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We observed high-purity correlated and entangled photon pairs generated through spontaneous four-wave mixing (SFWM) in a silicon wire waveguide (SWW). Employing a nano-scale silicon waveguide with a low loss mode size converter, we obtained a high coincidence to accidental coincidence ratio (CAR) of around 200 that was larger than that of cooled dispersion shifted fiber (DSF) by a factor 3.2, and observed the two-photon interference fringe of time-bin entangled photons with >95% visibility without subtracting the accidental coincidences.
©2008 Optical Society of America
1. Introduction
Entanglement is one of the most important resources for quantum information systems such as quantum key distribution (QKD) [1], quantum relay [2] and quantum computer [3] systems. The generation of entangled photon pairs in the 1.5 µ m telecom band is especially important for realizing quantum communication systems over optical fiber. Telecom band entangled photon pair sources based on spontaneous parametric down-conversion in periodically poled lithium niobate (PPLN) waveguides [4, 5] or spontaneous four-wave mixing (SFWM) in dispersion shifted fibers (DSF) [6, 7] have been studied and widely employed. However, there are problems with the above sources. In entanglement sources based on PPLN waveguides, timing jitter is induced by the walk-off between the pump and a photon pair, because of the group velocity mismatch between them. As a result, it is generally difficult to undertake quantum interference experiments such as Hong-Ou-Mandel experiments using two-photon pairs generated in two independent waveguides [8, 9, 10]. On the other hand, DSF-based entanglement sources are affected by the noise photons generated by spontaneous Raman scattering (SpRS). A large number of noise photons increases accidental coincidence counts, and leads to the degradation of quantum correlation and two-photon interference. DSF is often cooled with liquid nitrogen to suppress noise photons [11]. However, the need to cool the DSF complicates the system, which is undesirable.
Recently, photon pair generation using SFWM in a nano-scale silicon waveguide has been attracting much attention. After the report on correlated photon pair generation [13], our group reported the first entanglement generation experiments using a silicon wire waveguide (SWW) [14, 15]. A silicon waveguide exhibits very large third order nonlinearity compared with that of conventional optical fiber, because of its extremely small cross-sectional area and strong light confinement originating from its high refractive-index contrast [16]. As a result, the SFWM process is induced efficiently in the waveguide. Moreover, since the Raman spectrum of single-crystal silicon is 15.6 THz from the pump frequency with a relatively narrow width of about 100 GHz [17], the SpRS photons in silicon are suppressed by selecting signal and idler frequencies that are far from the Raman peak. Therefore, an SWW is expected to function as a high-purity photon pair generation device. However, in a previous study [14], the visibility of the two-photon interference was limited to about 73%, mainly because of the large coupling loss between the waveguide and the fiber and the lack of long-term stability. This result was better than that for a DSF at room temperature, but was comparable with that of a cooled DSF [18].
In this paper, we report a significant improvement in the quantum correlation characteristics of an SWW-based correlated/entangled photon pair source. By employing mode size converters on both sides of the waveguide, we reduced the outcoupling loss between the waveguide and external fibers. Moreover, we improved the fiber alignment system thus allowing us to align the SWW and external fibers precisely and stably. As a result, we successfully obtained a higher CAR than that of previous work [14], and we generated time-bin entangled photon pairs that exhibited two-photon interference fringes with >95% visibility without subtracting the accidental coincidences.
2. Experimental Setup
Figure 1 shows the experimental setup. A 1551.1 nm continuous pump light from an external cavity diode laser was modulated into double pulses with a 100 MHz repetition frequency using an intensity modulator (IM). The pulse width and interval were 100 ps and 1 ns, respectively. The double pulse was amplified by an erbium-doped fiber amplifier (EDFA), and filtered to eliminate amplified spontaneous emission noise from the EDFA. The polarization of the pump pulses was adjusted so that it was horizontal by passing the pulses through a polarizer and using a focusing module (FM) with a half wave plate (HWP). The pulses were then injected into an SWW. The waveguide was fabricated on a silicon-on-insulator (SOI) wafer with a Si top layer on a 3 µm SiO2 layer. The SWW was 460 nm wide, 220 nm thick, and 1.15 cm long, and required no temperature control. The loss of the SWW was 1.0 dB. It is difficult to connect an SWW and external fibers because the cross-sectional area of an SWW is about one-thousandth that of a standard optical fiber. To overcome this problem, mode size converters were constructed on both sides of the waveguide to reduce the outcoupling loss between the waveguide and the FM [12, 19]. This converter had a Si adiabatic taper that gradually became thinner toward the end and a second low-index waveguide that was 3 µm square and that covered the taper. We installed the SWW in a fiber alignment system and this enabled us to align the SWW and FMs precisely and stably through an operating computer system. Thanks to these technologies, we achieved an outcoupling loss of only 1.9 dB and significantly improved the long-term stability of our setup.
Fig. 1. Experimental setup. PG : pulse generator, PC : polarization controller, SPD1, SPD2 : single photon detectors for signal and idler photons.
