Abstract

Integrated sources of indistinguishable photons have attracted a lot of attention because of their applications in quantum communication and optical quantum computing. Here, we demonstrate an ultracompact quantum splitter for degenerate photon pairs based on a monolithic silicon chip. It incorporates a Sagnac loop and a microring resonator with a total footprint of 0.011mm2, generating and deterministically splitting indistinguishable photon pairs using two-photon interference. The ring resonator provides an enhanced photon generation rate, and the Sagnac loop ensures the photons travel through equal path lengths and interfere with the correct phase to enable the reversed Hong–Ou–Mandel (HOM) effect to take place. In the experiment, we observed a HOM dip visibility of 94.5±3.3%, indicating the generated photons are in a suitable state for further integration with other components for quantum applications, such as controlled-NOT gates.

© 2015 Optical Society of America

Integrated photonic circuits have emerged as a promising approach to quantum technologies such as quantum cryptography, which offers provably secure communication [1], and quantum information processing, where for certain computational tasks an exponential speed-up is predicted compared to classical information processing [2,3]. Sources of single photons and entangled pairs of photons are essential to many schemes for long-distance quantum communications and optical quantum computing, and, in particular, pairs of photons that are degenerate in wavelength and indistinguishable from one another have proven useful in proof-of-principle demonstrations of photonic logic gates [4], quantum algorithms [3], entanglement generation [5], and quantum simulations [6]. Degenerate pairs have traditionally been generated using spontaneous parametric downconversion in bulk nonlinear crystals [7]. However, on-chip photonic circuits with integrated sources of indistinguishable photon pairs are required in order to make this technology scalable.

Recently, pair generation has been demonstrated in silicon waveguides using spontaneous four-wave mixing (SFWM), potentially allowing integration of photon sources and circuits with electronic elements [810]. While nondegenerate photons can be split by wavelength demultiplexing, this is not possible for degenerate photon pairs, since the two photons share the same properties in all degrees of freedom: spatial, wavelength, and polarization [1113]. Splitting these photons probabilistically with a 5050 directional coupler means they are no longer useful for some tasks; for example, a Hong–Ou–Mandel (HOM) dip with probabilistically split photons is limited to a visibility of 50%. An elegant solution is to deterministically split the photons using time-reversed two-photon HOM interference. So far, this has been demonstrated in fiber Sagnac loops [1416] and with planar waveguides in a Mach–Zehnder interferometer (MZI) [17,18]. In those schemes, a degenerate pair is created in one of two waveguides, which are then combined at a 5050 coupler in-phase such that the pair splits into two single photons, in a reversal of the usual HOM experiment where two single photons meet at a coupler and bunch into a pair.

In this Letter, we demonstrate degenerate pair generation and deterministic splitting using an integrated Sagnac loop for the first time (to our knowledge). Additionally, the actual generation of photon pairs takes place in a ring resonator coupled to the Sagnac loop, providing a high nonlinearity and a much smaller footprint compared to conventional silicon nanowires, hence enhancing the generation efficiency of the photon pairs, as well as ensuring the photons are created in well-defined cavity modes and hence have suitable properties for quantum experiments [19,20]. This circuit is ultracompact, with a 50 times smaller area than the silicon MZI-based circuit in Ref. [17], and is intrinsically stable, requiring zero tunable elements. For previous implementations in fiber loops and on-chip MZIs, active tuning of the phase to split the photon pairs was required. In our Sagnac configuration, however, the photons in the generated pair are automatically in phase with each other. We believe that this compactness, its compatibility with current CMOS technology, and the absence of phase tuning will lead to convenient scaling to more complicated circuits requiring multiple sources.

