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Abstract
We present a highly efficient photon pair source using chirped quasi-phase-matched (QPM) devices with a ridge waveguide structure. We developed QPM waveguide devices with chirp rates of 3% and 6.7%. Spectrum measurements reveal that the generated photons have bandwidths of 229 nm and 325 nm in full width at half maximum (FWHM), alternatively, 418 nm and 428 nm in base-to-base width for the 3% and 6.7% chirped devices, respectively, which are much broader than the bandwidth of 16 nm in FWHM observed with a non-chirp device. We also evaluate the generation efficiency of photon pairs from coincidence measurements using two superconducting single photon detectors (SSPDs). The estimated generation efficiencies of photon pairs were 2.7 × 106 pairs/s·µW and 1.2 × 106 pairs/s·µW for the 3% and 6.7% chirped devices, respectively, which are comparable to the generation efficiency for the non-chirp device of 2.7 × 106 pairs/s·µW. We also measured the frequency correlation of the photon pairs generated from the 6.7% chirped device. The experimental results clearly show the frequency correlation of the generated broadband photon pairs.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Corrections
13 July 2021: A typographical correction was made to Ref. 34.
1. Introduction
Photonic quantum technology harnesses the principles of quantum mechanics for practical applications, such as quantum imaging [1], quantum sensing [2–4], and quantum communication [5,6]. The unique quantum feature of entanglement has been considered an important resource for bringing the effects of quantum mechanics into many applications. Frequency entanglement-based quantum applications in particular are drawing a lot of attention, such as, quantum information and communication with high-dimensional encoding [7,8] quantum optical coherence tomography [9], and enhancement of two photon absorption [10]. Almost all of these applications can benefit from utilizing broadband frequency correlated photon pairs.
Various methods to extend the bandwidth of frequency correlated photon pairs have been proposed and demonstrated. The generation of non-degenerate broadband photon pairs using lithium niobate (LN) thin film has been reported [11]. Moreover, a bandwidth of 160 nm has been realized by superposing spontaneous parametric fluorescence spectra generated from two nonlinear crystals [12]. For a broader bandwidth of frequency correlated photon generation, chirping of the poling periods of a quasi-phase matching (QPM) device has proven promising [13]. Using a chirped QPM bulk crystal, the generation of broadband (up to 300 nm bandwidth) frequency correlated photons has been reported [14]. The generation of the largest bandwidth of frequency correlated photon pairs of 820 nm has also been realized using a chirped QPM bulk crystal [15]. The highest resolution of 0.54 $\mu$m for two photon interference has also been realized with broadband photon pairs generated from a chirped QPM bulk crystal [16]. Chirped QPM crystal has also been used for preparing broadband telecom-near-infrared photon pairs [17]. Besides expanding the spectra, other uses for the devices with modified poling periods have also been developed, for instance, generation of spectrally pure photons using periodically-poled KTiOPO$_4$ (PPKTP) crystals [18,19]. Unfortunately, an extension of the bandwidth is accompanied by reduced brightness as a photon source.
For high efficient photon pair generation, strong confinement of light has been proposed by combining QPM structures [20]. Especially ridge waveguide with sharp index contrast produced record-high normalized conversion efficiency [21] in a telecom wavelength region. Even an efficient type-II photon source was presented with such a tight ridge waveguide [22]. However, achieving both an increased flux and an extended bandwidth of frequency correlated photons still remains challenging.
