1. Introduction

Correlated photon pairs at 1.55 μm have important applications in quantum communication [1–3], quantum metrology [4] and quantum computation [5–8] for their low loss transmission in commercial silica fibers. The generation, manipulation and detection of correlated photon pairs constitute a leading approach for the implementation of quantum technologies. The generation of correlated photon pairs at 1.55 μm on the basis of spontaneous parametric down-conversion (SPDC) in periodically poled lithium niobate (PPLN) waveguides [9–11], periodically poled KTiOPO₄ (PPKTP) [12], or that of spontaneous four-wave mixing (SFWM) in dispersion shifted fibers (DSF) [13–16] and silicon waveguides [17–19] has been widely studied. All-fiber photon pair sources at 1.55 μm can be realized by SFWM process in fibers, which are compatible with the technologies of conventional optical communications. On the other hand, integrated quantum photon circuit [20] is a stable and efficient way to realize manipulation of quantum state, which is promising to replace large scale free space optical setups. Silicon-based waveguide materials, like silica-on-silicon (SOS) [21,22] and silicon-on-insulator (SOI) [23,24], have been used to fabricate quantum photonic circuits, in which directional coupler (DC) or multi-mode interference (MMI) was a key component. For example, integrated optical control-NOT gate circuit was fabricated within silica-on-silicon material and a high fidelity was realized at wavelength around 800 nm [21]. Moreover, the ability to control and convert multiple degrees of freedom of photons on a SOI chip using SPDC through periodically poled potassium titanyl phosphate (KTiOPO₄) crystal has been realized at telecom wavelength [25]. However, these experiments mentioned about quantum photonic circuits above were operated using free-space optical quantum sources, which were unsuitable for integrated photonic quantum technologies. Up to now, the study about characterization of SOS chip by fiber photon-pair source at telecom band has not been reported yet. It is worth noting that the simple SOS chip can be used as a building block for constructing arbitrarily large N × N quantum optical circuit capable of implementing any unitary operation in a quantum computing networks [22].

The combine of SPDC sources and the SOI chip have been studied [24,26], and high visibility of degenerate-frequency photons have been achieved. Here, we investigate the generation, manipulation and detection of correlated photon pairs in a fiber-chip scheme. The telecom-band-correlated-photon pairs were generated by SFWM in an optical fiber which was connected to a SOS photonic chip with pigtail fibers. A high visibility of 99.6% was achieved in the interference with nondegenerate-frequency photon pairs. Interference with degenerate-frequency photon pairs was also achieved on our Mach-Zehnder interferometers (MZIs) chip, showing properties of quantum interference which is an important way to realize quantum-state manipulation.

2. Interference experiment with nondegenerate-frequency photon pairs

As shown in Fig. 1(a), our SOS photonic chip has four MZIs [26], where a MZI device contains two DCs and a thermo-optic phase shifter on one arm for on-chip quantum-state manipulation. MZI devices have been well studied for classical operation, while their capability for quantum operation with fiber source will be studied here. The SOS photonic chip was fabricated by standard semiconductor techniques of planar lightwave circuit (PLC) [27]. Firstly, a 15 μm buffer layer of undoped silica was thermally grown on a silicon substrate. Secondly, silica doped with germanium was deposited on the buffer by plasma-enhanced chemical vapor deposition (PECVD) as a core layer with a thickness of 6 μm. Then, the waveguides and MZIs were fabricated using PLC techniques, and a layer of 15 μm boron phosphorous silicate glass (BPSG) with a refractive index matching to that of the buffer layer was overgrown around the waveguides. The BPSG was used as a cladding layer for its advantages of superior liquidity as well as flatness in comparison to silica. Finally, Ti/Au electrodes were fabricated by lift-off technology as thermo-optic phase shifters to tune the internal phase of the MZIs. The schematic geometry of a silica-on-silicon waveguide of the MZI device is shown in Fig. 1(b). The refractive index contrast (△) could be extracted from formula $\Delta \text{=}\left({\text{n}}_{core}{}^2-{\text{n}}_{cladding}{}^2\right)/2{\text{n}}_{core}{}^2$, where $n_{core}$ and $n_{cladding}$ represent refractive index of the core layer and cladding layer, respectively. The refractive index contrast (△) was set to be 0.75% by controlling the doping concentration in the core layer, and waveguides with a core size of 6 μm × 6 μm were fabricated on the chip to achieve single mode operations at telecom band. The waveguide gap of the DC was optimized to be 2.8 μm according to our extensive simulations using beam propagation method (BPM) [28] (Fig. 1(c)). In our experiment, ports of the MZI device were formed by scribing approach and were coupled respectively to two single-mode 127-μm-spacing fiber arrays placed in a V type optical fiber positioning groove. The waveguide ports and fiber array were aligned carefully and stuck by ultraviolet curing adhesive. The SOS photonic chip with pigtail fibers could be integrated to all-fiber system in a convenient way.