Figure 1(a) shows a schematic of the working principle. A Sagnac loop is formed by a silicon multimode interference (MMI) coupler, whose two outputs are connected. A silicon ring resonator is coupled to the loop serving as the nonlinear device for degenerate photon-pair generation via the SFWM process, as illustrated in Fig. 1(b). When the ring is pumped at two resonant frequencies, ωp1 and ωp2, one photon at each frequency is annihilated to generate two correlated photons at the central resonant frequency ωs,i=(ωp1+ωp2)/2 according to energy conservation. When the ring is pumped simultaneously in both the clockwise (cw) and counterclockwise (ccw) directions, in a power regime where multipair generation is unlikely, the output photon pair state from the ring resonator is

|Ψring=|2cw|0ccw+eiδφ|0cw|2ccw2.
The δφ term in the equation indicates the relative phase of the photons generated between the cw and ccw directions. The probability of generating photon pairs in one direction should be exactly the same as the probability of generating photon pairs in the other direction. The corresponding output state after the MMI is given by
|ΨMMI=1eiδφ2|Ψ2002+i(1+eiδφ)2|Ψ11,
where |Ψ2002=(|2A|0B|0A|2B)/2 and |Ψ11=|1A|1B. A and B denote the two output ports of the MMI coupler for the photon pairs. The beam splitter transformation of the MMI gives a π/2 phase shift between the two directions for each pump, so that if the two pumps are injected into the same input, the total phase δφ=π, and the output state is |Ψ2002. However, by injecting the pumps from two separate input ports, we ensured a total relative phase of zero (δφ=0), with the π/2 phase shifts of the two pumps cancelling out. As a result, when the photon pairs generated from the ring resonator reach the MMI coupler from the Sagnac loop side, they will split deterministically, leaving |ΨMMI=|Ψ11.

 figure: Fig. 1.

Fig. 1. (a) Schematic of the working principle: waveguides A and B, connected to two grating couplers, reach the same side of a multimode interference coupler (MMI), whose two output ports are connected, forming a Sagnac loop; a silicon ring resonator is coupled to the Sagnac loop in order to enhance the photon-pair generation rate. (b) Schematic of degenerate photon-pair generation via SFWM. Two pump photons at different wavelengths are annihilated to create a pair of degenerate single photons.

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Figure 2 shows the experimental setup. The two pump waves were generated by spectrally slicing the broadband (30 nm bandwidth) output of a mode-locked erbium-doped fiber laser (38.6 MHz) using a spectral pulse shaper (SPS, Finisar Waveshaper). This allowed two short pump pulses to be synchronized temporally. The resulting pump waves were flattop-shaped with a spectral bandwidth of 0.1 nm centered at λp1=1540.8nm and λp2=1558.1nm, corresponding to two resonances of the ring resonator separated by four free spectral ranges. The 0.1 nm bandwidth for both pumps is approximately twice the full width at half-maximum (FWHM) of the ring’s resonances, ensuring the resonances are covered and that the cavity defines the spectra of the photons, not the pumps. After the spectral splicing, a low-noise erbium-doped fiber amplifier (EDFA, Pritel) was employed to amplify the pump power. A fiber 5050 coupler was used to split the pumps into two separate fibers, in order to inject pump 1 into port A and pump 2 into port B of the sample. Tunable filters (Santac and Dicon) were then used to let only one of the two pump waves pass, in order to prevent leakage from the undesired pump and ASE noise. Polarization controllers were used to match the pumps’ polarizations to the waveguide’s TE mode, as the on-chip grating couplers used to couple light to and from the sample and waveguides were designed to support the TE mode only. In our experiment, each grating coupler gave 5.7 dB loss at the wavelength of the degenerate photon pairs (1549.4 nm), and the grating couplers’ 3 dB bandwidths were measured to be 30nm. A circulator was used at each input to separate outgoing light for collection. The gray area in Fig. 2 shows a scanning electron microscope (SEM) image of the silicon-on-insulator sample. It was fabricated at IMEC through ePIXfab using 193 nm deep UV lithography [21] and has a device footprint of 207μm×54μm=0.011mm2. The splitting ratio of the MMI inside our device was measured to be 4951 near 1550 nm. The nanowires and the ring resonator have cross-section dimensions of 450nm×220nm, with a propagation loss of 3 dB/cm. This waveguide has an anomalous dispersion in the telecom C-band, and hence has a high SFWM efficiency. The effective interaction length in the resonator is much longer than the silicon bus waveguide, so SFWM from inside the ring is dominant compared to that of the bus waveguide. The on-chip ring resonator has a radius of 21 μm, and its Q factor was measured to be 4×104, with a free spectral range of 4.33 nm near 1550 nm. To minimize the device propagation loss, the total length of the silicon nanowires was kept <0.4mm, connected by tapered silicon waveguides on each side. During the experiment, the on-chip powers of the two pump waves were matched to maximize the degenerate SFWM efficiency [22].

 figure: Fig. 2.

