Observation of photon-pair generation in the normal group-velocity-dispersion regime with slight detuning from the pump wavelength

A non-classical light source is one of the key elements of quantum information processing systems, and several types of these sources have been investigated, including molecules [1], trapped atoms [2], quantum dots [3], diamond vacancy centers [4], spontaneous parametric down-conversion (SPDC) [5], and spontaneous four-wave mixing (SFWM) [6]. Among these processes, the SPDC and the SFWM processes create quantum-correlated photon pairs from one and two pump photons, respectively, and both processes require satisfying the energy conservation as well as phase matching [7]. Typically, the nonlinear coefficient of SPDC in second-order nonlinear crystals is larger than that of SFWM in amorphous single mode optical fibers as SFWM is a third-order nonlinear process. In the case of several hundred meters long single-mode fibers, however, the SFWM conversion efficiency from pump beam to photon pairs can be similar with that of the SPDC process in nonlinear crystals. In addition, the fiber based photon-pair sources are able to be directly coupled to fiber systems with negligible coupling loss, but waveguide-to-fiber coupling efficiency of a periodically poled SPDC crystal is reported about 50% [8]. The SFWM process has been studied intensively for the fiber-based photon generation [6, 9–20] for quantum information applications including quantum key distribution.

Photon-pair generation via SFWM is active near the zero group-velocity-dispersion (GVD) wavelength, λ_ZGVD, in the anomalous GVD regime [6, 9–15] or normal GVD regime [16–20]. In the normal GVD regime, the wavelength of the generated photon pairs is significantly detuned from the pump wavelength. In this case, Raman noise can be avoided, but the generated photon pair do not exhibit telecom-band wavelength together. On the other hand, in the anomalous GVD regime, the wavelength of the generated photon pair is slightly detuned from the pump in the telecom C-band and is strongly power dependent [16].

Since the wavelength of the generated pair is sensitive to the λ_ZGVD of the generation medium, several types of commercial fibers which have λ_ZGVD in the telecom C-band have been investigated as the telecom C-band pair sources. Even if commercial optical fibers have small tolerances in their physical properties, it is common to have sizeable λ_ZGVD variance along an optical fiber [21, 22]. Therefore, the precise measurement of the GVD spectrum is required, but it is often tricky with short length optical fibers. One way to overcome this problem is engineering the dispersion of a commercial fiber by heating and pulling the fiber, but this method is an ambitious research field [19, 20, 23]. On the other hand, if a slightly detuned pair can be generated in the normal GVD regime, the constraint for the λ_ZGVD of medium can be weakened, but it has not been reported to the best of our knowledge because phases are mis-matched in this regime due to the Kerr effects of the media.

Here, we investigate the conditions for generating low-noise photon pairs in the telecom C-band that are slightly detuned from the pump wavelength in the normal GVD regime of dispersion shifted fiber (DSF) for the first time. Experimental conditions are carefully chosen to obtain high coincidence-to-accidental ratio (CAR) values by lowering temperature as well as pump power, reducing photon losses of the system, using a polarizer to block the cross-polarized Raman background photons, and selecting signal/idler photon filters at a small shift from the pump wavelength. A CAR value of about 260 was achieved, which is the highest value reported in DSF at liquid nitrogen temperatures. In addition, an excellent heralded anti-bunching property was achieved (g_H⁽²⁾(0) ∼ 0.016), indicating that this pair generation scheme is a potential low-noise photon-pair source or a heralded single-photon source. The results prove that the slightly detuned photon pair generation in the normal GVD regime in DSF can be effectively exploited as telecom-band quantum light sources for quantum information applications.

The photon-pair generation by SFWM needs to satisfy energy conservation and phase matching conditions as given by,

$$\begin{eqnarray}&&2{\omega }_{{\rm{p}}}={\omega }_{{\rm{s}}}+{\omega }_{{\rm{i}}},\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&2{k}_{{\rm{p}}}={k}_{{\rm{s}}}+{k}_{{\rm{i}}}+2\gamma {P}_{{\rm{p}}},\end{eqnarray} \tag{ 2 }$$

where ω_j (j = p, s, i) is the frequency of pump, signal, and idler photons (ω_s > ω_i), respectively, and k_j ≡ n_j ω_j/c (j = p, s, i) is the wave vector of the pump, signal, and idler photons in a DSF, respectively. n_j (j = p, s, i) is the frequency dependent refractive index of the medium and c is the speed of light in a vacuum. γ represents the nonlinear Kerr coefficient of the DSF and P_p is the pump peak power.