In this work, we propose and demonstrate a scheme that, for the first time, enables the efficient generation of ultra-broadband parametric fluorescence. In our periodically-poled stoichiometric lithium tantalate (PPSLT) ridge waveguide device, based on chirped QPM via the type-0 SPDC process, we combine a chirped QPM with a ridge waveguide structure to achieve a large bandwidth together with high efficiency. The nonlinear optical material chosen in this work is Mg-doped SLT (Mg:SLT) for avoiding instability in short-wavelength pumping [23]. In violet light generation with Mg:LN waveguides [24], photorefractive effect induces unstable conversion at high power level. Although nonlinear coefficient is lower than Mg:LN, it is expected to built a stable photon source with Mg:SLT. We developed PPSLT chirped QPM waveguide devices with chirp rates of 3% and 6.7%. Spectrum measurements reveal that the generated photons have bandwidths of 229 nm and 325 nm in FWHM, alternatively, 418 nm and 428 nm in base-to-base width for the 3% and 6.7% chirped devices, respectively, which are much broader than the bandwidth of 16 nm in FWHM observed with a non-chirp device. We also evaluate the generation efficiency of photon pairs from the results of coincidence measurements of photon pairs using two superconducting single photon detectors (SSPDs). The estimated generation efficiencies of the photon pairs were 2.7 $\times$ 10$^6$ pairs/s$\cdot \mu$W and 1.2 $\times$ 10$^6$ pairs/s$\cdot \mu$W for the 3% and 6.7% chirped devices, respectively, which are comparable to the generation efficiency for the non-chirp device of 2.7 $\times$ 10$^6$ pairs/s$\cdot \mu$W. We also measured the frequency correlation of the photon pairs generated from the 6.7% chirped device using combinations of a tunable bandpass filter (BPF) and four fixed wavelength BPFs. The experimental results clearly show the frequency correlation of the generated broadband photon pairs.
This paper is organized as follows. In Section 2 we introduce the details of our waveguide devices and the method for simulating the generation of broadband photon pairs in a chirped QPM ridge waveguide with limited segments. In Section 3 we show second harmonic generation experiments and results for the non-chirped waveguide device. In Section 4 we demonstrate ultra-broadband photon pair generation experiments with single mode fiber coupling and their results. In Section 5, we discuss the evaluation of the generation efficiency of the photon pairs and the frequency correlation of the generated broadband photon pairs.
2. Chirped QPM ridge waveguides
A schematic view of our chirped QPM waveguide devices is shown in Fig. 1. On the slab waveguide layer, we added a ridge waveguide structure with a section size of $\sim 5\mu \rm {m} \times 5\mu \rm {m}$. SLT is used as the waveguide core (both the slab layer and ridge area). Resin is used as the waveguide cladding.
Fig. 1. Schematic view of the structure of the waveguide device. The trapezium waveguide core sits on the slab waveguide layer and is embedded in a 10 mm long chip surrounded by resin as the cladding material.
In the chirped QPM waveguide devices, multiple type-0 SPDC processes take place in multiple sections of a periodically poled structure (segments) with different poling periods that linearly increase from $\Lambda _{\min}$ to $\Lambda _{\max} = (1+r)\cdot \Lambda _{\min}$ along this 10 mm long waveguide, where $\it {r}$ is the linear chirp rate. We designed three kinds of waveguides with different chirp rates $\it {r}$: a regular non-chirped (0%) QPM waveguide, and chirped QPM waveguides with 3% and 6.7% chirp rates. The chirped QPM waveguides have 10 equal length segments along the device with different poling periods $\it {\Lambda (m)}$ which is defined as follows:
In a type-0 SPDC QPM ridge waveguide, pairs of photons with the same polarization are generated in the same spatial mode (guided mode of the waveguide), under the quasi-phase matching conditions $\Delta \beta = \beta _\textrm{p} - \beta _\textrm{s} - \beta _\textrm{i} - 2\pi / \it {\Lambda (z)}$, where $\beta _ {{i}}$ ($\it {i}$ = p, s, and i) is the wave vector of the pump, signal, and idler lights in the waveguide. The two photon wavefunction of the photon pair is given by $f(\omega _\textrm{s}, \omega _\textrm{i}) = \alpha (\omega _{0})\times \phi (\omega _\textrm{s},\omega _\textrm{i})$, $\alpha (\omega _{0})$ is the pump envelope function with pump light frequency of $\omega _{0}$, and $\phi (\omega _\textrm{s}, \omega _\textrm{i})$ is the phase matching function. In the chirped QPM device [25–27], the phase matching function of the $m$-th segment can be expressed as