Fig. 2. Experimental setup. A broadband mode-locked laser was spectrally sliced into two synchronized pumps using a spectral pulse shaper (SPS) and subsequently amplified by an erbium-doped fiber amplifier (EDFA); a fiber 5050 coupler was used to split the pumps into two; bandpass filters (BPFs) were used to ensure only pump λ1 was injected to port A and only pump λ2 was injected to port B; polarization controllers (PCs) matched the pumps to the TE mode required by the waveguide. Right before injecting the pump waves into the sample, a circulator on each side was inserted for collection of generated single photons. After coupling the photons out from the sample, BPFs were used to reject the pumps. The photons were then either directly connected to superconducting single photon detectors (SSPDs) or connected through a HOM setup consisting of tunable delay lines, PCs, and a fiber 5050 coupler (indicated inside blue lines); the gray area inside the figure shows a SEM image of the device.

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Light coupled off-chip, after having been separated from the incoming pump light by the circulators, was sent to two bandpass filters tuned to the degenerate photons’ wavelength of 1549.4 nm, to provide a total pump isolation of 100 dB. After the spectral filtering, the photons coming out from the two sides were directed to two separate superconducting single photon detectors (SSPDs, Single Quantum, 10% detection efficiency with 100 Hz dark count, polarization sensitive). Finally, coincidence measurements were conducted using a time interval analyzer (TIA). Degenerate photons generated and successfully split by the Sagnac and microring circuit should emerge from separate outputs and register as coincidences between the two detectors.

Throughout the experiment, the TIA was used to obtain the raw coincidence rate (Craw) and accidental coincidence rate (A) [10]. The true coincidence count was then calculated as Ctrue=Craw-A. We plotted the count rate versus total coupled average power in Fig. 3. Detected photon pair coincidences (red circles) far exceed the accidental coincidences (green triangles), demonstrating correlated photon-pair generation. A quadratic fit of the true coincidences is shown. The quadratic dependence of the coincidence rate on power is a signature for SFWM processes. A roll-off of the coincidence rate when power is above 100 μW is due to the two-photon absorption inside the ring resonator and corresponding free-carrier absorption [23]. We also plot the measured coincidence-to-accidental ratio (CAR) on the right y axis at different pump powers. In our experiment, we recorded a maximum CAR of 235±21 at an average pair detection rate of 1.4 Hz. At a greater detection rate of 3.9 Hz, the CAR was measured to be 61±3.

 figure: Fig. 3.

Fig. 3. Counts (left axis) and coincidence-to-accidental ratio (CAR, right axis, purple squares, with error bars) as a function of coupled average power. Measured raw coincidences (red circles, Craw), accidental coincidences (green triangles, A), and true coincidences (blue diamonds, Ctrue=Craw-A) are shown in the plot. The blue line is a quadratic fit of Ctrue, when coupled Pavg<90μW. With coupled power higher than 100 μW, the counts are rolling off from the fit due to two-photon absorption and free-carrier absorption.

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Detection of correlated pairs between the two outputs does not necessarily indicate that time-reversed HOM interference took place, because even if the photons behave according to classical statistics at the MMI, up to 50% of the pairs can emerge from separate outputs. In order to test the time-reversed HOM interference, we measured the splitting ratio of the photon pairs. Having first measured the coincidence rate between the two outputs, we added a 5050 coupler after the spectral filtering at each output from the sample, and connected the two outputs of the 5050 couplers to SSPDs. Any photon pairs emerging from the same output would probabilistically split at these couplers, yielding a 50% probability of measuring a coincidence count. In this way, we performed coincidence measurements purely from the photons that emerged from Port A, and then performed the same coincidence measurements purely from photons that emerged from Port B. Finally, by comparing the number of pairs coming out from the same port to the number of photon pairs coming out from two separate outputs of the sample, the splitting ratio can be calculated. At a total coupled pump power Pavg=36.4μW, we found that 88.9±6.7% of the pairs were emerging from separate outputs, indicating that the time-reversed HOM effect was successfully splitting the photons, as this is a significantly larger proportion than the 50% expected from probabilistic splitting.