 

Fig. 1 SOS integrated photonic chip. (a) Schematic of the integrated chip with four MZI devices, where a MZI device consists of two directional couplers and a voltage controlled thermo-optic phase shifter. (b) The cross-section of waveguide at the part of thermo-optic phase shifter. (c) An optical image showing the central coupling region of the DC where the gap of the waveguides is 2.8 μm and the simulation of the optical field propagation at 1550 nm in the DC by BPM.

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The correlated photon pairs at telecom band were generated by SFWM in optical fibers. SFWM is a third-order nonlinear optical process, in which two pump photons annihilate while a pair of correlated photons generate. Traditionally, the photon with higher frequency is named as signal photon, and the other one is named as idler photon. The energy conservation is satisfied in the SFWM process, with the frequency relation of ${\omega }_{p1}+{\omega }_{p2}={\omega }_s+{\omega }_i$, where ${\omega }_{p1}$, ${\omega }_{p2}$, ${\omega }_s$, ${\omega }_i$ denote the frequencies of two pump photons, signal and idle photons, respectively. The scalar SFWM with degenerate pump photons was used in the first experiment, they had the same polarization with ${\omega }_{p1}={\omega }_{p2}$. Two nondegenerate-frequency photons were generated in this process, also with the same polarization. Moreover, the vector SFWM with nondegenerate-frequency and orthogonal-polarization pump photons was used in the second experiment, two degenerate-frequency photons were generated, and they also had orthogonal polarizations with ${\omega }_s={\omega }_i$.

The first experiment setup is shown in Fig. 2. The pulsed pump light was generated by a gain-switched distributed feedback laser with a repetition rate of 8 MHz. It was amplified by an erbium doped fiber amplifier (EDFA). Cascaded dense wavelength division multiplexing (DWDM) devices were added so as to filter the amplified spontaneous emission (ASE) noise produced by the EDFA. The center wavelength and the pulse width of the pump light were 1552.52 nm (C31, ITU channel 31) and approximately 30 ps, respectively. After that, the pump light was launched into a piece of dispersion shifted fiber (DSF), which was 250-meters long and cooled in a Gifford-McMahon cryocooler in order to suppress the noise photons generated by spontaneous Raman scattering. Meanwhile, the signal photons at 1549.32 nm (C35, ITU channel 35) and idler ones at 1555.75 nm (C27, ITU channel 27) were generated in the DSF by SFWM process. Another cascaded DWDM devices connected to the output of the DSF acted as a filter to separate the signal photons and the idler photons. The FWHMs of them were both 70 GHz. The signal and idler photons were then fed into the MZI device on the photonic chip through input ports a₁ and a₂, respectively. We also used a delay line in one optical path ahead of the MZI device so as to adjust arrival times of the two photons, ensuring that they entered the MZI device simultaneously. After the photons propagated through the MZI device, they were finally detected by two NbN superconducting nanowire single photon detectors (SNSPDs) [29], which were operated at 2.2K in the same cryocooler with the DSF. Since the detection efficiency of SNSPD was polarization sensitive, two fiber polarization controllers were adjusted carefully to optimize the detection efficiency and the maximum system detection efficiency was ~40% under a dark count rate of 80 Hz. Coincidence counting could be performed by a time-correlated single photon counting (TCSPC) equipment (PicoHarp 400, PicoQuant).