where $\it {l}$ is the length of the segment, $\chi _m^{(2)}$ is the nonlinearity of the $m$-th segment, and $\Delta \beta _m$ is the phase mismatch in the $m$-th segment. In our 10-segment chirped QPM device, the total phase matching function can be considered as the superposition of $\phi _m$, and by assuming a monochromatic pump light, we can write the intensity of the phase matching function in our waveguide device asIn our simulation, we use a value calculated from the Sellmeier equation [28] for the refractive index of the waveguide core and used a constant value of n$_\textrm{clad}$ = 1.5 as the refractive index of the waveguide cladding. We simplified the waveguide core structure as a 10 mm long rectangular cuboid with a section size of 5 $\mu$m $\times$ 5 $\mu$m. Then, we calculated the effective refractive index of the fundamental mode using an finite-difference time-domain (FDTD) simulation. We used these results together with Eq. (3) to calculate the photon pair spectra. The wavelength of the continuous wave (CW) pump laser is set to be 405 nm. First, we independently calculate each phase matching function $\phi _m$ given by Eq. (2) for each segment, as shown in Figs. 2(a), (b). The first segment with a poling period of $\Lambda _0$ = 3.191 $\mu$m satisfies the degenerate condition while the other segments give a separated spectrum. Figure 2(c) shows the spectral intensity, which is the absolute square of the superposition of all phase matching functions. We found the non-chirp (regular QPM) device has a sinc-like shape spectrum due to the uniform $\Lambda _0$ along the device. On the other hand, increasing the chirp rate $r$ caused the spectra to expand. For the $r$ = 3% device, the bandwidth spans from 680 nm to 1000 nm, and for the $r$ = 6.7% device, the bandwidth spans from 630 to 1120 nm. The ripples shown in the curve for the 3% chirp device (yellow curve in Fig. 2(c)) are caused by interference between the phase matching functions while the multiple peaks for the 6.7% device (green curve in Fig. 2(c)) are given rise by the peaks in the phase matching functions shown in Fig. 2(b). Note that in the theoretical calculation of the phase matching function, we considered the temperature dependence of the Sellmeier equation (refractive index) of SLT crystal. On the other hand, we did not include the effect of the thermal expansion due to the temperature change.
Fig. 2. (a) Phase matching function $\phi _m$ for each segment of the 3% chirped QPM waveguide device. The colored curves represent phase matching functions for different segments. (b) Phase matching functions of the 6.7% chirp device. (c) Simulation spectra generated in the non-chirp and chirped QPM waveguides. The blue curve is the calculated spectrum for the non-chirp device, the orange line is the spectrum for the 3% chirped QPM waveguide, and the green line is the spectrum for the 6.7% chirped QPM waveguide.
In fabrication, we prepared resist patterns which are used for the fabrication of periodically poled structure in our QPM waveguides by photolithography with an accuracy of $\pm$ 0.1 $\mu$m. We fabricated 313 domains of the periodically poled structure for each segment in our chirped QPM waveguides.
3. SHG measurement and results
To test the performance of our waveguide device, we carried out a second harmonic generation (SHG) measurement with the non-chirped QPM waveguide. We pumped the device with 810 nm CW pump light and measured the upconverted light power with a power meter (Thorlabs, S130C) in free space while changing the device temperature (Fig. 3(a)). The results of the temperature dependence measurement show three peaks. It has been reported that the phase matching function inside a nonlinear waveguide is depending on the spatial mode [29–31]. Therefore, we also investigated the beamprofile of the upconverted light using a charge coupled device (CCD) camera (Coherent, LaserCam-HR II). The spatial mode profiles (inset of Fig. 3(b)) of the upconverted light suggest that the peak at a temperature of 78.6 $^\circ$C reflects the phase matching between the fundamental guided modes of pump, signal and idler lights inside waveguide. Figure 3(c) shows the upconverted light power while changing the pump power with the device temperature set to 78.6 $^\circ$C. The solid curve in Fig. 3(c) is the fitting curve given by $I_{2\omega } = \eta I^2_{\omega }$, where $\eta$ is the fitting parameter corresponding to the normalized SHG conversion efficiency, $\it {I}_{2\omega }$ and $\it {I}_{\omega }$ are the intensity of the up converted light and fundamental light respectively. The fitting curve reveals that $\eta$ is about 560% /W.
