Entangled photon-pairs are a critical resource for realizing the various quantum information processing protocols such as quantum teleportation [1][2] and quantum cryptography [3]. Because of the requirement of distributing entangled photons over long distances and the difficulty of coupling entangled photons produced by χ ⁽²⁾ nonlinear crystals into optical fibers, a source emitting entangled photon-pairs in the low-loss 1550-nm telecommunication band of silica fiber that could be directly spliced to the existing fiber network is desirable. Such a source has been recently developed by exploiting the χ ⁽³⁾ (Kerr) nonlinearity of the fiber itself [4][5]. When the pump wavelength is close to the zero-dispersion wavelength of the fiber, phase-matching is achieved and the probability amplitude for inelastic four-photon scattering (FPS) is significantly enhanced. In this process, two pump photons at frequency ω _p scatter through the Kerr nonlinearity of the fiber to create energy-time entangled Stokes and anti-Stokes photons at frequencies ω_s and ω_a , respectively, such that 2ω_p =ω_s +ω_a . Because of the isotropic nature of the Kerr nonlinearity in fused-silica-glass fiber, the scattered correlated-photons are predominantly co-polarized with the pump photons. By coherently adding two such orthogonally-polarized parametric processes, polarization entanglement can be created as well [5]. Following this approach, all four Bell states can be prepared, and a violation of Bell’s inequalities by up to 10 standard deviations of measurement uncertainty has been demonstrated [5]. However, in previous experiments with this source, the number of measured total-coincidences exceeded the number of accidental-coincidences by only a factor of 2.5 [4]. In this paper, we show that spontaneous Raman scattering accompanying FPS causes this problem. By reducing the detuning between the Stokes and pump photons and by using polarizers, we demonstrate that the accidental coincidences can be made less than 10% of the true coincidences at a production rate of about n̄=0.04 photon-pairs/pulse. Further improvement could be obtained by cooling the silica fiber.

 

Fig. 1. Experimental setup: scattered Stokes and anti-Stokes photons emerging from the port labelled “Out” are detected; FPC, fiber polarization controller; PBS, polarization beam splitter; G, gratting; QWP, quarter-wave plate; HWF, half-wave plate; “Signal-In” port is blocked during photon-counting measurement.

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Our experimental setup is shown in Fig. 1. Stokes and anti-Stokes photon-pairs at frequencies ω_s and ω_a , respectively, are produced in a nonlinear-fiber Sagnac interferometer (NFSI). We have previously used this NFSI to generate quantum-correlated twin beams [6], correlated photon-pairs [4], and polarization entanglement [5]. The NFSI consists of a fused-silica 50/50 fiber coupler spliced to 300m of dispersion-shifted fiber (DSF) with a zero-dispersion wavelength at λ ₀=1535±2nm. The efficiency of FPS in DSF is low because of the relatively low magnitude of the Kerr nonlinearity; only about 0.1 photon-pair is produced by a typical 5-ps-duration pump pulse that contains approximately 10 ⁸ photons. To reliably detect the scattered photon-pairs, a pump to photon-pair rejection ratio in excess of 100 dB is required. We achieve this by first exploiting the mirror-like property of the NFSI [7], which provides a pump rejection greater than 30 dB, and then sending the transmitted scattered photons along with the leaked pump photons through a free-space double-grating spectral filter (DGSF) that provides a pump-rejection ratio in excess of 75 dB. The filter consists of three identical diffraction gratings (holographic, 600 grooves/mm), G1, G2, G3, whose diffraction efficiencies for the horizontally and vertically polarized light are 90% and 86%, respectively. The doubly-diffracted Stokes and anti-Stokes photons are then re-coupled into fibers. The passbands for the Stokes and anti-Stokes channels are determined by the numerical apertures of the fiber and the geometrical settings of the optical elements composing the spectral filter.

