## Abstract

Near-infrared Hong-Ou-Mandel quantum interference is observed in silicon nanophotonic directional couplers with raw visibilities on-chip at 90.5%. Spectrally-bright 1557-nm two-photon states are generated in a periodically-poled KTiOPO_{4} waveguide chip, serving as the entangled photon source and pumped with a self-injection locked laser, for the photon statistical measurements. Efficient four-port coupling in the communications C-band and in the high-index-contrast silicon photonics platform is demonstrated, with matching theoretical predictions of the quantum interference visibility. Constituents for the residual quantum visibility imperfection are examined, supported with theoretical analysis of the sequentially-triggered multipair biphoton, towards scalable high-bitrate quantum information processing and communications. The on-chip HOM interference is useful towards scalable high-bitrate quantum information processing and communications.

© 2013 OSA

## 1. Introduction

In recent years, quantum information has been popular for its robust applications on cryptography [1–5], computation [6–8] and communication [9,10], and chip-scale cavity quantum electrodynamics [11] involving single photons and single excitons [12–16]. Working with biphoton or multiphoton states and atom-photon interactions, entanglement in various degrees of freedom [17–20], such as time-energy [21,22], spatial-momentum, and polarization [23] has been utilized to harness the efficiency and complexity of quantum information processing. While the recent breakthrough experiments are typically achieved in free-space, emerging measurements of on-chip bi-photon interference [24–29], C-NOT gates [26,29–31] and Hadamard gates [29] have benefited from the arrayed scalability in the nanophotonics platform and potentially robust phase-sensitivity of chip-scale samples albeit with the challenges of device nanofabrication, design, and low-fluence single photon level measurements against chip-scale Rayleigh-scattering photon and coupling losses. In the silica system with remarkable phase control, visibilities up to 98.2% were observed [24]; in the compact silicon system, raw visibilities up to 80% were observed [25]. Most chip-scale measurements have been performed at the visible wavelengths and with bulk nonlinear crystal sources, although there are some recent instances at near-infrared and telecommunications wavelengths [32–34].

Here we report observations of near-infrared Hong-Ou-Mandel (HOM) quantum interference in chip-scale silicon nanophotonics circuits, introducing the biphoton experiments to the integrated optics regime. Employing spectrally-bright type-II periodically-poled KTiOPO_{4} waveguides (PPKTP) as the entangled photon source, we demonstrate raw quantum visibilities up to 90.5% on-chip—one of the highest visibilities observed in the silicon CMOS-compatible platform. Furthermore, we evaluate the various sources of residual visibility degradation including multiphoton pairs, chip-scale excess loss and non-ideal splitting ratios, and polarization effects. The observed interference visibility matches our theoretical predictions, for the different symmetric and asymmetric integrated directional couplers examined.

## 2. Near-infrared Hong-Ou-Mandel experimental setup

Figure 1
illustrates the experimental setup. A 1-cm periodically-poled KTiOPO4 waveguide [35] from AdvR serves as the source for indistinguishable photons [36]; in this case, the waveguide is poled and designed for quasi-phase-matching and high-fluence spontaneous parametric downconversion (SPDC) at approximately 1556-nm to 1558-nm wavelengths. We use a relatively high power (100-mW; QPhotonics QLD-780-80S) semiconductor laser diode as the pump for sufficiently high biphoton rates at approximately 10^{7} per second, to compensate for minimal losses in the fiber and free-space chip coupling setup. The laser is thermally-tuned and stabilized by self-injection locking to 778.9-nm, which is exactly half of the center working wavelength of the PPKTP waveguide. The temperature of the PPKTP waveguide is typically controlled to ~25°C for optimal phase matching. A long-pass-filter with cutoff at 1064-nm (Semrock BLP01-1064R-25) blocks pump photons after the SPDC process, and a band-pass filter with 3-nm (Semrock NIR01-1570/3-25) passes the non-degenerate biphoton states. The polarization controller right before the fiber-based PBS is used to tune the polarization so that the fiber-based polarization beam splitter (PBS) spatially separates the correlated photons. In one branch, a tunable delay is realized by a retroreflector (Thorlabs PS971-C) and a picomotor stage with loss less than 1-dB. In both branches, polarization controllers are introduced to respectively change the polarization of each channel to match the transverse magnetic (TM) mode for coupling into the chip waveguides (Fig. 1(b)).