To further elaborate our result on the photon splitting ratio, we changed our pump configuration so that both pump waves were injected to the same input of the Sagnac loop, setting the relative phase of the photons’ state in the ring to δφ=π. As a result, when the photons generated from the ring resonator arrive at the MMI coupler, they should always bunch and emerge from the same output port (|ΨMMI=|Ψ2002). Under this new pump configuration, we measured the splitting ratio. As seen in Fig. 4 (bottom), 43.5±4.4% of the pairs came out together from port A of the Sagnac loop and another 44.7±4.5% of the pairs came out together from port B of the Sagnac loop; together, 88.2±9.0% of the photon pairs are emitted in a bunched state, |Ψ2002. Note that this is a NOON state with N=2 and has applications in quantum metrology for enhanced measurement of a phase [24].

 figure: Fig. 4.

Fig. 4. Count rate for split (|11) and bunched (|20 and |02) pairs. Top: When two pumps were injected separately into the two ports of the sample, a splitting ratio of 88.9±6.7% after subtracting noise was achieved. Bottom: When two pumps were injected together into one of the ports of the sample, a bunching ratio of 88.2±9.0% after subtracting noise was achieved.

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The deviation from the theoretical 100% photon splitting or bunching ratio is mostly caused by the coherent backscattering of light in the silicon ring resonator in the opposite direction, which has been investigated classically [25,26]. Here, backscattering in the ring will cause the cw and ccw pumps to interfere with each other, resulting in unbalanced pump powers and hence unbalanced pair-creation probabilities between the two directions. This will decrease the splitting and bunching ratios in their respective cases. If the generated photons are also backscattered, this will lead to an unwanted |1A|1B term inside the Sagnac, which will further decrease the splitting ratio. This is mostly due to the sidewall roughness of the ring resonators. By adopting improved waveguide fabrication technologies, the surface roughness can be reduced, which would directly reduce the backscattering, and hence a higher splitting or bunching ratio may be achieved.

A high splitting ratio does not necessarily imply that the photons are indistinguishable from one another, though this is expected if they are created in the same resonant mode of the ring. To test the indistinguishability of the split photon pairs, a HOM dip setup was added, as shown inside the blue lines in Fig. 2. Instead of connecting directly to the SSPDs after the spectral filters on each side, the photons were first coupled to fiber tunable optical delay lines (General Photonics, 1 ps step) and polarization controllers, and then they meet at a single-mode fiber-based 5050 coupler, where HOM interference took place. The two outputs of the last 5050 coupler were connected to two SSPDs. Changing the relative time delay (δt) with the tunable delay line varies the temporal overlap between the two photons. When the two photons were made to arrive simultaneously (δt=0), a reduction in coincidence count rate was observed, because the photons were bunching and were not expected to emerge at the separate outputs of the 5050 coupler. The coincidence results are plotted in Fig. 5, as a function of δt. The plot shows a HOM dip with raw visibility of 88.1±3.1% and corrected visibility of 94.5±3.3%, once the flat background of accidentals is subtracted. Both exceed the threshold of 50% possible for classical light sources or probabilistically split photon pairs, as well as demonstrating the indistinguishability of the photons. The noise present at relative delays beyond 50 ps is due to the coupling fluctuations over a long measurement time. We believe our measured visibility deviates from the theoretical 100% visibility mainly due to the imperfect splitting ratio at the Sagnac loop, which originated from the coherent backscattering in the ring resonator due to surface roughness during the fabrication processes. This clearly nonclassical behavior demonstrates the suitability of the compact Sagnac and ring resonator source design for use in larger quantum photonic circuits.

 figure: Fig. 5.

Fig. 5. Hong–Ou–Mandel experimental results. A visibility of 94.5±3.3% is observed after subtracting accidental coincidences. Green circles indicate raw coincidences (error bars are Poissonian), red squares indicate accidental coincidences, and black lines are the Lorentzian fit for the raw coincidences and linear fit for the accidental coincidences.