 

Fig. 2 Schematic of the experimental setup with nondegenerate-frequency photon pairs. EDFA: erbium doped fiber amplifier, DWDM: dense wavelength division multiplexing, DSF: dispersion shifted fiber, DL: delay line; FPC: fiber polarization controller, SNSPD: superconducting nanowire single-photon detector, TCSPC: time-correlated single photon counting.

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The correlation of the generated photon pairs was firstly demonstrated by coincidence counting without the SOS photonic chip. The output of SNSPD1 was employed as the trigger to start the timer in the TCSPC and the output of SNSPD2 was recorded. The recorded start-stop events were classified according to the time bins, and the bin width was set as 128 ps in our experiment. The measured histogram of the coincidence counts and accidental coincidence counts under a pump power of −1 dBm was inset in Fig. 3. The total coincidence counts (accidental coincidence counts) were extracted by summing contributions of the 6 time bins covering (not covering) the coincidence peak. Performance of the photon pair source was evaluated by the coincidence-to-accidental ratio (CAR), which were measured and shown in Fig. 3. Black squares in the figure were the measurement results under different pump power. It could be seen that the CAR was much higher than 1, and the highest one was up to 200, indicating the high correlation of the photon pairs.

 

Fig. 3 CARs under different pump power. The inset is a typical histogram of coincidence counting under a pump power of −1 dBm.

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The interference of the generated photon pairs on the photonic chip was then demonstrated. Firstly, the MZI device on the chip was characterized by a continuous wave (CW) laser at 1.55 μm. The insertion loss of the MZI device was measured to be less than 1 dB at 1.55 μm. Classical interference was observed by measuring the variation of light power at the two output ports of the MZI device when phase difference between the two arms is tuned by the phase shifter, which is denoted by $\phi$. The powers of two output ports varied sinusoidally with $\phi$ and the period was 2π. The classical interference fringes are shown in Fig. 4(a), where the experiment data points were fitted into sine curves. The applied voltage on the thermo-optic phase shifter varied from 0 V to 7 V. The phase difference $\phi$ was in proportion to the square of applied voltage. Period of the curve was 33.5 V² for one output-port, and the fringe visibility of the classical interference was 100 ± 1.7% calculated by $V=\raisebox{1ex}{$\left(N_{\max }-N_{\min }\right)$}\!\left/ \!\raisebox{-1ex}{$\left(N_{\max }+N_{\min }\right)$}\right.$, where maximum value $N_{\max }$ and minimum value $N_{\min }$ were extracted from the fitting sine curve, respectively.

 

Fig. 4 The measurement results of classical and single photon interference under different phase difference between the two arms of the MZI device. (a) Classical interference fringe measured by a continuous wave laser light, where the red line is the fitting curve of the output power at port c₁. The x-axis represents the varied phase difference by the square of the applied voltage on the thermo-optic phase shifter, and the y-axis represents the output power of the port. (b) Measured single-photon count rate when only the signal photons were injected into the input port a₁. The red line is the fitting curve for the single photon counting results at the output port c₁. The y-axis represents the measured single photon count rate (kHz/s).

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Then, single photon interference in the MZI device was measured by only injecting the signal photons into the input port a₁. The input state actually should be a thermal state. However, the probability of multi-photon events was much less than the probability of single photon events and so that the input state could be represented as ${|10〉}_{in}$. $|mn〉$ is the number state, where m and n are numbers of the photons for the input port a₁ and a₂, respectively . As the phase differnence $\phi$ of the MZI varies, the output state of the single photon is transformed into a superposition of the output states of ${|10〉}_{out}$ and ${|01〉}_{out}$ ($|10〉\to \cos \left(\raisebox{1ex}{$\phi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)|10〉+\sin \left(\raisebox{1ex}{$\phi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)|01〉$), resulting in the single-photon interference fringe. The probability of single photon counting at the output port is $C_{c_1}\propto \left(1-\cos \phi \right)$. In the experiment, when the phase difference between the two arms of the MZI device was changed, the single photon counts were recorded by the two SNSPDs connected to the output ports c₁ and c₂, respectively. The results are shown in Fig. 4(b), which was fitted into sine curve according to $C_{c_1}\propto \left(1-\cos \phi \right)$. The period of the interference fringe was 37.5 V² for port c₁, just similar to the result of classical interference. A fringe visibility of 100 ± 3.4% could be attained from the fitting curve for the result measured at output port c₁.