The pump is a 5-ps-duration mode-locked pulse train with a repetition rate of 75.3 MHz, obtained by spatially dispersing the output of an optical parametric oscillator (OPO) (Coherent Inc., model Mira-OPO) with a diffraction grating; its central wavelength can be tuned from 1525 to 1536 nm. To achieve the required power, the pump pulses are then amplified by an erbium-doped fiber amplifier (EDFA). Photons at the Stokes and anti-Stokes wavelengths from the OPO that leak through the spectral-dispersion optics and from the amplified spontaneous emission (ASE) from the EDFA are suppressed by passing the pump through a 1nm-bandwidth tunable filter (Newport, model TBF-1550-1.0). For alignment purposes, weak signal pulses at the Stokes wavelength, which are temporally synchronized with the pump pulses, are injected into the NFSI. During photon counting measurements, however, the input signal is blocked.

Photon counters consisting of InGaAs/InP avalanche photodiodes (APD, Epitaxx, model EPM 239BA) operated in a gated-Geiger mode are used to count the Stokes and anti-Stokes photons [4]. The 1-ns-wide gate pulses arrive at a rate of 588 kHz, which is 1/128 of the repetition rate of the pump pulses. The quantum efficiency for one detector is 25%, that for the other is 20%. The total detection efficiencies for the Stokes and anti-Stokes photons are about 8% and 6%, respectively, when the efficiencies of the NFSI (82%), 90/10 coupler, double grating filter (45% and 50% in anti-Stokes and Stokes channel, respectively), and other transmission components (about 90%) are included.

For the FPS occurring in the DSF, the scattered correlated photon-pairs are predominantly co-polarized with the pump photons. An investigation into the origin of the low ratio between the total coincidences and the accidental coincidences illustrates this point. A polarization beam splitter (PBS) is placed in both the Stokes and anti-Stokes channels. With proper settings of the half-wave-plate (HWP) and the quarter-wave-plate (QWP), which are placed in front of the double grating filter, the Stokes and anti-Stokes photons that are either co-polarized or cross-polarized with the pump photons can be rejected. We measure the number of scattered photons per pump pulse, co-polarized and cross-polarized with the pump, respectively, that are detected in the anti-Stokes channel, N_a , as a function of the number of pump photons per pulse, N_p , and the coincidence rate between the detected Stokes and anti-Stokes photons as a function of N_a . In both co- and cross-polarized cases, we fit the measured data with N_a =s ₁ N_p +s ₂ $N_p^2$, where s ₁ and s ₂ are the linear and quadratic scattering coefficients, respectively. Figure 2 shows the data obtained when the detuning Ω/2π of the Stokes (anti-Stokes) photons is 1.25 THz, where Ω=ω_p -ω_s =ω_a -ω_p , and the full-width at half maximum (FWHM) of the DGSF is 0.8 nm. As shown in the inset of Fig. 2(a), for the photons co-polarized with the pump, the quadratic scattering owing to FPS dominates over the linear scattering when N_p >0.4×10⁸ photons/pulse, whereas the opposite is true when N_p <0.4×10⁸ photons/pulse. The main body of Fig. 2(a) shows that the total-coincidence rate of the Stokes and anti-Stokes photons produced by the same pump pulse is much higher than the accidental-coincidence rate. The latter is obtained by measuring the coincidence rate between the Stokes and anti-Stokes photons produced by two adjacent pump pulses and fits the theory curve for two independent light sources very well [4]. Comparing the coincidence-measurement results in Fig. 2(a) with our previous results in [4], the ratio between the total coincidences and the accidental coincidences is improved. The results for the photons cross-polarized with the pump are shown in Fig. 2(b), where we find no difference between the total-coincidence rate and the accidental-coincidence rate. The linearly-scattered photons contribute much more than the quadratically-scattered photons, as shown in the inset of Fig. 2(b). Absence of true coincidences, which is quantified by the difference between the total-coincidence rate and the accidental-coincidence rate, implies that the Stokes and anti-Stokes photons that are orthogonally polarized with the pump are not correlated. We note that a small number of quadratically-scattered photons are observed; however, these come mainly from the leakage of the quadratically-scattered photons co-polarized with pump owing to imperfect rejection by the PBS. We corroborate this by making classical parametric-gain measurements in the low-gain region. When the polarization of the injected weak signal is perpendicular to that of the pump, the four-wave-mixing (FWM) gain is measured to be 20 dB less than the gain when the signal and pump are co-polarized.