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Many groups around the world are devoted to realizing the vision of a fully integrated quantum photonic system, including the integration of laser sources [27,28] and single photon detectors [29]; however, there are a number of steps required to make this vision a reality. Here we demonstrated, for the first time, an ultracompact quantum splitter for degenerate single photons based on a monolithic chip incorporating a Sagnac loop and a microring resonator. The device is compatible with current CMOS technology and has a footprint 50 times smaller than the previous published results, generating and deterministically splitting degenerate photon pairs using time-reversed HOM interference. We observed an off-chip HOM dip visibility of 94.5±3.3%, indicating that this degenerate pair photon source is in a suitable state for further quantum information processing. This takes us one step further toward a fully integrated quantum photonic system.

Funding

Australian Research Council (ARC) (CE110001018, DE120100226, DE130101148, FL120100029).

REFERENCES

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4. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, Science 320, 646 (2008). [CrossRef]  

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17. J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013). [CrossRef]  

18. H. Jin, F. M. Liu, P. Xu, J. L. Xia, M. L. Zhong, Y. Yuan, J. W. Zhou, Y. X. Gong, W. Wang, and S. N. Zhu, Phys. Rev. Lett. 113, 103601 (2014). [CrossRef]  

19. S. Clemmen, K. Phan Huy, W. Bogaerts, R. Baets, P. Emplit, and S. Massar, Opt. Express 17, 16558 (2009). [CrossRef]  

20. S. Azzini, D. Grassani, M. J. Strain, M. Sorel, L. G. Helt, J. E. Sipe, M. Liscidini, M. Galli, and D. Bajoni, Opt. Express 20, 23100 (2012). [CrossRef]  

21. S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, IEEE J. Sel. Top. Quantum Electron. 16, 316 (2010). [CrossRef]  

22. Q. Lin, F. Yaman, and G. Agrawal, Phys. Rev. A 75, 023803 (2007). [CrossRef]  

23. C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, Sci. Rep. 3, 3087 (2013).

24. V. Giovannetti, S. Lloyd, and L. Maccone, Nat. Photonics 5, 222 (2011). [CrossRef]  

25. F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, Appl. Phys. Lett. 96, 081112 (2010). [CrossRef]  

26. F. Ladouceur and L. Poladian, Opt. Lett. 21, 1833 (1996). [CrossRef]  

27. Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, Nature 498, 470 (2013). [CrossRef]  

28. T. Creazzo, E. Marchena, S. B. Krasulick, P. K. L. Yu, D. Van Orden, J. Y. Spann, C. C. Blivin, L. He, H. Cai, J. M. Dallesasse, R. J. Stone, and A. Mizrahi, Opt. Express 21, 28048 (2013). [CrossRef]  

29. W. H. P. Pernice, C. Schuck, O. Minaeva, M. Li, G. N. Goltsman, A. V. Sergienko, and H. X. Tang, Nat. Commun. 3, 1325 (2012). [CrossRef]  