Fig. 3. (a) Experimental setup. An 810-nm CW light is used as a pump. After coupling the light into the waveguide using an aspheric lens with a focus length of 7.5 mm, the upconverted light power is collected by another aspheric lens with a focus length of 13.8 mm, and is then measured in free space by a powermeter. (b) Upconverted light power associated with device temperature. Three peaks corresponding to three different phase matching conditions are observed. The measurement of beam profile is carried out with a CCD camera and the results are shown beside the corresponding peaks. The first two peaks at lower temperature are attributed to the phase matching condition of higher order modes in the waveguide, and the third peak at a temperature of 78.6 $^{\circ }$C is the phase matching between the fundamental modes of the waveguide. This result shows that multiple phase matching conditions can be satisfied in our device due to the multi-mode feature of our waveguide. (c) SHG power dependence on the input pump power at 78.6 $^{\circ }$C.
4. Spectra of photons generated by chirped QPM ridge waveguides
To evaluate the spectra of the parametric fluorescence, we carried out a spectral measurement. In this measurement, we use a Ti-sapphire ring laser (Coherent, MBR110) followed by a frequency doubler (Coherent, MBD200) as a narrowband CW pump laser ($\sim$ 100 kHz), with the pump light wavelength set to 405 nm. We choose an f = 13.8 mm aspheric lens for pump light coupling and an f = 7.5 mm achromatic doublet lens for collecting signal and idler photons. After eliminating the pump light by two 550 nm longpass filters, we coupled them into a single mode fiber (Thorlabs, P1-780PM-FC-2) which is followed by a spectrometer (Princeton, Acton SP2300), as shown in Fig. 4(a). To maximize the generation efficiency of the SPDC process in the fundamental modes for the pump, signal, and idler lights inside the waveguide, we set the device temperature to 70.8 $^{\circ }$C with a temperature accuracy of $\pm$0.02$^{\circ }$C. The temperature for degenerated phase-matching condition is different from that of the previous SHG experiments because a different pump laser has been used in this experiment.
Fig. 4. (a) Experimental setup for the SPDC spectra measurement. A 405 nm CW laser is used as a pump laser. After eliminating the pump light by two 550 nm longpass filters and single mode fiber coupling, the photons are fed into a spectrometer (Princeton, Acton SP2300). (b) Setup for the measurement of SPDC generation efficiency. 405 nm CW light is used as pump light. Since the twin photons are emitted collinearly, we use a 50:50 fiber beamsplitter (BS) to separate the photon pairs, then feed them into two single mode fibers for the detection of two SSPDs (Scontel, FCOPRS-CCR-SW60-LW60). Both single count events and coincidence are recorded. (c) Setup for frequency correlation measurement. After photons are separated into two optical paths at a 50:50 BS, a fixed wavelength bandpass filter (BPF) and a tunable BPF are placed in the two optical paths. After filtering the wavelength, photons are coupled into two multimode fibers and detected with two single photon counting modules (SPCMs). A coincidence count measurement is carried out while tunning the transmission wavelength of the tunable BPF.
We observed that the degenerated photon pairs have a sinc-like shape spectrum emitted from the non-chirped QPM waveguide. The bandwidth of this spectrum is 16 nm in FWHM, shown by the blue curve in Fig. 5(a). We also measured the spectra of the chirped QPM waveguides under the same experimental conditions, for the device with $r = 3\%$, we observed an expanded bandwidth of 229 nm in FWHM. In addition to FWHM, we use the base-to-base width defined as the width with a height of three times the standard deviation of the background. As shown in Fig. 5(b), the base-to-base width of a 3% chirped device is 418 nm. For the device with a chirp rate $r = 6.7\%$, we observed a bandwidth of 325 nm in FWHM and a base-to-base width of 428 nm.
Fig. 5. (a) Measured spectrum of degenerated parametric fluorescence photons with the non-chirp ridge waveguide after single mode fiber coupling. The FWHM is about 16 nm. (b) Spectrum measured with the 3% chirp ridge waveguide. The FWHM is about 229 nm and the base-to-base width (width of the height of three times the standard deviation of the background) is 418 nm, from 602 nm to 1020 nm. (c) Spectrum of the 6.7% chirp device. The bandwidth is about 325 nm in FWHM and the base-to-base width is 428 nm, from 600 nm to 1028 nm.
