1. Introduction

The potential importance of entangled photon pairs in practical applications in communication [1], cryptography [2] and sensing [3] has led to a substantial research in recent years towards designing and fabricating a source that is compact, efficient, inexpensive and can be integrated with other components, preferably at the microchip scale, and with relaxed cooling requirements. Though bulk crystals and fiber optics have been the traditional go-to sources [4–6], semiconductor devices (and especially, a silicon device) have gained interest as they can be made using wafer-scale, low-cost, scalable CMOS-compliant manufacturing processes. Photon pair generation by means of spontaneous four-wave mixing have been demonstrated in three types of silicon devices: waveguides (conventional and photonic crystal), (single) micro-resonators, and coupled-resonator waveguides [7–18]. Resonators use the optical pump power more efficiently than waveguides, but are highly temperature-sensitive. Compared to the single micro-resonator, the coupled micro-resonator structure can theoretically achieve a higher pair generation rate [10, 16, 19], and benefits from having multiple spectral resonances in each passband [20]. Thus, if the chip temperature were to vary, one has only to tune to the nearest resonance, which is much nearer than one-half the free spectral range (FSR). The spectral gap between adjacent resonances, and thus, the tuning requirement, is inversely proportional to the number of coupled resonators [21]. As micro-resonators are usually tuned by local temperature variations, lowering the thermal stabilization and heating requirements is important for practical reasons.

In the case of energy-time entanglement, quantum correlations are investigated through a Franson type experiment, by violating Bell’s inequality [22, 23]. For silicon photonics, such measurements have been shown recently for the (single) microring resonator [15, 17, 18] and the photonic-crystal coupled cavity waveguide [16]. Here, we perform a similar experimental test of entanglement on photon pairs generated by our coupled-microring structure.

2. Experimental details

The device, fabricated in the same batch as the one described in Ref. [20], was pumped for spontaneous four-wave mixing (SFWM) with a TE-polarized light with an average power of few mWs (typically 3 – 5mW) in the waveguide (wavelength λ_p ≈ 1561.5 nm, pulse width = 8 ns and repetition rate = 15 MHz). Figure 1 describes the experiment, which is a coincidence measurement setup in which the arrival times of the simultaneously generated photons are analyzed using two independent interferometers [22]. The pump pulse width has to be selected to be longer than the path-length imbalance of the interferometers, which in turn has to be longer than the timing jitter of the detectors. The generated energy-time correlated signal and idler pairs are at λ₁ ≈ 1546.5 nm and λ₂ ≈ 1576.5 nm, respectively (generation probability = 6.7 × 10⁻⁴ pairs/pump pulse). The chip temperature was stabilized at 30.2°C. Photons at the output of the chip were spectrally separated using a three-port add/drop filter. After further filtering for pump rejection, the filtered bandwidths of the photons were about 0.6 nm (76 GHz) for λ₁ and about 1.0 nm (122 GHz) for λ₂. Note that it would have been preferable to use two filters of same bandwidth, wide enough to capture the entire photons spectra, but despite extensive search, we were unable to find telecom components complying with our requirements. In both the arms, collective insertion loss from cascaded filters was about 6 dB each.

 

Fig. 1 Photon pair generation using diode-pumped SFWM and entanglement characterization measurement through Franson interferometry. Two separate Mach-Zehnder interferometers (MZIs) are constructed, and separately stabilized using feedback based on transmission of the classical pump light. EDFA = Erbium doped fiber amplifier, FPC = Fiber polarization controller, EOM = Electro-optic modulator, ASE = Amplified spontaneous emission, DAQ = Data-acquisition card, SPAD = Single photon avalanche photo diode, TEC = Thermo-electric cooler, TCSPC = Time-correlated single photon counting. Blue lines refer to polarization-maintaining single-mode fiber and green lines to non-polarization-maintaining single-mode fiber.

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The photons were input into two separate Mach-Zehnder interferometers (MZIs). One arm of each MZI was made of polarization maintaining fiber (long arm) and the other of free-space polarization-maintaining optics elements (short arm), with an optical path-length difference ∆L = 56.55 cm. Equivalently, the path-length difference corresponds to a time delay ∆τ = 1.88 ns, which is indeed greater than the typical timing jitter (0.5 ns) of the off-the-shelf InGaAs single-photon avalanche photodetectors (SPADs) used here. The two MZIs were matched carefully: the difference between the (long arm − short arm) imbalances of the two interferometers was less than 0.16 cm, verified by time-of-flight measurements.

Each free-space path-length was actively (and separately) stabilized by using a piezoactuated positioner under computer control using feedback from a power-level measurement of the classical pump light which was fed through the interferometers. Using error propagation calculations on the dependence of MZI output power with the arm imbalance (phase difference), the stability of the MZI was calculated to be about ±0.1 radian, indicating that the length of the MZI variable arm was stabilized within about ±25 nm relative to the fixed arm. During the measurements of visibility, the signal MZI was scanned, whereas the idler MZI was held stationary.