The λ_ZGVD of the DSF used in this study is 1555.98 nm. Using equations (1) and (2), the SFWM phase matching curve against the pump wavelength is calculated for the DSF with a peak pump power of 0 W (black dashed curves) and 0.1 W (red solid curves) as shown in figure 1(a). The y-axis represents the wavelength difference between the pump and the generated photons, and the photons with positive (negative) wavelength difference are idler (signal) photons. The regime with a shorter (longer) wavelength than λ_ZGVD = 1555.98 nm indicates the normal (anomalous) GVD regime and is represented as the gray (white) region.

Zoom In Zoom Out Reset image size

When the pump peak power is 0 W, three solutions (I, II, and III) satisfying equations (1) and (2) exist as seen by the three black circles on the black dashed curves in figure 1(a). Solution I and II are the fundamental solutions with k_p = k_s = k_i, and solution III in the normal GVD regime is for signal/idler photons far from the pump wavelength (k_p ≠ k_s ≠ k_i but 2k_p = k_s + k_i + 2γP_p). With a non-zero pump power, the photon pairs can be generated for the regime II and III (red curves in figure 1(a)) [6, 9–20], but the nonlinear Kerr effects, 2γP_p, in equation (2) cause difficulties in the generation of solution I for the normal GVD regime.

Figure 1(b) shows the normalized probability density spectrum of photon pair emission against the pump wavelength. Note that photon pairs close to the pump wavelength are created even in the normal GVD regime (solution I). The probability density spectrum of pair emission is based on the calculated joint spectral intensity through a 500 m DSF with a peak pump power of 0.1 W [15, 24]. The joint spectral intensity is proportional to sinc²(ΔkL/2), where L is the length of SFWM medium and Δk = 2k_p − k_s − k_i − 2γP_p is the phase mismatching. With an infinitely long DSF, the joint spectral intensity will be a delta function in the frequency domain and SFWM occurs only at the possible wavelengths from the phase matching curve as seen in figure 1(a). The phase matching can be, however, relaxed by using a finite length of SFWM medium and then photon pairs slightly detuned from the pump wavelength can be generated in the normal GVD regime as shown in figure 1(b).

Figure 2 shows the experimental setup used in this study. The pump source is a mode-locked pulse laser with a pulse width of about 10 ps and a repetition rate of 18 MHz. Since C-band fiber optic components are commercially available, the pump and the filter wavelengths are anchored on the ITU grid. The pump wavelength selected in this study is 1552.52 nm (ITU-grid channel no. 31) which is about 3.5 nm away from λ_ZGVD. A set of 100 GHz dense wavelength division multiplexing (DWDM) filters with a full-width at half-maximum (FWHM) bandwidth of about 0.6 nm is used as a band-pass filter to remove amplified spontaneous emission noise from the pump laser. A variable optical attenuator adjusts the input pump power. The pump beam travels through the band-pass filter and enters a 500 m DSF which is cooled down to the temperature of liquid nitrogen to reduce spontaneous Raman scattering (spRS) [10–14]. In addition, a fiber polarizer is placed after the DSF to remove the cross-polarized Raman-scattered photons [9–11]. The measured values of λ_ZGVD and the dispersion slope of the used DSF fiber are 1555.98 nm and 69.7 s m⁻³, respectively [25]. A set of notch filters with an FWHM bandwidth of 1.1 nm is used to attenuate the pump light by more than 120 dB. Furthermore, additional DWDM filters in the detection system suppress the pump light even more. The total suppression of the pump is more than 150 dB.

Zoom In Zoom Out Reset image size

The experimental setup is identical for all experiments except the detection systems. Insets (i)–(iii) in figure 2 show the detection systems used for the following measurements: (i) the single-photon spectrum, (ii) the coincidence to accidental ratio (CAR), and (iii) the heralded second-order self-correlation. The 100 GHz DWDM filters separate signal and idler photons with an FWHM bandwidth of 0.6 nm. The total detection efficiency of setup (i) is about −20 dB including −7 dB InGaAs single-photon detector efficiency and that of setup (ii) and (iii) is −15.6 dB. The detection efficiency of idler photons in setup (iii) is about −19 dB including an additional 3 dB directional coupler. The gate width and the dead time of the single-photon detectors are 1 ns and 10 μs, respectively. The coincidence window of the time-correlated single photon counting (TCSPC) module in the experiments is about 500 ps.

The single-photon count spectrum (red squares in figure 3(a)) through a 500 m DSF is measured using the setup as shown in figure 2 with the detection system of inset (i) and a peak pump power of P_p ∼ 0.3 W. The step size of the tunable filter is 25 GHz and the used notch filter has a flat transmittance reponse over the scanning range. Note that both the SFWM photons and spRS noise photons contribute to the single-photon count measurement (the red squares in figure 3(a)). Since the spRS spectrum does not depend on λ_ZGVD, the contribution of Raman noise photons to the single count spectrum can be estimated by the independent measurement of the spRS spectrum through a single-mode fiber (SMF, Corning (SMF-28)), as shown by the blue diamonds in figure 3(a). The different mode areas of the DSF and the SMF cause different photon noise rates, but the spectrums can be matched by applying a weight factor of about 1.5 to the SMF. Since the SMF has a λ_ZGVD at 1.3 μm, negligible photon-pair generation in this fiber is expected at 1552.52 nm.