Interference with nondegenerate-frequency photon pairs in our device was quantified by the splitting and the bunching probabilities, $P_{split}$ and $P_{bunch}$, at the output ports when the applied phase on-chip was varied. As shown in Fig. 2, when two photons in a pair are injected into the input ports a₁ and a₂ of the MZI device, the input state is ${\widehat{a}}_{s1}^{+}{\widehat{a}}_{i2}^{+}|0〉$, where ${\widehat{a}}_{s1}^{+}$, ${\widehat{a}}_{i2}^{+}$ denotes the creation operators of the photons at the input ports a₁ and a₂. After the first DC, the two-photon state is transformed to $|{\text{ψ}}_{middle}〉=\left[\frac{1}{2}\left({\widehat{b}}_{s1}^{+}+i{\widehat{b}}_{s2}^{+}\right)\times \left({\widehat{b}}_{i2}^{+}+i{\widehat{b}}_{i1}^{+}\right)\right]|0〉$. Signal and idler photons are frequency nondegenerate, therefore, all the four states, including ${|1_s{0}_i〉}_{b1}{|0_s{1}_i〉}_{b2}$, ${|1_s{1}_i〉}_{b1}{|0_s{0}_i〉}_{b2}$, ${|0_s{1}_i〉}_{b1}{|1_s{0}_i〉}_{b2}$ and ${|0_s{0}_i〉}_{b1}{|1_s{1}_i〉}_{b2}$, exist at the same time. The phase shifter on one arm of the MZI device provides a phase shift of $\phi$ on the quantum state. Then, the two photons propagate through the second DC and the quantum state at output ports c₁ and c₂ could be expressed by $|{\text{ψ}}_{out}〉=\left[\frac{1}{2}\left(e^{i\phi }\frac{{\widehat{c}}_{s1}^{+}+i{\widehat{c}}_{s2}^{+}}{\sqrt{2}}+i\frac{{\widehat{c}}_{s2}^{+}+i{\widehat{c}}_{s1}^{+}}{\sqrt{2}}\right)\times \left(\frac{{\widehat{c}}_{i2}^{+}+i{\widehat{c}}_{i1}^{+}}{\sqrt{2}}+i{e}^{i\phi }\frac{{\widehat{c}}_{i1}^{+}+i{\widehat{c}}_{i2}^{+}}{\sqrt{2}}\right)\right]|0〉$. P_split was measured by the coincidence counting of A_s × B_i and B_s × A_i, and P_bunch was measured by the coincidence counting of B_s × B_i. Here, A_s and A_i (B_s and B_i) represented respective output ports for the signal and idler photons from the DWDM after the MZI chip.

Hence, the quantum states of the input ports a₁ and a₂ and the output ports c₁ and c₂ are:

As shown in Fig. 2, if both photons in a pair output from the same port of the MZI chip, i.e. c₁ or c₂, it could be expressed by the bunched state $|{\psi }_{bunch}〉$, which means that photons bunch together in either c₁ or c₂ of MZI chip (i.e. A or B port of the DWDM). If they output from different ports of the MZI chip, it could be expressed by the splitting state $|{\psi }_{split}〉$, which means that photons split into c₁ and c₂ of MZI chip (i.e. A and B ports of the DWDM). Their expression and the corresponding coincidence possibilities are:

Here, P_{Bs × Ai} represents the coincidences possibility when signal photons output from B_s port (i.e. c₁ of the MZI) and idler photons output from A_i port (i.e. c₂ of the MZI), as well as P_{As × Bi}. On the other hand, P_{Bs × Bi} is the coincidences possibility when both the signal photons and the idler photons output from B port (i.e. c₁ of the MZI). It can be seen that the relation between P_{Bs × Bi} and the phase difference is a sine function with a period of π.

