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Abstract
Quantum frequency conversion (QFC), which involves the exchange of frequency modes of photons, is a prerequisite for quantum interconnects among various quantum systems, primarily those based on telecom photonic network infrastructures. Compact and fiber-closed QFC modules are in high demand for such applications. In this paper, we report such a QFC module based on a fiber-coupled 4-port frequency converter with a periodically poled lithium niobate (PPLN) waveguide. The demonstrated QFC shifted the wavelength of a single photon from 780 to 1541 nm. The single photon was prepared via spontaneous parametric down-conversion (SPDC) with heralding photon detection, for which the cross-correlation function was 40.45 ± 0.09. The observed cross-correlation function of the photon pairs had a nonclassical value of 13.7 ± 0.4 after QFC at the maximum device efficiency of 0.73, which preserved the quantum statistical property. Such an efficient QFC module is useful for interfacing atomic systems and fiber-optic communication.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Photons are essential for creating a quantum link between distantly located quantum systems, which is referred to as quantum entanglement. Numerous local quantum systems are expected to be used for quantum memories [1,2] and quantum computers [3], such as neutral atoms [4–6], ions [7], semiconductor quantum dots [8], and nitrogen-vacancy (NV) centers [9]. Many matter-based quantum systems experimentally demonstrated thus far interact with photons at visible wavelengths. However, in optical-fiber-based quantum communications, the wavelengths are far from the telecommunication band at approximately 1550 nm, making it difficult to efficiently transmit the photons emitted from the quantum systems over optical fibers. Quantum frequency conversion (QFC) [10] is a promising approach to eliminate the wavelength mismatch [11]. QFC changes the frequency of a single photon while preserving its quantum properties, such as photon statistics and entanglement. Experimental demonstrations related to QFC based on second-order nonlinearity in periodically poled lithium niobate (PPLN) have been widely reported [12–15]. Entanglement-preserving QFC using PPLN waveguides from/to visible to/from telecom wavelengths has been demonstrated [16,17]. QFC systems have been applied to establish entanglement between a matter system and a telecom photon using neutral atoms [18–21], ions [22,23], semiconductor quantum dots [24], and NV centers [25]. These developments have led to remarkable recent demonstrations in which distant matter quantum systems were entangled due to entanglement swapping between telecom photons initially entangled with the matter systems and sent to the middle point of two quantum systems through optical fibers [19,21].
Most of the aforementioned experiments were performed using QFC systems based on free-space optics. To connect the vast number of quantum systems participating in the quantum internet [26,27], integration of the QFC circuit into a single fiber-closed optical device with proper input/output ports for QFC is in high demand. Demonstrations of the frequency-conversion module aiming at plug-and-play QFC have been reported [28–30]. Quantum optical frequency up-conversion has been achieved [28]. However, for frequency down-conversion from visible to telecom wavelengths based on the fiber-optic module, the demonstrations have been performed using laser light [29,30]. Wavelength-division multiplexers (WDMs) were used for combining signal photons and pump light for QFC in those experiments. The insertion loss of fiber-based WDMs exceeds that of dichroic mirrors (DMs) used for free-space optics, which limits the system efficiency and signal-to-noise ratio (SNR) even with an efficient internal QFC process. The SNR in the frequency down-conversion is smaller than that in the frequency up-conversion because of the large amount of noise photons generated by the Raman scattering induced by the strong pump light [31]. Thus, a more efficient optical circuit design is required for quantum frequency down-conversion. Recently, a fiber-pigtailed PPLN module using a DM for combining a signal and pump light was used [32] in a demonstration of phase-sensitive parametric amplification. Since this demonstration, recent advances in device technology have enabled high-gain and low-noise amplification with a gain of >30 dB and noise figure of 1 dB [33], along with >6.3 dB continuous-wave (CW) squeezed light from the DC component to 6-THz sideband frequencies even in a fully fiber-closed optical system. This has been achieved by further reducing the loss of the PPLN module [34].
