GaAs–camera (Princeton Instruments) are slightly distorted from the ideal sinc² curve due to fabrication tolerances in the poling period of our waveguide [32] (see inset of Fig. 3(a)). These spectra have been Fourier–transformed and plotted as solid lines in Fig. 3(a). As one can see, the measured data points are in good agreement with the calculated curves. In the case of the idler photons, the calculated curve was additionally multiplied with 0.81 to account for the reduced maximal visibility.

 

Fig. 3 (a) The first order coherence functions of the unfiltered signal (black dots) and idler (red dots) photons. The solid lines are the theoretical curves calculated by the Fourier transform of the spectra (see Inset). (b) The first order coherence function of the filtered signal photons.

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The same measurement was repeated for the filtered photons. To this end, the FBG filtering system was introduced behind the interferometer. The resulting g⁽¹⁾–function of the signal mode is shown in Fig. 3(b). We observe an increased coherence time in the order of 10 ps and a clear change in the shape of the function. This is caused by the rectangular reflection spectrum of the FBG (see inset of Fig. 3(b)). The red solid line is again the calculated curve obtained from the Fourier transform of the spectrum. The slight deviation of the calculated curve most probably is caused by our spectrometer’s resolution limit of 20 GHz, which is in the order of the FWHM of the FBG spectra.

The second order coherence function, on the other hand, yields information on the SPDC photon statistics. To determine this function, we apply a direct measurement of the photon statistics with a Click/No–Click (CNC) method combined with a maximum–likelihood estimation [33,34] and an indirect method via the heralded g⁽²⁾–function.

For the CNC measurements we place an InGaAs–SPAD in the idler channel behind the second WDM. The InGaAs–SPADs are well–suited for the CNC measurements because they operate in the gating mode whereby a pulsed excitation of the SPDC–process is not necessary. The different detection efficiencies are realized by attenuating the beam with neutral density filters. At first we investigate the statistics of the idler mode separately. The InGaAs–SPAD is operated with an internal trigger rate of 1 MHz and a gate width of 5 ns. From theory, we expect a thermal distribution of the photons due to multi–pair production in the waveguide [35]. However, we can only measure this distribution if the gate width of the SPAD is much smaller than the coherence length of the photons (about 1 ps). As this condition is not fulfilled, a Poissonian distribution should be visible. The result is shown in Fig. 4 (black bars). The inset shows the same data set in a logarithmic scale to illustrate the contribution of the two–photon states. A comparison with a Poissonian distribution with the same average photon number reveals a compliance with a fidelity of 99.99%. Thus we measured a Poissonian distribution as expected. In a next step, we investigate the influence of the heralding process on the photon statistics. Therefore the InGaAs–SPAD is externally triggered by the SSPD, which detects the herald photons (in this case the signal photons). The resulting statistics with heralding is also shown in Fig. 4 (red bars). One can see that the probability to find zero photons per gate is decreased to 0.374 ± 0.016, which is in good agreement with the expected value of 1−0.64 = 0.36 deduced from the heralding efficiency of 64%. We emphasize that the CNC method takes into account the limited detection efficiency of the APD (25%), thus the heralding efficiency instead of the Klyshko efficiency is the relevant parameter. At the same time, the peaks with one or more photons per gate are increased. Important at this point is, that the ratio P(2)/P(1) remains almost unchanged by the heralding process (P(1): probability of having a single photon, P(2) of having two photons); we get P(2)/P(1) = 2.89 ± 0.18% without heralding and P(2)/P(1) = 2.73 ± 0.15% with heralding. What we expect is a slight increase of the ratio as the heralding detector is not a photon-number-resolving detector, which leads to an increased likelihood to detect higher order photon number contributions. However, this increase is smaller than our error bars, which hinders quantitative evidence. If we again compare the photon statistics with a Poissonian distribution, we get now a reduced fidelity of the measured statistics with a Poissonian state of 80.15%. The value g⁽²⁾(0) can be calculated with equation: [36]

This equation holds for P(2) ≪ P(1), which is fulfilled in our case. If we calculate this value for the statistics without heralding, we get g⁽²⁾(0) = 1.001 indicating a coherent state. In summary, we can use the heralding process to generate anti-bunched light at telecom wavelengths from an originally thermal light source.

 

Fig. 4 The photon statistics measured with the Click–/No–Click method at a pump power of 7 µW. The black bars depict the case where the statistics of the idler photons without respect of the signal photons was measured while the red bars were measured with heralding of the signal photons. The inset shows the same data in a logarithmic scale.

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In a second approach, the heralded single–photon properties are determined by the heralded g⁽²⁾–function. To this end, the signal photons are guided to a fiber–based Hanbury–Brown Twiss (HBT) setup consisting of a fiber beam splitter and two InGaAs–SPADs. The SPADs are externally triggered by the SSPD detecting the idler photons. In this case, no spectral filters are inserted. The correlation of all three channels reveals the heralded g⁽²⁾–function calculated with the method described in [36]. The inset of Fig. 5(a) shows the function at a pump power of 20 nW. A photon anti-bunching with g⁽²⁾(0) = 0.001 ± 0.0003 is clearly visible. For higher pump powers, we expect an increase of g⁽²⁾(0) caused by noise due to accidental correlations. With the help of the SBR, we can estimate the value for g⁽²⁾(0) using the following equation:

With a SBR depending in a hyperbolic way on the pump power, we can fit the data with Eq. (2). The result is the red line in Fig. 5(a). The curve fits quite well the data for higher pump powers, while it underestimates the data for lower pump powers. This is caused by additional noise of the InGaAs detectors. Their noise increases with the trigger rate and therefore with the pump power in a second–order polynomial manner. Furthermore, we have a pump power independent contribution resulting from the dark counts of the SSPD. In summary, we can model the SBR with the detector noise to

 

Fig. 5 (a) Heralded g⁽²⁾(0) as function of the pump power. The data points were extracted from the g⁽²⁾(0)–functions (see Inset: g⁽²⁾–function at 20 nW pump power, g⁽²⁾(0) = 0.001). The blue and red line are the theoretical curves with and without consideration of the detector noise, respectively. (b) The SBR as function of the pump power.