When we disregard pump depletion, the SFWM interaction in the waveguide is described by the following Hamiltonian
where χ is proportional to the square of the pump field and ↠x (âx) is a creation (annihilation) operator for mode x (=s,i). Here, we assumed that the pump is strong and can be treated as a classical oscillator. The state of the total system at time t is given by
The exponential term represents the time-development operator and |m,n〉 is the number state, where m and n are the numbers of photons for the signal and idler, respectively. By using the disentangling theorem shown as Eq.(5.63) in [20], the wavefunction becomes
If the pump power is very weak, there is negligible multi-photon generation, and the wavefunction is rewritten as follows
As a result, we can post-select a single pair state by employing the coincidence counts between the signal and idler.
By employing a coherent double pump pulse as the pump for the SFWM, we can generate a time-bin entangled photon pair, which is a coherent superposition of two pair photon states located at different temporal positions. The generated state is expressed as
Here, |k〉x represents a state in which there is a photon in the kth time slot in a mode x, signal (s), or idler (i). ϕ is a the phase difference between the two pump pulses. The photons from the waveguide were input into a fiber Bragg grating (FBG) to suppress the pump photons, and subsequently input into an arrayed waveguide grating (AWG) to separate the signal and idler photons. The selected signal and idler photon wavelengths were 1547.9 and 1554.3 nm respectively. The signal and idler photons were input into an optical band pass filter (BPF) to further reduce the pump photons, and then launched into 1-bit delay Mach-Zehnder interferometers fabricated using planar lightwave circuits (PLC) based on silica waveguide technology [21]. The PLC interferometers convert a state |k〉x to , where θ x is the phase difference between the two paths of the interferometer for mode x(=s,i). The path length difference between the short and long paths was 20 cm, and the phase difference between the two paths was precisely adjusted by controlling the temperature of the interferometer. Both PLC interferometers had an excess loss of 2.0 dB. Once the photons have passed through the PLC interferometers, the state becomes , where an amplitude term that is common to all product states is omitted for simplicity, and noncoincidence terms are discarded because they do not appear in coincidence measurements. We can obtain the two-photon interference by counting the coincidence events in the 2nd time slot. The photons from the PLC interferometers were detected by photon counters that used InGaAs APDs operated in a gated mode whose gate frequency was as fast as 100 MHz. This fast gated mode operation was made possible by using the self-differentiation technique reported in [22]. The quantum efficiency and dark count probability per gate of the photon counters were 10% and 6×10-6 for the signal and 10% and 2.1×10-5 for the idler, respectively. The afterpulse probabilities of the photon counters were 1.5% for the signal and 1.2% for the idler. The signals detected from the photon counters for the signal and idler channels were used respectively as start and stop pulses for a time interval analyzer (TIA). The losses of the setup, including those of the FBG, AWG, BPF and PLC interferometer, are estimated to be approximately 7.8 and 7.0 dBm for the signal and idler photons, respectively.
3. Results
We first removed the PLC interferometers and employed a single pulse with a 100 MHz repetition frequency as a pump, and investigated the CAR of the photon pairs generated using the SWW by changing the peak power of the pump pulse. CAR represents the strength of the temporal correlation between two photons, and a higher CAR indicates a stronger correlation. Typical CAR data are shown in Fig. 2 (a) as a function of the average idler photon number per pulse n i. We obtained the maximum CAR at about 200 with n i=0.0013. We also carried out CAR measurements using a cooled and an uncooled DSF with the same pump source, optical filter system, and detectors. The DSF was 500 m long and was cooled by being soaked in liquid nitrogen. The losses of the cooled DSF including connector losses and splice losses were estimated to be approximately 1.5 dB. This result is shown in Fig. 2 (b). It is clear that the CAR of the SWW was significantly better than that of the cooled DSF. This clearly suggests that the number of noise photons in the SWW is very small compared with that in the cooled DSF.
Next we installed PLC interferometers and employed double pump pulses, and generated time-bin entangled photon pairs by changing the idler interferometer temperature. The average number of photon pairs per pulse was set at approximately 0.04. We fixed the signal interferometer temperature at 20.62° or 20.82° and counted the coincidences while changing the idler interferometer temperature. The results are shown by the circles and squares in Fig. 3, which reveal the clear modulation of the coincidence count. The points shown in Fig. 3 are raw data and we did not subtract any accidental coincidence counts caused by multi-pair emission events and detector dark counts. The circles and the squares represent two nonorthogonal measurement bases for the signal photons. The visibilities of the fitted curves are 96.3% (solid line) and 95.2% (dotted line). Note that these values are limited by the dark count of the single photon detectors, which is generally much larger than that for short wavelength bands, not by the imperfection of the source. Thus, we successfully confirmed the generation of a high-purity entangled state.
Fig. 2. Plot of the coincidence to accidental coincidence ratio (CAR) as a function of the number of idler photons per pulse using an SWW (a) and cooled DSF (b). The inset in Fig. 2 (b) is a plot of the CAR using DSF at room temperature.
Fig. 3. Coincidence count per signal count as a function of the temperature of the PLC interferometer for the idler. The solid line (circles) and dotted line (squares) are two-photon interference fringes at 20.68° and 20.88°, respectively.
4. Conclusion
We have observed improved correlated and time-bin entangled photon pairs in the 1.5 µm band using a silicon wire waveguide. We confirmed that the CAR of a silicon-based photon pair source was larger than that of a cooled DSF-based source by a factor of about 3.2, and obtained a time-bin entanglement with >95% visibility without temperature control. This means that an SWW is a useful tool for quantum information systems such as quantum key distribution and quantum relay systems over optical fiber networks.
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