In this study, using the low-loss design of the PPLN module [33,34], we demonstrated QFC from 780 nm to 1541 nm. In the experiments, we used a single photon at 780 nm, which was produced by spontaneous parametric down-conversion (SPDC), with a heralding signal from the detection of the idler photon. Using a fiber-pigtailed frequency converter based on a PPLN waveguide (PPLN-WG), which we refer to as the 4-port QFC module hereinafter, the 780-nm photon was converted into a 1541-nm photon. We achieved a conversion efficiency 0.70 of our module based on small bulk optics, which is much higher than previously reported values for fully-fiber-based QFC modules [29,30]. The low loss module leads to the successful QFC experiment with observation of cross-correlation between the converted and idler photons surpassing the classical limit of 2. Based on the results, we showed the applicability of the 4-port QFC module to the conversion of photons emitted from rubidium atomic systems.
2. Theory of QFC
We describe the theory of QFC with single-mode light participating in difference frequency generation (DFG) [10,13,17] in a second-order nonlinear optical medium. When the pump light at an angular frequency $\omega _p$ is sufficiently strong, the effective Hamiltonian is expressed as
In this model, the maximum conversion efficiency at $|\xi |\tau =\pi /2$ is unity. However, under actual experimental conditions, there is a nonzero mode mismatch between the propagation mode of the signal light and $\hat {a}_\mathrm {sig}$ for DFG in the nonlinear optical medium, which limits the conversion efficiency. To treat these situations, we model the propagation mode $\hat {a}_\mathrm {sig, exp}$ in the medium as $\hat {a}_{\mathrm {sig, exp}} = \sqrt {\eta _\mathrm {int}} \hat {a}_{\mathrm {sig}} + \sqrt {1-\eta _{\mathrm {int}}} \hat {\bar {a}}_\mathrm {sig}$, where $\hat {\bar {a}}_{\mathrm {sig}}$ satisfies $[\hat {a}_\mathrm {sig}{,} \hat {\bar {a}}_{\mathrm {sig}}^{\dagger }] = 0$ and does not interact with any other mode, including $\hat {a}_\mathrm {con}$. $\eta _\mathrm {int}=|[\hat {a}_\mathrm {sig},\hat {a}^\dagger _\mathrm {sig, exp}]|^2$ denotes the mode overlap between $\hat {a}_\mathrm {sig, exp}$ and $\hat {a}_\mathrm {sig}$. In this case, the conversion efficiency $\eta (=\eta (P_\mathrm {P}))$ is expressed as
3. Experiments
3.1 Experimental setup
Figure 1 shows the experimental setup for the single-photon frequency conversion based on the 4-port QFC module, where the input photon at 780 nm was converted into a photon at 1541 nm with 1580-nm pump light. The 4-port QFC module packaged the optical components for frequency conversion with four pigtailed fibers for two input (port1 and port2) and two output (port3 and port4) ports, as shown in Fig. 1. The pump light and the signal photon emerging from port1 and port2 were combined at a DM and then focused onto the 45-mm PPLN-WG using pairs of aspherical lenses [34]. The converted photon and the pump light were coupled to the output fiber denoted as port3. The signal photon remaining after QFC was coupled to another output fiber denoted as port4.
For preparation of the signal photon, we used SPDC with a CW laser pumping at 517 nm at PPLN-WG2, which produced non-degenerated photon pairs at 780 nm and 1541 nm. The 780- and 1541-nm photons are called signal and idler photons, respectively. The photons were separated by a DM. The 1541-nm photon passed through the DM and was coupled to a single-mode fiber (SMF). The SMF was connected to a bandpass filter (BPF) with a bandwidth of 0.10 nm followed by a superconducting nanowire single photon detector (SNSPD2). Detection of the 1541-nm photon heralded the signal photon at 780 nm. The 780-nm photon was reflected by the DM and passed through two BPFs with bandwidths of 3.0 nm and 0.4 nm and a Bragg grating (BG) with a bandwidth of 0.3 nm. Then, the photon was coupled to a polarization-maintaining fiber (PMF). The PMF was connected to SNSPD1 for measuring the SPDC photon pair without QFC. The coincidence events between SNSPD1 and SNSPD2 were recorded using a time-to-digital converter (TDC) with a 400-ps coincidence window.