The experimental setup for the measurement of signal-idler photon bunching is shown in Fig. 2. A DWDM was connected to one output c₁ of the MZI device, then coincidence counting of Bs and Bi was measured for $P_{bunch}$ (i.e. P_{Bs × Bi}). The experiment results are shown in Fig. 5. The single side count rates recorded in the two SNSPDs under different phase difference was plotted in Fig. 5(a), showing a sinusoidal fringe under the increasing applied voltage from 0 V to 7 V. The fitting curves of the results of signal and idler photons had opposite phases. The periods of the two fitting curves were 34 V² and 34.2 V², and their fringe visibilities were 97.6$\pm$1.6% and 97.2$\pm$4.8%, respectively. Coincidence counts of signal and idler photons were attained by the TCSPC and are shown in Fig. 5(b). The experiment results were fitted by a cosine curve according to Eq. (9) (i.e., $P_{bunch}\propto \left(1-\cos 2\phi \right)$). It had a period of 17.4 V², which was a half of the fringe period of the classical interference. The measured fringe visibility was 99.6 ± 3.1%.

 

Fig. 5 Measurements of signal-idler photon bunching and splitting, showing non-degenerate photons interference. (a) Single photon count rate as function of relative phase when measuring signal photon and idler photon in one output c₁. (b) Non-degenerate photons bunching interference, when measuring signal photon and idler photon in one output c₁. (c) Single photons counts rate when measuring signal photons in output c₁ and idler photons in output c₂. (d) Non-degenerate photons splitting interference, when measuring signal photons in output c₁ and idler photons in c₂. An asymmetric similar cosine fringe occurs due to nondegenerate frequency of two photons. Error bars are given by Poissonian statistics based on raw coincidences.

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Figure 2 also shows the experimental setup for the measurement of signal-idler photon splitting. Two DWDMs were added to the two outputs of the MZI devices, and coincidence counting of B_S and A_i (A_S and B_i) was measured for P_split. The results of single side counts are shown in Fig. 5(c), with applied voltage changing from 0 V to 7 V. We also fitted the data into cosine curves, while the phases of curves for the signal photons and idler photons were the same in this case. Periods of the two curves were 37 V² and 40 V², and their fringe visibilities were 92.7 ± 3.7% and 93.7 ± 4.8%, respectively. On the other hand, coincidence counts of the signal and idler photons were measured by TCSPC and are shown in Fig. 5(d). The experiment results were fitted according to Eq. (7) and (8) (i.e., $P_{split}\propto {\left(1\pm \cos \phi \right)}^2$). It can be seen that the fitting curves exhibit asymmetric periodic fringes, which have the same periods with that of the single side counting results. It is due to the nondegenerate-frequency property of the photon pairs used in this experiment.

In order to realize good fringe visibility in the interference with nondegenerate-frequency photon pairs, the case for bunching probability was measured using photon pairs with 6 nm signal-idler frequency spacing. The results indicated that high visibility could also be achieved by nondegenerate-frequency photon pairs through proper post selection. Moreover, the displayed results were all raw experimental data without subtraction of accidental coincidence counts. The high visibility realized in the experiment was mainly due to the high CAR of the fiber-photon-pair source, high performance of the integrated SOS chip and the SNSPDs.