References

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  • |

  1. N. Gisin and R. Thew, Nat. Photonics 1, 165 (2007).
    [Crossref]
  2. L. Grover, Phys. Rev. Lett. 95, 150501 (2005).
    [Crossref]
  3. A. Politi, J. Matthews, and J. O’Brien, Science 325, 1221 (2009).
    [Crossref]
  4. A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, Science 320, 646 (2008).
    [Crossref]
  5. D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
    [Crossref]
  6. A. Aspuru-Guzik and P. Walther, Nat. Phys. 8, 285 (2012).
    [Crossref]
  7. D. Höckel, L. Koch, and O. Benson, Phys. Rev. A 83, 013802 (2011).
    [Crossref]
  8. J. Sharping, K. Lee, M. Foster, A. Turner, B. Schmidt, M. Lipson, A. Gaeta, and P. Kumar, Opt. Express 14, 12388 (2006).
    [Crossref]
  9. K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, IEEE J. Sel. Top. Quantum Electron. 16, 325 (2010).
    [Crossref]
  10. C. Xiong, C. Monat, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. Krauss, J. Rarity, and B. Eggleton, Opt. Lett. 36, 3413 (2011).
    [Crossref]
  11. J. He, A. S. Clark, M. J. Collins, J. Li, T. F. Krauss, B. J. Eggleton, and C. Xiong, Opt. Lett. 39, 3575 (2014).
    [Crossref]
  12. Y. Guo, W. Zhang, S. Dong, Y. Huang, and J. Peng, Opt. Lett. 39, 2526 (2014).
    [Crossref]
  13. J. Fan, A. Migdall, and L. Wang, Opt. Lett. 30, 3368 (2005).
    [Crossref]
  14. J. Chen, K. Lee, C. Liang, and P. Kumar, Opt. Lett. 31, 2798 (2006).
    [Crossref]
  15. J. Chen, K. Lee, and P. Kumar, Phys. Rev. A 76, 031804 (2007).
    [Crossref]
  16. L. Yang, F. Sun, N. Zhao, and X. Li, Opt. Express 22, 2553 (2014).
    [Crossref]
  17. J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
    [Crossref]
  18. H. Jin, F. M. Liu, P. Xu, J. L. Xia, M. L. Zhong, Y. Yuan, J. W. Zhou, Y. X. Gong, W. Wang, and S. N. Zhu, Phys. Rev. Lett. 113, 103601 (2014).
    [Crossref]
  19. S. Clemmen, K. Phan Huy, W. Bogaerts, R. Baets, P. Emplit, and S. Massar, Opt. Express 17, 16558 (2009).
    [Crossref]
  20. S. Azzini, D. Grassani, M. J. Strain, M. Sorel, L. G. Helt, J. E. Sipe, M. Liscidini, M. Galli, and D. Bajoni, Opt. Express 20, 23100 (2012).
    [Crossref]
  21. S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, IEEE J. Sel. Top. Quantum Electron. 16, 316 (2010).
    [Crossref]
  22. Q. Lin, F. Yaman, and G. Agrawal, Phys. Rev. A 75, 023803 (2007).
    [Crossref]
  23. C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, Sci. Rep. 3, 3087 (2013).
  24. V. Giovannetti, S. Lloyd, and L. Maccone, Nat. Photonics 5, 222 (2011).
    [Crossref]
  25. F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, Appl. Phys. Lett. 96, 081112 (2010).
    [Crossref]
  26. F. Ladouceur and L. Poladian, Opt. Lett. 21, 1833 (1996).
    [Crossref]
  27. Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, Nature 498, 470 (2013).
    [Crossref]
  28. T. Creazzo, E. Marchena, S. B. Krasulick, P. K. L. Yu, D. Van Orden, J. Y. Spann, C. C. Blivin, L. He, H. Cai, J. M. Dallesasse, R. J. Stone, and A. Mizrahi, Opt. Express 21, 28048 (2013).
    [Crossref]
  29. W. H. P. Pernice, C. Schuck, O. Minaeva, M. Li, G. N. Goltsman, A. V. Sergienko, and H. X. Tang, Nat. Commun. 3, 1325 (2012).
    [Crossref]

2014 (4)

2013 (4)

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
[Crossref]

C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, Sci. Rep. 3, 3087 (2013).

Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, Nature 498, 470 (2013).
[Crossref]

T. Creazzo, E. Marchena, S. B. Krasulick, P. K. L. Yu, D. Van Orden, J. Y. Spann, C. C. Blivin, L. He, H. Cai, J. M. Dallesasse, R. J. Stone, and A. Mizrahi, Opt. Express 21, 28048 (2013).
[Crossref]

2012 (3)

W. H. P. Pernice, C. Schuck, O. Minaeva, M. Li, G. N. Goltsman, A. V. Sergienko, and H. X. Tang, Nat. Commun. 3, 1325 (2012).
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S. Azzini, D. Grassani, M. J. Strain, M. Sorel, L. G. Helt, J. E. Sipe, M. Liscidini, M. Galli, and D. Bajoni, Opt. Express 20, 23100 (2012).
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A. Aspuru-Guzik and P. Walther, Nat. Phys. 8, 285 (2012).
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2011 (3)

D. Höckel, L. Koch, and O. Benson, Phys. Rev. A 83, 013802 (2011).
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C. Xiong, C. Monat, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. Krauss, J. Rarity, and B. Eggleton, Opt. Lett. 36, 3413 (2011).
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V. Giovannetti, S. Lloyd, and L. Maccone, Nat. Photonics 5, 222 (2011).
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2010 (3)