The insertion loss of each MZI was 7 and 8 dB respectively, including ∼1dB excess loss at each of the input and output ports of the 50%/50% splitters, 3 dB loss at the fiber collimators, ∼1.5 dB excess loss at the fiber TE polarizer and ∼1 dB excess ∼ loss at the output 90%/10% coupler. In order to maintain a good signal-to-noise ratio for our coincidence measurements, we matched the singles rate of the two SPADs by balancing their respective quantum efficiencies in order to compensate for the insertion loss difference, as seen in Fig. 2(a). These loss values could be reduced in the future using an on-chip interferometric structure; however, the timing jitter of the InGaAs SPADs required that the MZI arm-length imbalance had to be about 56.55 cm (in air), and would require very low loss waveguides on chip (e.g., 0.5 dB/cm loss in waveguides with refractive index approximately 4). In this experiment, we did not attempt to make such waveguides, although the state-of-art in silicon waveguide fabrication is already not too far off this goal, and the requirements are eased if the timing jitter of the SPADs can be reduced [24].

 

Fig. 2 Full Franson Interferometer: (a) Singles from SPAD 1 (Signal) and SPAD 2 (Idler). (b) Output of the TCSPC for three gate configurations (corresponding to the SL, SS+LL and LS events) for two different interferometer phases (Φ = Φ₀ and Φ = Φ₀ + 180°). Each bin represented here is of 400 ps in width and the measurement time was 900 seconds for each events.

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To date, there have not been many measurements of Franson interferometry of pairs generated using silicon photonic waveguides or microrings, and there has been a few report each of using InGaAs SPADs [18] and superconducting detectors [15, 17]. One may contemplate that two-photon interference could be used as an on-chip entanglement monitor, thus stabilizing the performance of a practical device; however, the need for cryogenic cooling reduces one of the main benefits of silicon pair sources: room-temperature operation. In contrast, thermo-electrically cooled InGaAs SPADs have more modest cooling needs, and are used in many terrestrial, airborne and space systems at low cost. However, such off-the-shelf modules have greater timing jitter (∼0.5 ns), a larger hold-off time (∼10 µs) and a lower-bound (∼3 ns) on the electrical gate width. Here, photons were detected using InGaAs SPADs with an estimated 15% quantum efficiency and a gate width of 2.5 ns. The measured dark counts were 310 Hz and 115 Hz, for detector 1 and 2, respectively. Note that the detector temperature here (234K), and most likely in Ref. [18], was much higher than other Franson experiments, e.g., 77K [25] using Ge SPADs or 4K [15, 16] using superconducting detectors. Coincidence measurements were performed with a time-correlated single-photon counting (TCSPC) board (TimeHarp 260 PICO) over a period of 900 seconds, by cumulatively adding the contributions of 10 bins of width 100 ps.

3. Results and discussion

The goal of these measurements is to show that the coupled-resonator tunable-JSI pair source [20] generates entangled pairs using two-photon interferometry (rather than simply relying on a Schmidt decomposition of the JSI as we did earlier [20]). Such a measurement has recently been done for single silicon micro-resonators and photonic crystal structures but not yet for the coupled-microring device.

In each MZI, a photon (labeled ‘1’ or ‘2’) can take two equally-probable paths, short (S) or long (L), leading to four possible scenarios for the coincidence events measured at the TCSPC: |S₁L₂〉, |S₁S₂〉, |L₁L₂〉, and |L₁S₂〉. In the case of |S₁L₂〉 and |L₁S₂〉 since the two photons have acquired a relative time lag larger than the two photon correlation time, they are distinguishable from each other as well as from |S₁S₂〉 and |L₁L₂〉. For the remaining two processes, the intrinsic uncertainty in the emission time of a photon pair within the duration of a pump pulse makes them indistinguishable from each other. Thus, the bi-photon state |Ψ〉 reaching the detectors can be written as $|\Psi 〉=\frac{1}{\sqrt{2}}\left(|{\mathrm{S}}_1{\mathrm{S}}_2〉+|{\mathrm{L}}_1{\mathrm{L}}_2〉\right)=\frac{1}{\sqrt{2}}\left(|{\mathrm{S}}_1{\mathrm{S}}_2〉+e^{i\mathrm{\Phi }}|{\mathrm{S}}_1{\mathrm{S}}_2〉\right)$, where Φ = ϕ₁ + ϕ₂, with ϕ₁ and ϕ₂ being the phases of signal and idler MZI, respectively. The associated coincidence rate should exhibit an interference pattern, which should go from constructive to destructive for a phase change ∆Φ = π, as verified in Fig. 2(b). The incomplete disappearance at ∆Φ = π is attributed towards the background accidentals count.