The chip coupling setup is built with six aspheric lenses, each mounted on individual three-axis precision stages. The two input and output beams are separated by a D-shaped mirror after 60 cm divergence to avoid crosstalk. Single and coincidence measurements are performed by two InGaAs single photon Geiger-mode avalanches detectors D_{1} and D_{2} from Princeton Lightwave, with ~300 ps gate widths and ~20% detection efficiencies. The clock of D_{1} is set to 15 MHz, and its output signal triggers D_{2}. This allows the coincidence rate to be read directly from the D_{2} counting rate, with the optical delay calibrated to compensate the electronic delay.

## 3. Design and fabrication of silicon chip-scale two-photon interference directional coupler

To ensure good quantum interference on-chip, we examined the design space of the directional couplers, in both transverse electric (TE) and TM polarization states as shown in Fig. 2
. Differential gap widths (*g*), cross-over coupling lengths (*l _{c}*) and waveguide widths (

*w*) are illustrated for the optimal coupling length and splitting ratios. The silicon waveguides are designed with a 250-nm thickness and for operation at 1550-nm wavelengths.

To calculate the phase velocity of different polarization and symmetry, we use the frequency-domain Maxwell equation fully-vectorial eigenfrequency solver (MPB), which computes by preconditioned conjugate-gradient minimization of the block Rayleigh quotient in a planewave basis [37]. The cross-over coupling length *l _{c}* of the two waveguides is then represented as ${l}_{c}=\pi /({v}_{p,sym}-{v}_{p,anti\text{s}ym}),$ in which the phase change of

*π*between the symmetric mode and anti-symmetric mode [38] allows for complete crossover from one waveguide to another [39] in an ideal scenario. For a perfect 50-50 splitting ratio, the desired length for the coupler should be

*l*is the effective coupler length for the incoming and outgoing bend regions, which can be estimated by an integral of coupling length as a function of gap size along the bending region and computed to be 3-um in our designs (Fig. 1(b)). In addition to the MPB and integral computations, the designs were examined with both rigorous finite-difference time-domain computations and semi-vectorial BeamPROP method from RSoft. With the birefringent character of the directional coupler, we work with the TM mode rather than the TE mode due to its shorter coupling length and greater length control sensitivity. Furthermore, our simulation models and experimental measurements confirm lower loss in the TM mode for straight waveguide as well as the directional coupler regime due to lower electromagnetic field amplitude at the sidewalls (typically rougher than the top and bottom surfaces) [40–43]. The lower loss helps to increase the coincidences count rates and reduce the internal phase shift fluctuations of directional coupler. A quantitative calculation suggests the loss of TE mode is 7.4 times higher than TM mode for a consistent sidewall roughness. In one optimized instance, the waveguide width and coupler length for TM symmetric splitting is chosen to be 400-nm and 15-um, respectively, as illustrated in Fig. 2 (Design 1). In this design, the corresponding TM-polarization splitting ratio imbalance (SR), or the ratio of the transferred light to the transmitted light, was numerically computed to be less than -20-dB, limited by the computational accuracy. The TE-polarization SR is computed by to -9-dB. The excess loss at the optimized directional coupler of Design 1 is estimated to be 0.1-dB by finite-difference time-domain computations.

_{eff}Further increasing the coupler length will change the SR, which could be determined by:

_{$V={\text{2SR/(1+SR}}^{2})$}[24,44]. The visibility is 100% for a perfect beam splitter but is estimated to reduce to 97%, 80% and 47% for splitting ratio imbalances of 1-dB (1.27 × ), 3-dB (2 × ), and 6-dB (4 × ) respectively. For balanced chip-scale splitting, we note that multi-mode interference [25] and Y-splitters are also good elements for physical realization. Directional couplers on the other hand provides differential and accurate thermal tuning on the SR, enabling controlled asymmetries such as for various C-NOT gate [26,30,31], quantum cloning [45,46], and Fock state filtration [47,48] applications.