Zoom In Zoom Out Reset image size

As shown in figure 3(a), the SMF spectrum (blue diamonds) and DSF spectrum (red squares) show a meaningful difference between 1548 and 1557 nm. By subtracting these two spectra, the single-count spectrum due only to SFWM (black squares in figure 3(b)) is obtained. Since the photon generation rate by this process decreases rapidly and the photon noise rate due to spRS increases further away from the pump wavelength, the closer the signal and idler frequencies to the pump frequency, the larger the achievable signal-to-noise photon ratio. Considering the bandwidth of the notch filter and pump photon leakage through this filter as well as the DWDM, two commercially available DWDM channels of ITU-grid no. 35 (1549.32 nm) and 27 (1555.75 nm) are selected as the signal and idler photon filters, respectively. Their center frequency spacing from the pump is 400 GHz. The spectral shapes of the DWDM filters are shown in figure 3(b) as the gray areas.

The single count rate of each single-photon detector is measured for various pump peak powers using the detection system in inset (ii) of figure 2. The pair photons, spRS photons, and detector dark counts contribute to the count rate of each single-photon detector. The single count rate of each detector, C_A and C_B, can be written as [14],

$$\begin{eqnarray}&&{C}_{{\rm{A}}}={\mu }_{{\rm{P}}}{\alpha }_{{\rm{s}}}{{P}_{{\rm{p}}}}^{2}+{\mu }_{{\rm{Rs}}}{\alpha }_{{\rm{s}}}{P}_{{\rm{p}}}+{D}_{{\rm{s}}},\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{C}_{{\rm{B}}}={\mu }_{{\rm{P}}}{\alpha }_{{\rm{i}}}{{P}_{{\rm{p}}}}^{2}+{\mu }_{{\rm{Ras}}}{\alpha }_{{\rm{i}}}{P}_{{\rm{p}}}+{D}_{{\rm{i}}},\end{eqnarray} \tag{ 4 }$$

where μ_j (j = P, Rs, Ras) is the generation rate of photon pairs, Stokes Raman photon, and anti-Stokes Raman photon, respectively. D_s (D_i) is the dark counts of the signal (idler) channel single-photon detector, P_p is the peak pump power, and α_s(α_i) is the product of the total transmittance and the quantum efficiency of the detector for each channel.

The square markers in figures 4(a) and (b) are the measured signal and idler count rates against the peak pump power, respectively. The theoretical fit obtained using equations (3) and (4) are shown as black solid curves superimposed on the experimental data. The dashed and dotted curves represent the quadratic and linear contributions of the fitting functions corresponding to the photon-pair generation and the spRS rates, respectively. The dark count rates in this experiment are negligible (∼50 Hz).

Zoom In Zoom Out Reset image size

The single count rate in figures 4(a) and (b) has a maximum count value of 10.8 kHz, which is limited by the detector performance and not the photon-pair source. The InGaAs single-photon detectors used in this experiment are operated with 10 μs dead time to avoid the after-pulsing effects, and the pair generation rate is reduced to prevent the saturation effects of the detectors. In addition, the −15.6 dB total detection efficiency needs to be improved for fast measurements. Much higher single and coincidence count rates are expected if fast and efficient single-photon detectors are used such as superconducting nanowire detectors [12, 14] or up-conversion detectors [26]. In addition, the active spatial multiplexing method of multiple photon-pair sources can increase the pair generation rate while keeping low CAR [27].

Figure 4(c) shows the result of the CAR measurements against the pump power, where a maximum CAR value of 260 is obtained. The red squares mean the measured CAR values, the horizontal error bar is the pump power fluctuation during measurement, and the vertical error bar represents the shot noise assuming a Poisson distribution of photons. Under our experimental conditions, the accumulation times of each data point in figures 4(c) and (d) differ from each other for reducing the total measurement time. Therefore, the size of the error bars fluctuates due to the uneven accumulation time, but the power dependence of the measured CAR values is not affected and is in close agreement with the predicted CAR values (red solid curve in figure 4(c)).