There are several factors that contribute towards the accidentals counts, as observed in other reports [7–18], such as the amplified spontaneous emission of the pump leaking through the filters, the detector dark counts and the propagation losses encountered by the photon pairs in propagating from the output of the chip to the detectors via the filters and interferometers, which can cause broken pairs and thereby result in start-stop pair counting between separated time slots, rather than coincidences. The coincidence-to-accidentals ratio (CAR) is a simple quadratic function of the pair-generation probability per pump pulse, and is inversely proportional to it when the pair-generation probability increases (e.g., by stronger pumping). In fact, if maximizing the CAR was the only goal, it can be shown that the optimal pair-generation rate goes to zero as the losses improve or as the detector dark counts decreases e.g., with better technology. Since a vanishingly-small pair generation rate is neither useful nor measurable, we operated our device at a pair-generation rate of approximately 10 kHz (without scaling for the duty cycle of the pump pulses, or approximately 83 kHz after multiplying by the duty cycle of the pump), which results in an accidentals rate that is stable over the duration of the measurement to about an order-of-magnitude less than the coincidence rate. In similar 11-coupled-microring devices at lesser pump power, we have previously measured CAR of about 80 [9].

The path imbalance ∆τ ≫ τ_p (single-photon coherence time) ensures no single-photon interference events [22, 23]. Here, the single photon coherence time was estimated through the bandwidth (∆ν) of the detection filter: ∆ν ≈ 0.8 nm at 1550 nm implies τ_p ≈10 ps ≪ 1.88 ns. Figure 2(a) confirmed the absence of single-photon interference through the independence of the singles rate on Φ for both the SPADs. We also verified the independences of |S₁L₂〉 and |L₁S₂〉 coincidence counts over the same variation.

The cumulative value of the counts under the central peak shown in red in Fig. 2(b) was measured as the MZI phase of the signal interferometer was varied. The measured data were assumed to have an error bar of magnitude $\sqrt{\mathrm{N}}$, N being the number of coincidences measured during 900 seconds. The phase (horizontal axis) was inferred from the transmission of the classical pump light beam, using the standard power-versus-phase-imbalance relationship of a MZI. A fitting procedure, based on the Levenberg-Marquardt non-linear least-square curve fitting algorithm, confirmed the sinusoidal variation of coincidences with phase, as shown in Fig. 3. Each set of measurements took about 4 hours, over which time we could maintain the stability of both the MZIs, and of the input pump pulse-train in power and polarization, and both input and output chip-fiber couplings. An average value of accidentals, averaged over all the phase values, was subtracted from the measured coincidences, as shown by the dotted lines. A two-photon interference pattern fringe visibility V ≥ 70.7% implies that the generated pairs are quantum-mechanically correlated, i.e., entangled [26], without necessarily providing a test of local realism. In Fig. 3, we show V in excess of this threshold value for two adjacent spectral peaks in the transfer function of the device after subtracting the accidentals (the raw V without subtracting accidentals are 68.1±5% and 55.1±4.2% for Fig. 3(a) and Fig. 3(b), respectively).

 

Fig. 3 Two photon interference pattern of |Ψ〉 for two different pump wavelengths: 1561.64 (a) nm, (b) 1561.86 nm. These wavelengths correspond to adjacent transmission resonances within a single passband of the device. Red circle = experimental coincidence data, Black solid curve = Fit to the experimental data, Black dashed line = Average accidentals, Black circle = Individual accidentals.

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In Fig. 3, the pump wavelength was aligned to two adjacent peaks of the transmission spectrum which were separated by 0.2 nm. As we have shown earlier [20], this range of wavelength tuning is equivalent to varying the chip temperature by 7°C. The presence of multiple transmission peaks in the passband of the coupled-resonator struture makes it possible to vary the pair generation properties by tuning to a nearby peak that is only 0.2 nm away. In contrast, a single microring device would have to tune by at least one-half of the FSR, which corresponds to changing the chip temperature by more than 40°C [9] before encountering another resonance.