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To compare the results obtained by the two methods, the result of the CNC measurement is added to Fig. 5(a) (green data point). As visible from Fig. 5(a) the result of the CNC measurement fits well to the results of the heralded g⁽²⁾ measurement, which is a good check for consistency.

3.3. Purity

A crucial disadvantage in the cw–excitation utilized up to now is that it is not possible to generate photons in a deterministic way. However, in large quantum networks a synchronous source is favorable to ensure temporal overlap between photons from remote quantum nodes. Furthermore, cw–excitation hinders the generation of photons with a high purity (unless strong spectral filtering is applied). The reason are spectral correlations between signal and idler modes due to energy and momentum conservation leading to the emission of the photons into a large number of correlated temporal modes [37]. Thus, the heralded photon is projected into a mixed state precluding its capability for quantum interference effects, which are crucial in entanglement swapping schemes [38]. In order to produce single photons suitable for quantum networks, a pulsed excitation is necessary. In doing so, it is possible to generate pure photons either by spectral filtering to get rid of the remaining spectral correlations [39,40] or by a dispersion–engineered nonlinear crystal [41,42]. The latter has the advantage that a decrease of heralding efficiency and pair rates can be avoided. However, our waveguide chip was originally designed for a quantum frequency conversion experiment, hence it was not optimized in sense of dispersion, wavelength and phase-matching. Nevertheless, we can demonstrate as proof-of-principle the generation of pure photons via spectral filtering with a reduced heralding efficiency of 1.8%.

To measure the purity, we follow the scheme described in [43]. It relies on the observation of Hong–Ou–Mandel interference between down–converted signal photons from two consecutive pump pulses. The setup is shown in Fig. 1(c). The waveguide is pumped by a pulsed Ti:Sapphire laser (Tsunami, Spectra Physics) with a repetition rate of 80 MHz, a pulse width of 2 ps, a central wavelength of 712.2 nm and an average pump power of 130 µW. As before, signal and idler photons are fiber–coupled and filtered with our Fiber–Bragg–Gratings. The signal photons pass a Mach–Zehnder–interferometer, which is necessary to superimpose the photons from two consecutive pump pulses. To achieve this goal, the interferometer has to be unbalanced with a delay of 12.5 ns, which is the inverse of the laser’s repetition rate. We realized the interferometer with two fiber beam splitters, one arm with a constant fiber length and one free–space arm with a variable path length. Via the translation stage in the free–space arm, we can vary the delay between 12.417 ns and 12.577 ns. A quarter and a half wave plate in the free-space arm compensate the polarization rotation in the fiber parts to guarantee the indistinguishability in polarization at the second beam splitter where the HOM interference occurs (this has been pre–aligned with a laser). We detect the photons with two InGaAs–SPADs. To achieve a maximal interference contrast, both photons must be projected into a single–photon state. Therefore, it is necessary to measure the 4–fold coincidence function between both signal and both idler photons. We realized this by splitting the idler photons with a beam splitter and detect them with a second SSPD. Thus, we post–select those events where the two SSPDs clicked with a delay of 12.5 ns. The resulting coincidence function in dependance on the delay of the HOM interferometer for a pump power of 130 µW is shown in Fig. 6(a). We can identify a clear HOM dip with a visibility of 45%. It fits quite well to the theoretical curve (solid black line), which is given by 1 − V × g⁽¹⁾(τ) with V being the visibility. The limited visibility is due to multi–photon–pairs, a low SBR caused by the inefficient heralding scheme and the non–perfect visibility of the Mach–Zehnder–interferometer (V = 78%). We can increase the visibility by decreasing the pump power, hence reducing the multi–photon probability and the detector noise. The dependance on the pump power is sketched in Fig. 6(b). The data has been corrected with the finite visibility of the HOM interferometer of 78%. For low pump powers, the visibility is close to 100% indicating a high purity of the photons.

 

Fig. 6 Purity measurement (a) Hong–Ou–Mandel interference dip at 130 µW pump power. The raw visibility is 45%. (b) The corrected visibility in dependance on the average pump power.

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4. Conclusion

In conclusion, we implemented a heralded single–photon source in the telecom regime based on a PPLN ridge waveguide. The source features a high conversion efficiency of 4×10⁻⁶ and a good heralding efficiency of 64% at the same time. The conversion efficiency of 4× 10⁻⁶ in the 4 cm long crystal is to our knowledge among the highest efficiencies reported up to now. Comparable efficiencies better than 1 × 10⁻⁶ have been obtained also with waveguide-based SPDC sources by Jechow et al. [23] (3.3 × 10⁻⁶), Ding et al. [22] (1 × 10⁻⁶) and Meyer-Scott et al. [21] (3.1 × 10⁻⁶). With one photon in the C–band and one photon in the O–band and the high conversion/heralding efficiency, the source is well–suited for applications in, and metrology relating to, fiber-based quantum communications, an example of the latter being the calibration of telecom single-photon detectors.