In this paper we investigate uncorrelated noise from spontaneous Raman scattering (SpRS) and its effect on photon-pair generation in chalcogenide (As2S3). We measure a coincidence-to-accidental ratio (CAR) of 4.2 in a 7 cm As2S3 single-mode fiber, with enhancements from our previous result attributed to pulsed pumping and cooling. Using an analytical model we characterize the magnitude of the SpRS at different temperatures. Our analysis shows that even after cooling to liquid nitrogen temperature (77 K), SpRS is still significant. For large detunings from the pump, the dependence on temperature for the Stokes SpRS intensity becomes negligible, so cooling is not a complete solution to improve the quality of the photon source.
© 2012 OSA
The search for low-noise, high brightness integrated photon sources in the low-loss telecommunications band is ongoing, from on-demand sources such as quantum dots  and impurities in diamond  through to probabilistic photon pair sources from nonlinear devices. The former require complex experimental techniques to implement such as liquid helium cooling and confocal microscopy and samples that emit in the desired near-infrared telecommunications C-Band have yet to be reported. The latter have emerged as the choice for quantum computation and communication research, whether they are based on χ(2) materials such as periodically poled lithium niobate (PPLN)  or χ(3) materials such as silicon [4–6]. These each have their inherent drawbacks with PPLN requiring bulky temperature control and silicon suffering from two photon absorption and associated free carrier effects causing high losses. An oft chosen method is to generate pairs of photons in amorphous glass devices, such as silica fibers [7–11] or chalcogenide waveguides [12,13]. In these devices the dominant source of noise is frequently attributed to spontaneous Raman scattering (SpRS), with the technique of immersing the device in liquid nitrogen repeatedly hailed as a solution to suppress this uncorrelated noise [14–16].
In this paper we investigate how SpRS impacts on correlated photon pair generation in chalcogenide glass, a highly nonlinear material which, unlike silica, can be used to fabricate ultra-compact photonic chip devices . We show using an As2S3 chalcogenide device that we can attain a marked improvement to our coincidence-to-accidentals ratio (CAR) from 0.5 at room temperature to 4.2 at a temperature of 77 K. The order of magnitude improvement at room temperature from our previous work can be attributed to the use of a pulsed pump, while the 7 times further improvement is due to a reduction in SpRS noise when cooling. Taking a CAR measurement for multiple powers and theoretically fitting the data we find that there is still a large dominant source of noise that is linearly proportional to peak power, consistent with the presence of SpRS photons. We analyze the statistics behind SpRS and find that the impact of cooling becomes less significant as the photon channels are further detuned from the pump wavelength.
The photon generation method exploited in this work is that of spontaneous four-wave mixing (SFWM) in a χ(3) nonlinear medium. In this process, shown in Fig. 1(a) , two pump photons are annihilated to generate signal and idler photons, of higher and lower energy respectively. These photons are correlated in time, allowing the detection of one photon to herald the other, making this a useful source for experiments in quantum information research. The quality of this source is reliant upon many experimental parameters which can introduce uncorrelated photons or noise into the system, such as leaked pump, detector dark counts or SpRS. The former two noise components can be avoided through filtering and improved detector technology, but the latter is a source of noise that is in the same spectral band as the signal and idler photons. The SpRS process is shown in Fig. 1(b), in this case the Stokes process. A pump photon scatters in the medium resulting in a lower energy photon and a phonon signified by the red arrow.
Here we will carry out an experiment to analyse the effect of SpRS noise in photon-pair sources. Cooling a waveguide and the required alignment stages with liquid nitrogen is technically impractical. Instead a 7 cm long As2S3 single-mode fiber was used for these measurements, with chalcogenide exhibiting many desirable properties for nonlinear photon-pair generation  including an ultra-strong Kerr nonlinearity comparable to that in silicon but with low two-photon absorption and without the detrimental free carriers present in semiconductor materials. The fiber was fabricated by tapering a multimode fiber, with a cladding diameter of 140 μm and a core diameter of 5 μm, through a heating and drawing process  until the desired single-mode guidance could be achieved at a cladding diameter of 80 μm and core diameter of 2.8 µm. At this diameter the nonlinear coefficient is measured to be γ ~1.7 W−1 m−1  with a dispersion of −397 ps.nm−1km−1 at 1550 nm and a calculated SFWM bandwidth (full width at half maximum) of 2.4 THz. This provides a nonlinear phase shift γPL = 0.059. The chalcogenide fiber was butt coupled to high NA silica fiber and secured with UV-cured index matching glue, before being spliced to SMF pigtails with connectors and placed in an insulated container to allow immersion in liquid nitrogen.