3. Interference experiment with degenerate-frequency photon pairs

We further investigated the interference with degenerate-frequency photon pairs as comparison [30,31]. The experimental setup is shown in Fig. 6. The degenerate-frequency photon pairs were generated by the vector SFWM process in a piece of DSF, which was initiated by two pump lights with different frequencies (1548.51 nm and 1556.52 nm) and orthogonal polarizations. The generated signal and the idler photons also had orthogonal polarizations. The photon pairs with the same frequency were selected by an optical filter with a central frequency of $\left({\omega }_{p_1}+{\omega }_{p_2}\right)/2={\omega }_s={\omega }_i$. Then, they were separated by a polarization beam splitter. A delay line was placed in the path for one photon, while a fiber polarization controller was placed in the path for the other photon in a pair to adjust the arrival time and polarizations of the two photons. By proper adjustment, the polarization and temporal indistinguishabilities between the two photons would be realized, which was demonstrated by the experiment of Hong-Ou-Mandel (HOM) interference through a beam splitter. In the experiment a 50:50 fiber coupler was used. Figure 7(a) shows the result of HOM interference between the generated degenerate-frequency photon pairs, in which there is a dip near the zero delay in their photon arrival time. The raw visibility V = 72.5% ± 0.8% demonstrates the quantum behavior of the generated photon pairs in the interference. The visibility of HOM as a function of the internal loss of a MMI had been investigated [24]. The insertion loss of the fiber coupler we used was similar to that of the MMI. Moreover, the SFWM process in fiber was initiated by continuous wave pump light, in which the generation rates of noise photons caused by spontaneous Raman scattering process were high. Therefore, a relative low visibility of 72.5% was achieved in part due to the intrinsic losses, in part due to the noise photons generated by spontaneous Raman scattering process.

 

Fig. 6 Schematic of the interference experiment with degenerate-frequency photons.

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Fig. 7 (a) Measurement result of Hong-Ou-Mandel interference with degenerate-frequency photons. (b) Measurement result of two-photon interference with degenerate photons using the MZI device.

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To realize the interference with degenerate-frequency photon pairs, the generated signal and idler photons were injected into the two ports of the MZI device simultaneously, as shown in Fig. 6. Meanwhile, the coincidence measurement was proceeding in the TCSPC under different voltages applied on the MZI. Two-photon $|11〉$ state was used, when one photon was injected into port a₁ and the other into port a₂. This input state leads to quantum interference at the first DC and after propagating through the phase shifter, transforms to the two-photon entangled state $\frac{1}{\sqrt{2}}\left(|20〉+e^{2i\phi }|02〉\right)$. Quantum interference at the second DC leads to output probability of coincidence measurement $P\propto \frac{1}{2}\left(1-\cos 2\phi \right)$, which has a period of π, half of that of the classical interference. The coincidence counts under different applied voltages on the phase shifter of the MZI, were measured and shown in Fig. 7(b). The voltage applied on the phase shifter was varied from 0V to 6V. The period of the fitting curve was 19.4 V², and the raw visibility was 73.2 ± 2.2%. Compared with previous works of interferences with degenerate-frequency photon pairs [23,24,26], the achieved visibility was relatively low. It was mainly due to the noise photons caused by spontaneous Raman scattering process, since the vector SFWM process was initiated by continuous wave pump light in this experiment. It can be expected that the visibility could be improved by using pulsed pump light or farther cooling the fiber to reduce the Raman noise photons.

It is worth noting that the two experiments with degenerate- and nondegenerate-frequency photon pairs are different in their interference processes. In the experiment of interference with degenerate-frequency photon pairs, the two interfered photons are undistinguishable, hence the path-entangled state, i.e. the NOON state, was achieved after the first DC. Although the raw visibility was not high, it showed properties of quantum interference. While in the experiment of interference with non-degenerate-frequency photon pairs, two photons are distinguishable in frequency, hence the NOON state could not be achieved after the first DC. In order to realize high visibility in the interference with nondegenerate-frequency photon pairs, bunching probability was measured. In both experiments, the MZI device performed well, showing that it could realize high visibility two-photon interferences on chip.

4. Conclusion

Scalability is the ultimate goal for any integrated quantum system. The SOS photonic chip fabricated by PLC technology was packaged with pigtail fibers and its insertion loss was successfully reduced to 1 dB. It was found that the small coupling loss between waveguides and fibers was one of the major advantages of the chip, which significantly improved the transmittance of photons and long-term stability of our setup. Interferences with both degenerate- and nondegenerate-frequency photon pairs were demonstrated in our integrated SOS chip, which were in telecom band and generated by SFWM in a DSF. A high visibility of 99.6% was achieved in the interference with nondegenerate-frequency photon pairs. The properties of quantum interference were demonstrated in the interference with degenerate-frequency photon pairs. These results proved the high performance of our chip and demonstrated its great potential applications for the fiber-chip scheme in quantum networks.