For the QFC experiment, the PMF for the heralded 780-nm photon was connected to port2 of the QFC module. The pump light at 1580 nm for QFC was produced by a vertically polarized CW laser amplified by an erbium-doped fiber amplifier (not shown). The pump light was diffracted by a BG with a bandwidth of 1 nm and then coupled to a PMF connected to port1 of the QFC module with a maximum power of 156 mW. Together with the 780-nm photon coming from port2, the 1541-nm photon was produced at the QFC module. The 1541-nm photon and 1580-nm pump light coming from port3 were connected to a free-space-based optical circuit once. At the circuit, they were separated by a short-pass filter (SPF). The pump light reflected by the SPF was used for monitoring the pump power. The 1541-nm photon was diffracted by a BG with a bandwidth of 1 nm and coupled to a PMF. Using a BPF with a bandwidth of 0.10 nm corresponding to $\Delta f_\mathrm {con} = {13}\;\textrm{GHz}$, we further cleaned the spectrum of the 1541-nm photon and measured it via SNSPD3.
3.2 Experimental results
Before performing the quantum experiments using photons, we estimated the conversion efficiency of the QFC module. We inputted a 780-nm CW laser with a power of $P_{\mathrm {sig,in}}$ = 15 mW to port2 of the QFC module. For different values of the pump power $P_\mathrm {P}$, we measured the output power $P_\mathrm {sig,out}$ of the signal light at port4. Additionally, instead of using SNSPD3, we measured the power $P_\mathrm {con,out}$ of the converted light after it passed the BPF. The measured values of $P_\mathrm {sig,out}$ and $P_\mathrm {con,out}$ are shown in Fig. 2. From the result and module transmittance $T_{\rm sig}=0.49$ of the signal light from port2 to port4, we estimated the overall conversion efficiency of the QFC system, including the QFC module and the frequency filter system, to be $\eta _{\mathrm {sys}}(P_\mathrm {P}) = P_{\mathrm {con, out}}(P_\mathrm {P}) \lambda _{\mathrm {con}}/(P_{\mathrm {sig, in}}\lambda _\mathrm {sig})$, where $\lambda _{\mathrm {con}}={1541}\;\textrm{nm}$ and $\lambda _{\mathrm {sig}}={780}\;\textrm{nm}$. $P_\mathrm {P}$ represents the pump power at port1 estimated from the transmittance $T_{\mathrm {P}}=0.65$ of the pump light from port1 to the power meter. The estimated maximum efficiency was $\eta _\mathrm {sys, max} = 0.073$ at $P_\mathrm {P}={139}\;\textrm{mW}$.
Fig. 2. Experimental results for DFG of 780-nm laser light. Orange circles represent the power $P_{\mathrm {sig}{,} \mathrm {out}}$ of the signal light measured at port4. Blue squares represent the power $P_{\mathrm {con}, \mathrm {out}}$ of the converted light measured at the place before SNSPD3. The horizontal axis indicates the input pump power $P_{\mathrm {P}}$ at port1 estimated from the observed power after SFP using $T_{\mathrm {P}} = 0.65$.