Comparing these results with our simulation results, we found that the non-chirp device seems to have a broader bandwidth, i.e. 13 nm for the simulation result and 16 nm for the experimental result. This difference may be caused by imperfect temperature control, because of this, the device is not heated to the exact temperature for the degenerated phase-matching condition. The two sub-peaks at 668 nm and 678 nm in Fig. 5(a), which are not seen in the simulation result (Fig. 2(c) non-chirp), may be SPDC photons with phase matching of higher order modes of the waveguide. The results for the $r$ = 3% and $r$ = 6.7% devices seem to have more frequency components than the simulation results at the shorter wavelength side due to higher mode phase matching occurring in the waveguides. The result for the $r$ = 6.7% chirp waveguide lacks the longer wavelength components seen in the simulation results. This is mainly due to two reasons. The first is the chromatic aberration of the lenses used in our setup for collecting photons with broadband spectra into a single mode fiber. The other is the reduced quantum efficiency at the longer wavelength side of the CCD used in our spectrometer. For instance, the detection efficiency is about 5% at 1000 nm, while the longer wavelength (> 1100 nm) photons cannot be detected by this spectrometer.
5. Correlation measurement of photons generated from chirped QPM ridge waveguides
5.1 Coincidence detection of unfiltered photons using a fiber beamsplitter
To evaluate the photon pair generation efficiency for our non-chirp and chirped QPM waveguides, we carried out correlation measurements. In this experiment, to ensure proper single mode fiber coupling for broadband photons, we use achromatic doublet lenses for collecting photons into single mode panda fibers. After the single mode fiber coupling, we fed the photons into two superconducting single photon detectors (SSPDs) (Scontel, FCOPRS-CCR-SW60-LW60), as shown in Fig. 4(b), and recorded the single count events from two detectors together with the coincidence counts obtained with a time analyzer (ID Quantique, id800) with an effective coincidence time window of 4 ns. The recorded counting events versus the power of the pump light inside the waveguide are shown in Fig. 6(a) for the non-chirped QPM device, and Fig. 6(b),(c) for the 3% and 6.7% chirped QPM devices. The single count rates and coincidence count rates for both non-chirped and chirped QPM devices are proportional to the pump power, with the background counts subtracted. Note that the coincidence counts are approximately halved by the effective loss caused by the fiber beam splitter.
Fig. 6. (a) Single count events and coincidence events (blue dots are for the signal light, orange dots are idler lights and the green dots denote counting events of the coincidence count) for the non-chirp ($r$ = 0%) device. (b) and (c) Single and coincidence counts recorded for the $r$ = 3% chirp and $r$ = 6.7% chirp waveguide devices.
To estimate the generation rate for the collinear emission photon pair sources, we use the method developed by Suezawa and Kiyohara [32] (See Appendix for derivation):
Table 1. The comparison of the generation rate of waveguide devices with different chirp rates.
We compared this result to our previous experiment using a chirped QPM bulk device [16]. In that work, a 20 mm long, $r$ = 6.7% chirped QPM bulk crystal device with 100 segments was used as the photon source that emitted photon pairs non-collinearly. The single photon count events reported in that work were $\sim$1 $\times$ 10$^7$ Hz, and the coincidence count events were $\sim$5 $\times$ 10$^5$ Hz under a pumping power of 100 mW, i.e. the generation rate was about 2$\times$10$^3$ pairs/s$\cdot \mu$W. In the current work our chirped QPM ridge waveguide with $r$ = 6.7% offers a generation efficiency of 1.2 $\times$ 10$^6$ pairs/s$\cdot \mu$W, which is about 600 times greater. Note that this enhancement may come not only from the energy confinement within the waveguide, but also from the smaller number of segments. Note also that we can obtain the average photon flux per nano meter of wavelength by dividing $\it {N}_\textrm {0}$ by the bandwidth (FWHM) in Table 1, for instance, which is 3.7 $\times$10$^3$ pairs/(s$\cdot \mu$W$\cdot$nm) for the 6.7% chirped device.
5.2 Frequency correlation measurements using bandpass filters
To investigate the frequency correlation of photon pairs with ultra-broadband spectrum, we performed a frequency correlation measurement using the 6.7% chirped QPM device. In this measurement, photons are separated using a 50:50 beamsplitter after the waveguide device then coupled into two multi-mode fibers (Thorlabs, M42L02). We placed a fixed wavelength bandpass filter (BPF) in one of the optical paths after the beamsplitter. In the other path, we placed a tunable BPF (Edmund optics, linear variable bandpass filter) with a tunable range from 600 nm to 910 nm with a bandwidth of 22.6$\pm$1.2 nm in FWHM for the given experimental condition.