Figure 1(c) shows the experimental setup. A picosecond pulsed fiber laser generates 10 ps pump pulses at 1550.1 nm, with 0.3 nm bandwidth and a repetition rate of 10 MHz. An isolator protects the laser from back reflections and a variable attenuator and polarization controller condition the pump pulse intensity and polarization. A 1550/980 WDM blocks any leaked 980 nm cavity pump photons. A 90/10 coupler allows the input power and spectrum to be monitored. Correlated photon pairs are generated in the As2S3 fiber via SFWM and the output is fed into a 0.5 nm bandwidth fiber Bragg grating (FBG) centered on the pump frequency to block any further pump photons. Signal and idler photons are input to an arrayed waveguide grating (AWG) separating the higher and lower wavelength photons. AWG output channels are spaced evenly by 100 GHz, with a bandwidth of 45 GHz. A tunable band-pass filter at each of the AWG outputs further remove leaked 1550nm pump photons to give a total pump suppression >100 dB. The signal and idler photons were detected by InGaAs single photon detectors (ID210) with a 1 ns window synchronized with the pump laser. At 20% detection efficiency, a dead time of 20 µs and 5 MHz triggering rate, the detector dark count rate was ~100 s−1. SFWM gain and pump leakage both decreased as signal and idler channels were detuned further from the pump, with optimum performance achieved at 700 GHz, which is used for all coincidence measurements, positioning the signal and idler at wavelengths of 1544.5 nm and 1555.7 nm respectively. We measured the CAR, defined as the ratio of correlated events to the system noise, for various input pump powers. A true coincidence event is when two photons generated via SFWM in the As2S3 fiber and originating from the same pump pulse are detected simultaneously. We measure accidental coincidences by looking at photons that arrive at the detectors synchronized with the pump clock but separated by one period which include detector dark counts, pump leakage, multiple-pair generation and SpRS noise photons.
3. Results and analysis
The results at room temperature and when the device is immersed in liquid nitrogen are shown in Fig. 2 . At room temperature the maximum CAR is 0.5, an order of magnitude increase over the previously published result using a continuous wave (CW) laser in a chalcogenide waveguide  where the nonlinear phase shift γPL was similar to that used here, as the higher peak power compensates for the reduced nonlinearity of the device. The increased CAR is achieved due to the pulsed pumping providing time-of-arrival information for the generated photons, allowing better detection capabilities. At liquid nitrogen temperature (77 K) the maximum CAR is improved by a further order of magnitude to 4.2. Cooling neither affects the detector settings nor the coupled power; hence the dark counts, pump leakage and multi-pair generation remained constant. We therefore attribute the increase in CAR to a reduction in SpRS noise photons. Further improvements to the filtering, for example the inclusion of a broadband FBG to block more pump leakage, are expected to further increase the maximum CAR. A 5 dB drop in the single photon detection rate was observed after cooling the As2S3 fiber. As the input power was constant, this is again due to the reduction in Raman noise photons in the separate channel counts.