 

Fig. 2. Measured coincidence rates as a function of the number of scattered photons per pump pulse (labelled Single Counts/Pulse) in the anti-Stokes channel for (a) scattered photons co-polarized with the pump and (b) scattered photons cross-polarized with the pump. In both cases λ_p =1536nm and Ω/2π=1.25THz; the diamonds represent the total-coincidence counts produced by a single pump pulse, the triangles represent the accidental-coincidence counts produced by two adjacent pump pulses, and the line represents the calculated coincidence counts for two independent light sources. The insets show the number of scattered photons per pump pulse detected in the anti-Stokes channel as a function of the number of photons in the pump pulse (hollow circles). A second-order polynomial, N_a =s ₁ N_p +s ₂ $N_p^2$, is shown to fit the experimental data (dot-dashed line). The contributions of linear scattering, s ₁ N_p , (dashed line) and quadratic scattering, s ₂ $N_p^2$, (dotted line) are plotted separately as well. For the inset in (a): s ₁=0.00436 and s ₂=0.01046; for the inset in (b): s ₁=0.00381 and s ₂=0.00033.

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Fig. 3. Same as in Fig.2, except λ_p =1525nm. For the inset in (a): s ₁=0.00688 and s ₂=4.38×10^-5; for the inset in (b): s ₁=0.005 and s ₂=0.

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The linear dependance of the scattering rate of the Stokes and anti-Stokes photons on N_p , which is proportional to the pump power, indicates that the uncorrelated photons cross-polarized with respect to the pump are caused by spontaneous Raman scattering. This has also been verified experimentally and theoretically in the context of the noise-figure of parametric amplifiers made with fused-silica fiber [8, 9, 10]. To further confirm this point, we tune the central wavelength of the pump to 1525 nm, which is in the normal dispersion region of the DSF, where the phase-matching condition for FPS is not satisfied, and, therefore, no correlated photon-pairs are expected to be produced by the FPS process. Setting the detuning ω/2π of the Stokes and anti-Stokes channels to 1.25 THz, we make the same measurements again. For the photons co-polarized with the pump, linear scattering dominates in this region, though we measure a very small probability of quadratic scattering (less than 150 times that of linear scattering), as shown in the inset of Fig. 3(a). For the coincidence measurements shown in the main body of Fig. 3(a), we find no difference between the total-coincidence rate and the accidental-coincidence rate. Within the error bars of our experimental data, the true coincidence rate between the co-polarized photons in the Stokes and anti-Stokes channels is at most 10^-6/pulse. For the photons cross-polarized with the pump, as shown in Fig. 3(b), we also find no difference between the total-coincidence rate and the accidental-coincidence rate, and the number of the scattered photons in the Stokes and anti-Stokes channels depends linearly on the pump power.

 

Fig. 4. Optical transmission spectrum of the double-grating filter. The pump at 1536 nm is rejected by more than 75 dB compared to the peak transmissions in the Stokes and anti-Stokes channels.

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It is well known that in the low-gain low-detuning region, the number of Stokes and anti-Stokes Raman-scattered photons in a given time interval is proportional to n _th+1 and n _th, respectively, where n _th=1/[exp(ℏω/kT)-1] is the Bose population factor and the resultant Raman-gain coefficient g_R (Ω/2π) is very small [11, 12]. When the detuning Ω/2π is less than 1.5 THz, the co-polarized Raman-gain coefficient in pure-silica fiber follows g _R (Ω/2π)=0.02(Ω/2π)+0.04(Ω/2π)³, where the peak of the Raman-gain coefficient is normalized to one [13]. It is then clear that at the frequency detuning we are interested in, the probability of Raman scattering depends on the detuning and the temperature; the lower the detuning and the temperature, the lesser the probability of Raman scattering. Therefore, to improve the fidelity of our photon-pair source, suppression of the Raman scattering is essential. So, to further improve our results we reduce the detuning Ω/2π to 0.5 THz. The passband spectrum of the DGSF is shown in Fig. 4, wherein the isolation of the pump is still greater than 75 dB and the FWHM is about 0.8 nm, which is obtained by adjusting the DGSF. At this reduced detuning, the improved measurement results are shown in Fig. 5. Comparing the results with those in Fig. 2, for the Stokes and anti-Stokes photons co-polarized with the pump, as shown in the inset of Fig. 5(a), the quadratic-scattering coefficient is increased, the linear-scattering coefficient is decreased, and the ratio between the total-coincidence rate and the accidental-coincidence rate is improved. Taking into account the total detection efficiency of 6% in the anti-Stokes channel, at the production rate of about n̄=0.04 photon-pairs/pulse, the ratio between the total coincidences and the accidental coincidences is 13. For the scattered photons cross-polarized with the pump, as shown in Fig. 5(b), the results are similar to those in Fig. 2(b), except that the linear-scattering coefficient is reduced. These improved results imply that when using this fiber source of correlated photons for creating polarization entanglement, a visibility of two-photon interference greater than 85% would be obtained without subtracting the accidental-coincidence counts.