F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, Appl. Phys. Lett. 96, 081112 (2010).
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S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, IEEE J. Sel. Top. Quantum Electron. 16, 316 (2010).
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K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, IEEE J. Sel. Top. Quantum Electron. 16, 325 (2010).
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2009 (2)

2008 (1)

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, Science 320, 646 (2008).
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2007 (3)

N. Gisin and R. Thew, Nat. Photonics 1, 165 (2007).
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J. Chen, K. Lee, and P. Kumar, Phys. Rev. A 76, 031804 (2007).
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Q. Lin, F. Yaman, and G. Agrawal, Phys. Rev. A 75, 023803 (2007).
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2006 (2)

2005 (2)

1999 (1)

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Q. Lin, F. Yaman, and G. Agrawal, Phys. Rev. A 75, 023803 (2007).
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Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, Nature 498, 470 (2013).
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A. Aspuru-Guzik and P. Walther, Nat. Phys. 8, 285 (2012).
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Baets, R.

S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, IEEE J. Sel. Top. Quantum Electron. 16, 316 (2010).
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S. Clemmen, K. Phan Huy, W. Bogaerts, R. Baets, P. Emplit, and S. Massar, Opt. Express 17, 16558 (2009).
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Benson, O.

D. Höckel, L. Koch, and O. Benson, Phys. Rev. A 83, 013802 (2011).
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S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, IEEE J. Sel. Top. Quantum Electron. 16, 316 (2010).
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S. Clemmen, K. Phan Huy, W. Bogaerts, R. Baets, P. Emplit, and S. Massar, Opt. Express 17, 16558 (2009).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
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Cai, H.

Canciamilla, A.

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J. Chen, K. Lee, and P. Kumar, Phys. Rev. A 76, 031804 (2007).
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Clemmen, S.

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C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, Sci. Rep. 3, 3087 (2013).

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A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, Science 320, 646 (2008).
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D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
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F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, Appl. Phys. Lett. 96, 081112 (2010).
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C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, Sci. Rep. 3, 3087 (2013).

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S. K. Selvaraja, W. Bogaerts, P. Dumon, D. Van Thourhout, and R. Baets, IEEE J. Sel. Top. Quantum Electron. 16, 316 (2010).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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N. Gisin and R. Thew, Nat. Photonics 1, 165 (2007).
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W. H. P. Pernice, C. Schuck, O. Minaeva, M. Li, G. N. Goltsman, A. V. Sergienko, and H. X. Tang, Nat. Commun. 3, 1325 (2012).
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H. Jin, F. M. Liu, P. Xu, J. L. Xia, M. L. Zhong, Y. Yuan, J. W. Zhou, Y. X. Gong, W. Wang, and S. N. Zhu, Phys. Rev. Lett. 113, 103601 (2014).
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D. Höckel, L. Koch, and O. Benson, Phys. Rev. A 83, 013802 (2011).
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C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, Sci. Rep. 3, 3087 (2013).

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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, Nature 498, 470 (2013).
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K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, IEEE J. Sel. Top. Quantum Electron. 16, 325 (2010).
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D. Höckel, L. Koch, and O. Benson, Phys. Rev. A 83, 013802 (2011).
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Krauss, T.

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J. He, A. S. Clark, M. J. Collins, J. Li, T. F. Krauss, B. J. Eggleton, and C. Xiong, Opt. Lett. 39, 3575 (2014).
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C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, Sci. Rep. 3, 3087 (2013).

Kumar, P.

Ladouceur, F.

Lee, K.

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C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, Sci. Rep. 3, 3087 (2013).

Li, J.

Li, M.

W. H. P. Pernice, C. Schuck, O. Minaeva, M. Li, G. N. Goltsman, A. V. Sergienko, and H. X. Tang, Nat. Commun. 3, 1325 (2012).
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Liang, C.

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Liscidini, M.

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H. Jin, F. M. Liu, P. Xu, J. L. Xia, M. L. Zhong, Y. Yuan, J. W. Zhou, Y. X. Gong, W. Wang, and S. N. Zhu, Phys. Rev. Lett. 113, 103601 (2014).
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V. Giovannetti, S. Lloyd, and L. Maccone, Nat. Photonics 5, 222 (2011).
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Marshall, G. D.