The coincidence counts were recorded using two single photon counting modules (SPCMs) (Excilitas, AQHR-14-FC) and a time analyzer (ID Quantique, id800). Figure 7(a), (b), (c) and (d) show the coincidence counts while scanning the center wavelength of the tunable BPF for the fixed bandpass filter with the center wavelengths of 740 nm, 800 nm, 850 nm, and 1064 nm, respectively. In Fig. 7, accidental coincidence counts are subtracted. We observed the coincidence peaks at the wavelengths of 895 nm, 820 nm, 774 nm, and 654 nm in Fig. 7(a), (b), (c) and (d), respectively, which correspond to the center wavelength of each fixed wavelength BPF. The red curves indicate the theoretical calculations using the SPDC spectrum and transmission spectra of BPFs, calculated from the following equation:
Fig. 7. Coincidence counts while scanning the tunable BPF with accidental coincidence counts subtracted. The blue dots and the red curve are the experimental data and the theoretical calculation using the SPDC spectrum and transmission spectra of BPFs, respectively. The error bars are calculated assuming Poissonian statistics for the coincidence counts before the subtraction of accidental coincidence counts. The results without subtracting accidental coincidence counts are also shown as inset of each subplot. (a) The result when using the BPF with a center wavelength of 740 nm and the bandwidth of 20 nm. (b) The result when using the BPF with a center wavelength of 800 nm and the bandwidth of 10 nm. (c) The result when using the BPF with a center wavelength of 850 nm and the bandwidth of 40 nm. (d) The result when using the BPF with a center wavelength of 1064 nm and the bandwidth of 10 nm. The data points with the coincidence counts below 0 can be explained by the subtraction of the accidental coincidence counts which have Poisson fluctuation.
6. Conclusion
We developed QPM waveguide devices with chirp rates of 3% and 6.7%. We showed that the generated photons have a bandwidth of 229 nm and 325 nm FWHM, alternatively, 418 nm and 428 nm in base-to-base width, respectively, which are much broader than the bandwidth of 16 nm FWHM observed for a non-chirp device. We also evaluated the generation efficiency of the photon pairs from coincidence measurements using two superconducting single photon detectors (SSPDs). The estimated generation efficiencies of the photon pairs were 2.7 $\times$ 10$^6$ pairs/s$\cdot \mu$W and 1.2 $\times$ 10$^6$ pairs/s$\cdot \mu$W for the 3% and 6.7% chirped devices, respectively, which are comparable to the generation efficiency for the non-chirp device of 2.7 $\times$ 10$^6$ pairs/s$\cdot \mu$W. We also performed the frequency correlation measurement of the photon pairs generated from the 6.7% chirped device. We found that the experimental results clearly show the frequency correlation of the generated broadband photon pairs. Although we evaluated the source via postselection of the cases where photons are successfully separated by a 50:50 beamsplitter, there is a way to efficiently separate the generated photon pairs into two independent spatial modes using a multiple photon interference, which can be considered as a time-reversal process of the HOM interference [33]. In addition, the photon pairs generated collinearly can also be used for quantum nonlinear interferometer [34], and even for the quantum optical coherence tomography with careful postselection of the recorded data [35]. In a future experiment, we will examine reducing the spectra ripples by increasing the number of segments in the device.
Appendix. Derivation of Eq. (4)
The single count events at one of the single photon detectors (detector A) can be expressed as follow:
Funding
Core Research for Evolutional Science and Technology (Grant Number JPMJCR1674); Ministry of Education, Culture, Sports, Science and Technology (MEXT Q-LEAP Grant Number JPMXS0118067634); Precursory Research for Embryonic Science and Technology (JPMJPR15P4).
Acknowledgments
We wish to thank Zhenghao Yin for help in the simulation of the effective refractive index and Kyohei Hayama for help with the experiments. We also wish to thank Shun Suezawa and Takayuki Kiyohara for developing the method of evaluating collinear emitted photon pair generation efficiency and for their advice regarding our work.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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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