In principle, further reduction of the detuning will further reduce the contribution of the Raman-scattered photons, which are proportional to (n _th+1) g_R (Ω/2π) on the Stokes side and n _th g_R (Ω/2π) on the anti-Stokes side. Although it is hard to bring the frequencies of the correlated Stokes and anti-Stokes photons closer to the pump frequency while maintaining the necessary isolation of the pump photons with use of the DGSF presently employed in our setup, such reduction in detuning is possible by employing array-waveguide gratings or similar dense-wavelength-division-multiplexing (DWDM) filters that are used in modern fiber-optic communication systems. Ultimately how small a detuning can be achieved is limited by the spectral bandwidth of the Gaussian-shaped pump pulse. The detuning should be large enough to make sure that the number of pump photons leaking into the Stokes and anti-Stokes channels is negligible. Since the Raman-gain coefficient g_R (Ω/2π) may vary from fiber to fiber, a detailed investigation of the Raman gain in the low-detuning regime, which we are presently conducting, is necessary before one can determine the optimal detuning for generating correlated photons with the highest true-coincidence to accidental-coincidence ratio.

 

Fig. 5. Same as in Fig.2, except Ω/2π=0.5THz. For the inset in (a): s ₁=0.00317 and s ₂=0.0132; for the inset in (b): s ₁=0.00259 and s ₂=0.00025. In (a), taking into account the detection efficiency of 6% in the anti-Stokes channel, at a photon-pair production rate of 0.04 (0.067) per pulse the ratio between the total coincidence rate and the accidental coincidence rate is 13:1 (7.5:1).

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In conclusion, we have demonstrated a four-fold improvement over our previous results for the production of quantum-correlated photon pairs using the four-photon scattering process in silica fiber. This was achieved by suppressing the creation of Raman-scattered photons by reducing the detuning of the Stokes and anti-Stokes photons from the pump and by placing a PBS in both the Stokes and anti-Stokes channels. At a production rate of about n̄=0.04 photon-pairs/pulse, the accidental coincidences measured are less than 10% of the true coincidences. Further improvement could be achieved by cooling the fiber.

An additional feature of our fiber-based source of quantum-correlated photon pairs is that it is integrable with the modern fiber-optic technology. The OPO used for obtaining the pump pulses could be replaced by a mode-locked fiber laser, leading to the possibility of repetition rates well over 10 GHz. Moreover, the DGSF could be replaced by fiber-pigtailedDWDMfilters that have lower loss. We also emphasize that the spatial profile of the photon-pair generated is the well characterized, guided, transverse mode of the optical fiber. Thus the main advantage of a fiber source of quantum-correlated photon pairs is the almost perfect coupling efficiency (0.01dB fiber-to-fiber splice loss) that is possible from the source to the transmission fiber in long-distance quantum communication applications. In contrast, fiber coupling of correlated photons from a χ ⁽²⁾-crystal based source is very delicate; the best result to date is a coupling loss of 2.4 dB [14]. The main disadvantages of the fiber source are the existence of Raman scattered photons and the loss incurred in filtering of the pump, which, in principle, could be made very small by use of fiber Bragg-grating filters. Finally, the coupling efficiency advantage of the fiber source would become even more significant when it is used for realizing complex quantum networks involving multiple entangling operations. Thus, our improved results show that an all-fiber source of entangled photon pairs can be a very promising tool for realizing various quantum information processing protocols.

This research was supported in part by the U.S. Army Research Office under a collaborative MURI grant DAAD190010177.