The estimated value $\eta _\mathrm {sys, max}$ included the mode matching $\eta _\mathrm {int}$ given by Eq. (4). From the best fit of the function $1-\eta (P_\mathrm {P})$ to the observed values of $P_\mathrm {sig,out}(P_\mathrm {P})$ in Fig. 2, $\eta _{\rm int}=0.95$ and $\eta _{\rm nor}L^2 = 17.8/{\rm W}$ were estimated. Using the observed transmittance $T_{\rm f}=0.10$ of the frequency filter system from port3 to the place immediately before SNSPD3, we obtained $\eta _\mathrm {mod} = \eta _\mathrm {sys, max}/(\eta _\mathrm {int}T_{\rm f})\sim 0.73$ which is the product of the coupling efficiency from port1 to the PPLN-WG and that from the PPLN-WG to port3 for the signal and converted photons, respectively. This implies that the integration of the free-space-based QFC circuit with the fiber-optic module was achieved at an efficiency of 0.73. The maximum conversion efficiency of this module, excluding the transmittance of the filtering system, was $\eta _\mathrm {mod} \eta _\mathrm {int}\sim 0.70$. This value is higher than those of other fiber-closed QFC modules [29,30], thanks to the low loss small bulk optics instead of using fiber-based optical circuits with WDM technologies.
Next, we demonstrated QFC using the SPDC photon pair. Without QFC, the cross-correlation function $g^{(2)}_{\mathrm {sig,idl}}$ between the signal and idler photons was estimated as $g^{(2)}_{\mathrm {sig,idl}} = 40.45 \pm 0.09$ from the coincidence measurement between SNSPD1 and SNSPD2, as shown in Fig. 3(a). With QFC, we measured the cross-correlation function $g^{(2)}_{\mathrm {con, idl}}$ between the converted photons and idler photons from the coincidence measurement for various values of $P_\mathrm {P}$. The experimental results of the coincidence measurement for $P_\mathrm {P} = {139}\;\textrm{mW}$ are presented in Fig. 3(b). As shown, the observed value of $g^{(2)}_{\mathrm {con,idl}}$ at the maximum conversion efficiency was estimated to be $13.7\pm 0.4$. Figure 4(a) presents the dependence of $g^{(2)}_{\mathrm {con, idl}}$ on the pump power $P_{\mathrm {P}}$. As shown, the QFC system preserved high values of $g^{(2)}_{\mathrm {con,idl}}$ that significantly surpassed the classical limit of 2 [36].
Fig. 3. (a) Observed coincidence counts in 60 s between the signal and idler photons. (b) Observed coincidence counts in 60 s between the converted and idler photons with $P_{\mathrm {P}}=$139 mW.
Fig. 4. (a) Observed cross-correlation function $g^{(2)}_{\mathrm {con}, \mathrm {idl}}$ (blue circles). The error bars represent $\pm 1$ standard deviation, assuming a Poisson distribution error in photon detection. The solid curve was obtained using Eq. (6). (b) Relationship between the input pump power and noise counts detected by SNSPD3 (blue dots) without a signal. The fitting function is given by Eq. (5).