Supported by these designs, the devices were next fabricated at the Institute of Microelectronics. Silicon-on-insulator wafers were used, with 248-nm deep-ultraviolet lithography for resist patterning. Sidewall roughness was minimized by optimized lithography, resist development and etching. The measured linear scattering loss of 3-dB/cm in the channel waveguides is determined by folded-back (paperclip) waveguide structures. The inverse couplers are implemented with a tapered silicon nanotaper [49] and top oxide cladding as shown in Fig. 1(c). The samples are diced and prepared for measurement. The typical total lens-chip-lens coupling loss is approximately 11-dB, or a -14-dB transmission including the -3-dB on-chip splitting. With a measured waveguide propagation loss of 3-dB/cm, the estimated facet coupling loss is 4-dB/facet. Taking into account the waveguide-to-fiber coupling, transmission efficiencies of optical components, and detector efficiencies, the overall single photon detection efficiency is estimated near 1% from source to detector.

## 4. 1557.8-nm Hong-Ou-Mandel visibilities on-chip

For a pump power of 2.5-mW, the single photon rates after the chip are determined to be about 1000 per second, with dark count rates around 200 per second. The coincidence rate is about 1 pair per second through the silicon photonic chip, with about 1/600 accidental photon pairs per second. With our sequential triggering approach (detector D_{2} triggered by D_{1}), instead of time-tagging, the coincident dark counts are negligible. An example coincidence versus the relative optical delay is illustrated in Fig. 3(a)
, with the observed near-infrared Hong-Ou-Mandel quantum interference on-chip.

These measurements are performed on a device carefully selected from an array of devices, particularly one with splitting ratio imbalance of less than 1-dB. The sweep resolution and integral time near the dip are set at 50-um and 1200-seconds respectively, which are twice higher compared to that away from the zero-delay point. During the 21-hour measurement, we observed small coupling drifts with slightly lower coincidence rate on the negative relative delays. The optimized lowest coincidence is 25 per 600 seconds with a swing coincidence (away from the zero-delay point) of 499 per 600 seconds, giving a raw quantum visibility of 90.5%. The visibility is 90.8% after background accidentals subtraction. An inverse triangle fit [50,51] is used to estimate the shape of the dip. The measured base-to-base width of Hong-Ou-Mandel dip is 1.36 mm ± 0.07 mm, corresponding to two-photon coherence time of 4.53 ps, or an obtained two-photon bandwidth of 1.79 nm, comparable to 3nm bandpass filtering bandwidth.

## 5. Degradation of on-chip HOM interference visibility

To further uncover the degradation of HOM interference visibility, we compare it with that of a fiber beam splitter (without chip) as illustrated Fig. 3(b). We plot the visibility against different pump powers or the mean photon pair number to estimate the effects of the chip on the visibility. Since a higher pump power with more biphoton pairs will cause a higher probability of multiple biphoton pairs in one detector gate window, the visibility is inversely proportional to the pump power [35]. Here we note that the effect of multipair biphoton generation in our sequential triggering approach is slightly different from the time-tagging approach. For a baseline model, we assume that the two detectors have uniform detection efficiencies, gate widths and response times, with small timing jitter compared to the gate width. Then the probability of *n* photon pairs generated in the gate time *τ* obeys Poisson distribution: $p(t,n){|}_{t=\tau}={(\lambda \tau )}^{n}{e}^{-\lambda \tau}/n!={a}^{n}{e}^{-\alpha}/n!,$ where *α* is mean pair number within the gate [52]. To maximize the coincidences, the photon transmitted to the triggered detector is delayed by half the gate time (*τ/2)* to guarantee it will always appear within the gate whenever the other photon arrives first (Fig. 4(a)
). To calculate the swing coincidences, or the probability of the coincidence event when two photons are relatively delayed and totally distinguishable, we consider only one photon pair per gate to neglect higher order terms (Fig. 4(a)):

*η*denotes the overall detection efficiency. To calculate the probability of coincidence when two photons are indistinguishable, we consider only one and two photon pairs within the gate. Here we notice that even when there is only one photon pair within the detection gate of triggering detector D

_{1}, there are still some coincidences contributions (Fig. 4(b)):

_{1}, there are four possible situations: (a) the first photon pair is in the path to D