Based on our earlier studies [20], the neighboring spectral peaks in the transmission spectrum are also expected to be useful in generating entangled photon pairs with visibilities V ≥ 70.7%. To confirm this, we used a folded Franson interferometer [25]: a simplified experimental set-up, where both the photons go through a single MZI, as represented in Fig. 4. This experimental configuration is simpler to use and stabilize, enables all the spectral filtering to be performed after the interferometer, and would occupy less space on a chip when integration is attempted in the future. The relative group delay shift accumulated between the ‘signal’ and ‘idler’ photons, separated in wavelength by about 30 nm, in propagating through a few meters of SMF-28e fiber was ignored in comparison to the SPAD timing jitter. The singles-versus-phase plot and coincidence binning plots for this set-up are shown in Fig. 5; in this case, the singles counts were not intentionally balanced as in the previous case. Because of mechanical damage to the chips during repeated and prolonged testing, we had to use a different device in these additional measurements, which had a similar, but not identical, transmission spectrum. Nevertheless, when the pump wavelength was aligned within the passband to the same transmission peaks as used in Fig. 3, the measurement of interference patterns in the folded Franson interferometer shown in Fig. 6(c) and (d) resulted in values of V similar to those reported in Fig. 3. Since this experiment was easier to operate, involving one feedback-stabilized interferometer, rather than two, we also measured V for two other transmission resonances of the pump, as shown in Fig. 6(a) and (b). We believe that there is a relationship between the two-photon interference visibilities, V, and the two-photon Joint Spectral Intensities (JSI’s) measured in Ref. [20], but have not fully investigated the connection yet.

 

Fig. 4 Photon pair generation using diode-pumped SFWM and entanglement characterization measurement through a folded Franson interferometry. Notice the simpler apparatus for stabilizing the interferometer, compared to Fig. 1.

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Fig. 5 Folded Franson Interferometer: (a) Singles from SPAD 1 (Signal) and SPAD 2 (Idler). (b) Output of the TCSPC for three gate configurations (corresponding to the SL, SS+LL and LS events) for two different interferometer phases (Φ = Φ₀ and Φ = Φ₀ + 180°). Each bin represented here is of 300 ps in width and the measurement time was 900 seconds for each events.

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Fig. 6 Two photon interference pattern of |Ψ〉 for four different pump wavelengths: (a) 1555.66 nm, (b) 1555.99, (c) 1556.21 nm, and (d) 1556.39 nm. These wavelengths correspond to transmission resonances within a single passband of the device. Red circle = experimental coincidence data, Black solid curve = Fit to the experimental data, Black dashed line = Average accidentals, Black circle = Individual accidentals.

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4. Conclusion

In summary, we have shown two-photon (Franson) interference of spectral lines of photon pairs generated using a silicon photonic chip at room-temperature, pumped by only a few milliwatts of optical pump power, and using commercially-available thermo-electrically cooled InGaAs SPADs at 234K. We have reported measurements of time-energy entangled photons using both unfolded and folded Franson interferometers. Taken together, these results suggest it may be possible to realize an inexpensively-fabricated, chip-scale entangled photon pair source with low tuning power consumption, integrated with an entanglement monitor operating at a modest cooling budget, which may be useful for practical applications.

5. Appendix

5.1. Device: Coupled resonator optical waveguide (CROW)

Our devices were fabricated at IME - Singapore using CMOS-compatible process on SOI wafers. Two etch steps were used to give a rib waveguide cross-section of height 220 nm, width 550 nm, and slab thickness 70 nm. The device collectively spans a distance of 0.23 mm on the silicon chip, consisting of 11 micro-ring resonators in a racetrack configuration, with bending radii R = 10 µm, directional couplers of interaction length L_c = 10 µm, and interwaveguide gap of 300 nm. The waveguide supports two transverse electric (TE) and one transverse magnetic (TM) polarization but due to bending loss from the micro-ring only lowest order of TE polarization survives and propagates. They were singulated into chips for testing using edge-coupled waveguide-to-fiber tapers. Based on a separate calibration measurement, the respective fiber-to-waveguide insertion loss and the device propagation loss were estimated to be 4.3 dB and 1.4 dB. As shown in Fig. 7, the transmission spectrum of the CROW consists of a series of passbands and stopbands. In our 11 ring CROW, the spectral width of each passband was about 1.75 nm with a free spectral range (FSR) of 7 nm. The light was transmitted through the chip in a disorder-tolerant slow light regime, with a wavelength dependent group index between 24 and 40 (greater values at the shorter wavelengths) [27]. Even though there were 11 resonance peaks (Bloch modes) in a given passband, due to fabrication imperfections, only the central five peaks (P1–P5) contributes to the measured JSI [20].

 

Fig. 7 Classical transmission for 11 ring CROW. Signal, Idler, and Pump passbands are shown in green (left), blue (right), and red (center), respectively. The most prominent central five peaks are labeled as P1 – P5. P1, P3, P4, and P5 are used in the measurement. (a) Chip used for Full Franson measurement. (b) Chip used for folded Franson measurement

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Since CROW supports multiple resonant wavelengths in a given passband with energy and momentum conditions satisfied, different pump wavelengths within a span of few nanometers can be used to generate photon pairs.

Acknowledgments

The authors are grateful to Xianshu Luo and Guo-Qiang Patrick Lo (IME, ASTAR, Singapore), Nick Bertone (Optoelectronic Components), Jim Rose (Keysight Technologies) and the National Science Foundation for support (ECCS 1201308).

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