To evaluate the number of noise photons induced by QFC, we measured the photon counts caused by the pump light without signal input. Figure 4(b) shows the relationship between the noise count rate $N(P_{\mathrm {P}})$ detected at SNSPD3 and the pump power $P_{\mathrm {P}}$. We fitted the data using the following function considering the influence of frequency conversion of the noise photons [37]:
4. Discussion
We discuss the cause of the degradation of the intensity cross-correlation function $g^{(2)}_{\mathrm {con}, \mathrm {idl}}$ between the converted photons and the idler photons. From Ref. [37], $g^{(2)}_{\mathrm {con}, \mathrm {idl}}$ is theoretically described using $g^{(2)}_{\mathrm {sig}, \mathrm {idl}}$ before QFC and the overall SNR $\zeta (P_{\mathrm {P}})$ after QFC as
We estimate $\zeta (P_{\mathrm P})$ as follows. We assume that the bandwidth of SPDC photons is sufficiently broad and that all the BPFs used in the experiment are Gaussian. We also assume that the acceptable bandwidth of the PPLN-WG is 60 GHz. The ratio of the overall efficiency of QFC with the filter system for the signal photons to that for cw light is $\eta _{\mathrm {filter}} \approx 0.07$. Using the experimentally observed or estimated values of $\eta _{\mathrm {filter}}$, $\eta _\mathrm {sys}(P_\mathrm {P}), N(P_\mathrm {P})$, the signal photon count rate $N_\mathrm {in}=2.3{\times}10^{6}\;\textrm{cps}$ at SNSPD1, the detection efficiency $\eta _{\mathrm {d}{,}\mathrm {sig}} \sim 0.3$ of SNSPD1 including fiber coupling losses, and the specification value of the detection efficiency $\eta _{\mathrm {d}{,}\mathrm {con}} = 0.88$ of SNSPD3, the overall SNR is expressed as
From this equation and $g^{(2)}_{\mathrm {sig}, \mathrm {idl}}=40.45$, we determined the pump-power dependence of $g^{(2),\mathrm {th}}_{\mathrm {con}, \mathrm {idl}}(P_{\mathrm {P}})$ in Eq. (6), as indicated by the blue curve in Fig. 4(a). The curve agreed well with the experimental results. Therefore, the reason for the degradation of the intensity cross-correlation function is explained by the SNR through the QFC process.
Next, we discuss the applicability of the proposed QFC system to photons emitted from atomic systems. We consider the observed data reported in Ref. [37], in which the intensity cross-correlation is $g^{(2)}_{\mathrm {sig}, \mathrm {idl}} = 22$, the detection probability of the signal photon before it reaches the QFC system is $p_{\mathrm {sig}} = 0.0049$, the detection efficiency of 780 nm photons is $\eta _{\mathrm {d}{,}\mathrm {sig}}= 0.43$, the full width at half maximum (FWHM) of the temporal profile of converted photons is $\Delta t_{\mathrm {ref}} = {13}\;\textrm{ns}$ as the coincidence window, and the bandwidth of the frequency filter is $\Delta f_{\mathrm {ref}}=$ 2.5 GHz. Assuming that the noise photons detected with the converted light are temporally and spectrally broad, the detection probability of noise photons in the coincidence window is expressed as $N(P_\mathrm {P})\Delta t_\mathrm {ref}\Delta f_\mathrm {ref}/\Delta f_\mathrm {con}$. In this case, the expected intensity cross-correlation function after QFC by the proposed system is $\sim 17$ at $P_{\mathrm {P}} =$139 mW, which is comparable to a previously reported value of approximately 15 [38]. In addition, the internal conversion efficiency ($\eta _\mathrm {int}=0.95$) and the transmittance of the QFC module ($\eta _\mathrm {mod} \sim 0.73$) are comparable to previously reported values [19,37,38]. These results indicate that our module is useful for QFC of photons emitted from atomic systems in terms of the SNR and efficiency.
5. Conclusion
We developed and tested a fiber-pigtailed 4-port frequency converter based on a PPLN-WG. We demonstrated QFC of a 780 nm photon to a 1541 nm photon using SPDC photon pairs. A nonclassical cross-correlation function with a value of $13.7\pm 0.3$ was observed after QFC, which surpassed the classical limit of 2. The experimental results indicated the applicability of the proposed QFC system to the conversion of photons emitted from atomic systems. We believe that this system will accelerate the development of quantum networks, including various quantum information systems.
Funding
Program for Leading Graduate Schools: Interactive Materials Science Cadet Program; Japan Society for the Promotion of Science (JP20H01839, JP21H04445, JP22J20801); Core Research for Evolutional Science and Technology (CREST) (JST JPMJCR1671); Moonshot Research and Development Program (JST JPMJMS2066, JST JPMJMS226C).
Acknowledgments
R.I., N.I., and T.Y. acknowledge the members of the Quantum Internet Task Force for the comprehensive and interdisciplinary discussions on the quantum internet.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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