_{1}, and second photon pair is in the path to D

_{2}(Fig. 4(c)); (b) the first photon pair is to D

_{2}, and the second photon pair is to D

_{1}; (c) both photon pairs are to D

_{2}; (d) both photon pairs are to D

_{1}. Thus we have

From fitting the on-chip result with the same slope as suggested by the above theory, 6% of the imperfect visibility is therefore likely due to the multiphoton pairs. The residual 3% is likely to be induced by the chip. To further understand the chip mechanisms for visibility reduction, we next compared the visibility for different splitting ratios. We selected two devices with coupler lengths of 28-and 30-um (Design 2 and 3), which has the TM mode splitting ratio imbalance of about 3-dB and 6-dB as measured. The comparison of the coincidence measurements between the three silicon chip devices is shown in Fig. 5(a) . The inverse triangular fit is utilized to estimate the visibility and corresponding deviations. For the 28-um directional coupler, the visibility is measured to be 74 ± 8%, close to the theoretical estimate of 80%. For 30-um directional coupler, the visibility after fitting is 31 ± 11%, compared to the theoretical estimate of 47%, in similar ballpark. The deviations here from theory are due to on-chip directional coupler internal loss and high pump power. For our optimal 15-um directional coupler (Design 1), the less than 1-dB splitting ratio imbalance (limited by the precision of lens-chip coupling loss variations) with its 97% theoretical visibility can therefore account for a sizable portion of the residual 3% decrease in visibility.

Moreover, to understand the quantum interference effect with variation of polarization, we rotate the polarization for one branch of the input path before the chip using a half-wave plate. The resulting visibility versus the linear polarization angle is depicted in Fig. 5(b). The result shows cosinusoidal behavior that reaches maximum visibility with no polarization rotation, and diminished visibility with orthogonal polarization. The maximum visibility in this set of measurements is 83% due to the higher pump power of 5-mW. Here we note that the different splitting ratio of TE mode does not affect the visibility, as it does not participate in the quantum interference. In our measurements, the input polarizations are optimized and hence unlikely to be cause of the residual 3% decrease in visibility.

Another major possible contribution to the chip-induced visibility reduction can be from excess loss of the directional coupler. An ideal free space beamsplitter gives a 180˚ phase shift for one path of reflection and 0˚ for the other path, while fiber-based beamsplitter or directional coupler should give both 90˚ phase shifts for reflected light compared to transmitted light (not the relative phase shift of the biphoton state) to satisfy energy conservation. The sum of these phase shifts, or the inherent phase shift, accounts for the 180˚ phase difference between the probability amplitude of the *A _{tt}*and

*A*

_{rr}_{causing the Hong-Ou-Mandel dip. When the on-chip directional coupler has excess loss Lexcess, however, the inherent phase shift will not be 180˚ anymore. Performing a matrix optics calculation, we have the inherent phase shift $\psi $ as $\mathrm{cos}(\psi )={L}_{excess}^{2}{(1+SR)}^{2}/2SR-1,$ or $2{L}_{excess}^{2}-1$for an ideal symmetric (SR = 0-dB) directional coupler. The visibility reduction caused by the excess loss of the directional coupler can therefore be expressed as}

## 6. Conclusion

We have observed 1550-nm Hong-Ou-Mandel interference in silicon quantum photonic circuits, with raw quantum visibility up to 90.5% in near-symmetric directional couplers. With thermally-stabilized spectrally-bright PPKTP chip-scale waveguides as the entangled biphoton source, we examined the constituents of residual visibility degradation through numerically-designed directional couplers, multiphoton pairs, polarization effects, excess loss, and imperfect internal phase shifts. With our sequential triggering approach for negligible coincidental dark counts, we present the theoretical analysis for multipair biphoton contribution to Hong-Ou-Mandel visibility reduction. The results presented here support the scalable realization of two-photon interaction elements on-chip, for quantum information processing and communications.

## Acknowledgments

The authors acknowledge discussions with Fangwen Sun, Philip Battle, Tony Roberts, Joseph Poekert, Mark Itzler, Xingsheng Luan, Andrzej Veitia, and Felice Gesuele. We acknowledge the scanning electron micrograph images of Fig. 1(c) from James F. McMillan. This work is supported by the DARPA InPho program under contract number W911NF-10-1-0416.

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