The coincidence count rate, C_AB, is given by μ_Pα_sα_iP_p² + C_AC_B, where C_AC_B is the accidental coincident rate including pair–pair, Raman–Raman, and pair–Raman coincidences. This relation explains why the CAR value is about 25 for a 0.3 W pump peak power in figure 4(c), even though the measured spRS single count rate (N_spRS ∼ 1300 Hz) in figure 3(a) is higher than the measured SFWM single count rate (N_SFWM ∼ 450 Hz) in figure 3(b). The pair generation rate per pulse is given by μ_PP_p²/R = (N_SFWM/η)/R, where η represents the total detection efficiency and R is the pump repetition rate. Similarly, the Raman generation rate is μ_RsP_p/R = (N_spRS/η)/R. From the above coincidence count rate C_AB, the true coincidence count rate is {(N_SFWM/η)/R} × α_sα_iR and the accidental coincidence count rates by multiple pairs, Raman photons, and the combination of them are {(N_SFWM/η)/R + (N_spRS/η)/R}² × α_sα_iR. The accidental due to the dark counts of two detectors is neglected. The CAR is given by {(N_SFWM/η)/R}/{(N_SFWM/η)/R + (N_spRS/η)/R}² and the estimated CAR value is about 26 using the parameters of R = 18 × 10⁶ (MHz) and η = −20 dB for the setup (i) in figure 2, showing excellent agreement with the experimental result of 25 in figure 4(c).

The highest CAR value 260 at a peak pump power of 20 mW is smaller than that of the Raman-free pair photon generation processes. However, the CAR value of 260 is about twice as large the previously reported value for DSF at the same temperature of 77 K in the anomalous GVD regime [10–12]. This result implies that a CAR of 3000 is expected if a DSF is cooled down to the temperature of liquid helium at about 4.2 K [12].

To characterize the heralded single-photon property of the generated photons, the conditional Hanbury-Brown and Twiss (HBT) experiment is performed to measure the heralded second-order self-correlation, g_H⁽²⁾(0). The detection system of the conditional HBT experiment is shown in inset (iii) of figure 2. Signal photons are used as the heralding photons (D3), and the self-correlation of the idler photons is measured under the heralded condition. The three-fold coincidence of D1, D2, and D3 is counted using a TCSPC module with a coincidence window of about 500 ps. Using the pulsed pump, g_H⁽²⁾(0) is given by [27, 28],

$$\begin{eqnarray}&&{{g}_{{\rm{H}}}}^{(2)}(0)=\displaystyle \frac{{C}_{{\rm{ABH}}}(0){C}_{{\rm{H}}}}{{C}_{{\rm{AH}}}(0){C}_{{\rm{BH}}}(0)},\end{eqnarray} \tag{ 5 }$$

where C_ABH is the three-fold coincidence counts of D1, D2, and D3, C_AH (C_BH) is the heralded coincidence counts of D3 and D1 (D3 and D2), and C_H is the heralding single counts of D3.

Figure 4(d) shows the measured g_H⁽²⁾(0) values (blue diamond dots) against the peak pump power. The horizontal error bar represents the pump power fluctuation while the vertical error bar represents the shot noise. The blue dashed curve represents the g_H⁽²⁾(0) values using equation (5) and the single count measurements in figures 4(a) and (b). As the peak pump power decreases, g_H⁽²⁾(0) is reduced and the measured minimum value was 0.0167 ± 0.0075. Therefore, the SFWM source used in this experiment can create photon pairs with strong temporal correlation and can be an excellent heralded single-photon source with a high signal-to-noise ratio.

In summary, photon pairs that are slightly detuned from the pump wavelength in the normal GVD regime are observed in the telecom C-band through a DSF for the first time. The photon noise due to spRS is reduced by lowering the temperature to 77 K, using a polarizer, and employing a low Raman scattering wavelength. A high CAR value of 260 was obtained and this value is the maximum value reported in DSF at liquid nitrogen temperature. The excellent anti-bunching property of the heralded single photons is confirmed using the conditional HBT experiment with a minimum g_H⁽²⁾(0) value of 0.0167 ± 0.0075. The results show that the slightly detuned photon pair generated in the normal GVD regime has good temporal correlation properties that are comparable to photon pairs generated in the anomalous GVD regime. The generation scheme used in this paper shows potential for application as an efficient photon-pair source or pure heralded single photon generation source in the telecom C-band. Even though pair generation through a DSF is limited by spRS noise, our results show that the DSF system in the normal GVD regime can be used as a practical photon-pair source that would have a direct positive impact on quantum information processing.

These relaxed phase matching conditions extend the terms of photon pair generation. We believe that the relaxed phase matching conditions will occur not only in DSF but also in all the SFWM media such as photonic crystal fiber, highly nonlinear fiber, and silicon waveguide. Therefore, the relaxed phase matching scheme will be useful for the development of efficient photon-pair sources along with the techniques of engineering the chromatic dispersion of optical waveguides.

Acknowledgments