By using a simple analytical model  we fit the CAR plots for the different temperatures to further investigate the noise. The true coincidences per pulse, C, in the system arise from our SFWM interaction and can be described as C = ηsηiμ where μ is the number of pairs generated per pulse and ηs,i are the lumped collection efficiencies including coupling efficiencies, component losses and detector efficiencies in the signal and idler arms respectively. Accidental coincidence counts per pulse, A, are defined as A = NsNi where Ns,i are the detected counts in the signal and idler arms. These singles counts can be written as Ns = (μ + μNs)ηs + Ds and Ni = (μ + μNi)ηi + Di, where μNs,Ni are the probability of generating a noise photon per pulse and Ds,i are the detector dark counts, both for the signal and idler arms respectively. If we take the standard formula for the CAR = C/A we can substitute for C and A to get the following fitting functionEq. (1) we can fit our data to find the free parameters μNs,Ni. In doing so we find that the ratio of μNs and μNi in the cooled and room temperature cases show that SpRS is reduced in both the signal and idler channels by a factor of 3.16 and 3.31 respectively. Taking the signal and idler count rates with respect to input power in the two temperature regimes and fitting with a second-order polynomial, we find that the ratios of the linear noise terms are 3.07 and 3.27 respectively, in good agreement with the values extracted from the CAR plots. It should be noted that although this is a significant reduction in the SpRS and results in a marked improvement tothe CAR achieved, it is still two orders of magnitude from the ideal CAR of ~315 in the case where μNi,Ns → 0.
To analyze the impact of cooling in this sample we must look at the source of SpRS, namely the photon-phonon scattering interaction. The anti-Stokes component of SpRS is always less intense than the Stokes component, so the latter is the dominant source of noise impacting the correlated photon pair statistics and the case that we will focus on. The number of SpRS photons in the sample is given by 
These are shown in Fig. 3 for the room temperature and liquid nitrogen cooled cases. One can see that although the Raman gain is low at small detuning the phonon population tends towards infinity, meaning that there are in fact a large number of photons being scattered in this region. As the detuning increases into the near detuned region (0 to 6 THz) the Raman density of states increases while the phonon populations decrease but are still significant. Here the effect of cooling is most effective as the ratio of the phonon populations is highest. After this point, in the far detuned cases, the phonon population tends towards zero and the high and low temperature cases converge, so cooling the device has a negligible effect on the SpRS. It should be noted that there is a low Raman point between 7.4 and 8 THz detuning,shown in purple in Fig. 4 , that was previously investigated theoretically  where cooling would not be required in a device to exhibit a high CAR.
To quantify the effect of cooling on SpRS we calculate the number of SpRS photons at room temperature, NRoom Temp, and the number at liquid nitrogen temperature, N77K, in the experimental filter bandwidth as the position of the filter is shifted from the pump. The ratio of NRoom Temp to N77K with respect to detuning from the pump is shown in Fig. 4. It can be clearly seen that as the detuning increases the effect of cooling decreases. At 700 GHz detuning the ratio is 3.3, in good agreement with the values calculated from the fitting of the CAR plots of 3.16 and 3.31 for signal and idler respectively.
In conclusion we have investigated the impact of Raman scattering on photon-pair generation in chalcogenide at different temperatures through analysis of the photon statistics. We have shown an order of magnitude increase in the CAR achieved in a chalcogenide photon-pair source at room temperature when moving to a pulsed pump regime. We have demonstrated a further order of magnitude increase when cooling the device in liquid nitrogen at a signal and idler channel detuning of 700 GHz from the pump wavelength. We have taken measurements for the CAR at various input pump powers in both temperature regimes and after fitting the data find that there is approximately three times less SpRS photons, after cooling at this detuning. We have theoretically investigated the source of this reduction by looking at the phonon populations at different temperatures and find that although the cooling makes a marked difference in the near-detuned regime, it does not increase the CAR to the desired level of over 10 and is far from the ideal value of approximately 315. In the far-detuned region cooling is shown to have a negligible effect on the number of Stokes SpRS photons and will therefore provide little improvement to photon sources operating in this regime. A region of low SpRS is present at a photon channel detuning of around 7.4 THz in which enhanced photon-pair statistics can be expected without the requirement of cryogenic cooling with the requirement that the SFWM bandwidth be extended out to this range.
We acknowledge the support of the Australian Research Council (ARC) Centre of Excellence program, the ARC Federation Fellowship Program and the Discovery Early Career Researcher Award (DECRA) Program. The Centre for Ultrahigh-bandwidth Devices for Optical Systems (CUDOS) is an ARC Centre of Excellence (project number CE110001018).
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