J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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C. Xiong, C. Monat, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. Krauss, J. Rarity, and B. Eggleton, Opt. Lett. 36, 3413 (2011).
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F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, Appl. Phys. Lett. 96, 081112 (2010).
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A. Politi, J. Matthews, and J. O’Brien, Science 325, 1221 (2009).
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F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, Appl. Phys. Lett. 96, 081112 (2010).
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Minaeva, O.

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Monat, C.

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F. Morichetti, A. Canciamilla, M. Martinelli, A. Samarelli, R. M. De La Rue, M. Sorel, and A. Melloni, Appl. Phys. Lett. 96, 081112 (2010).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, Nature 498, 470 (2013).
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A. Politi, J. Matthews, and J. O’Brien, Science 325, 1221 (2009).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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D. Bouwmeester, J.-W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 82, 1345 (1999).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, Sci. Rep. 3, 3087 (2013).

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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, Nature 498, 470 (2013).
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N. Gisin and R. Thew, Nat. Photonics 1, 165 (2007).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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H. Jin, F. M. Liu, P. Xu, J. L. Xia, M. L. Zhong, Y. Yuan, J. W. Zhou, Y. X. Gong, W. Wang, and S. N. Zhu, Phys. Rev. Lett. 113, 103601 (2014).
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J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Hadfield, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, Nat. Photonics 8, 104 (2013).
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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic of the working principle: waveguides A and B, connected to two grating couplers, reach the same side of a multimode interference coupler (MMI), whose two output ports are connected, forming a Sagnac loop; a silicon ring resonator is coupled to the Sagnac loop in order to enhance the photon-pair generation rate. (b) Schematic of degenerate photon-pair generation via SFWM. Two pump photons at different wavelengths are annihilated to create a pair of degenerate single photons.
Fig. 2.
Fig. 2. Experimental setup. A broadband mode-locked laser was spectrally sliced into two synchronized pumps using a spectral pulse shaper (SPS) and subsequently amplified by an erbium-doped fiber amplifier (EDFA); a fiber 5050 coupler was used to split the pumps into two; bandpass filters (BPFs) were used to ensure only pump λ1 was injected to port A and only pump λ2 was injected to port B; polarization controllers (PCs) matched the pumps to the TE mode required by the waveguide. Right before injecting the pump waves into the sample, a circulator on each side was inserted for collection of generated single photons. After coupling the photons out from the sample, BPFs were used to reject the pumps. The photons were then either directly connected to superconducting single photon detectors (SSPDs) or connected through a HOM setup consisting of tunable delay lines, PCs, and a fiber 5050 coupler (indicated inside blue lines); the gray area inside the figure shows a SEM image of the device.
Fig. 3.
Fig. 3. Counts (left axis) and coincidence-to-accidental ratio (CAR, right axis, purple squares, with error bars) as a function of coupled average power. Measured raw coincidences (red circles, Craw), accidental coincidences (green triangles, A), and true coincidences (blue diamonds, Ctrue=Craw-A) are shown in the plot. The blue line is a quadratic fit of Ctrue, when coupled Pavg<90μW. With coupled power higher than 100 μW, the counts are rolling off from the fit due to two-photon absorption and free-carrier absorption.
Fig. 4.
Fig. 4. Count rate for split (|11) and bunched (|20 and |02) pairs. Top: When two pumps were injected separately into the two ports of the sample, a splitting ratio of 88.9±6.7% after subtracting noise was achieved. Bottom: When two pumps were injected together into one of the ports of the sample, a bunching ratio of 88.2±9.0% after subtracting noise was achieved.
Fig. 5.
Fig. 5. Hong–Ou–Mandel experimental results. A visibility of 94.5±3.3% is observed after subtracting accidental coincidences. Green circles indicate raw coincidences (error bars are Poissonian), red squares indicate accidental coincidences, and black lines are the Lorentzian fit for the raw coincidences and linear fit for the accidental coincidences.

Equations (2)

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|Ψring=|2cw|0ccw+eiδφ|0cw|2ccw2.
|ΨMMI=1eiδφ2|Ψ2002+i(1+eiδφ)2|Ψ11,

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