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Abstract
Backward-wave three-wave mixing is a difficult χ(2) interaction to observe, because it requires ultrashort poling periods to achieve phasematching. Having realized sub-micrometer periods in periodically poled KTiOPO4 (PPKTP), we demonstrate for the first time first-order quasi-phasematched, backward-wave spontaneous parametric downconversion (BW SPDC). We pumped the PPKTP crystal at 800 nm and obtained a forward-wave signal at 1400 nm and a backward-wave idler at 1868 nm. We estimated an internal pair production rate of 4.0 × 104 pairs/s/mW. The backward-wave phasematching constraints lead to the unique tuning property that spectral features of the pump are transferred to the forward-wave signal photons, which makes BW SPDC an attractive source of spectrally shaped, heralded single photons. These spectrally shaped photons are useful for quantum computing and quantum interconnects. For the first time, we experimentally show this effect by observing frequency translation between a spectrally shaped pump beam and the BW SPDC signal photons. Due to their unique properties, BW-SPDC-based devices will be important building blocks for quantum information processing.
1. Introduction
Backward-wave (BW) three-wave mixing was first proposed by S.E. Harris in 1966 [1]. However, due to the very small quasi-phasematching (QPM) [2,3] periods required (typically less than 1 µm for first-order QPM), it was not experimentally realized until 2007 in a backward-wave optical parametric oscillator (BW OPO) [4]. Since then, substantial progress in fabrication of QPM gratings with sub-micrometer periodicities has been made, allowing further experimental studies of BW OPOs [5–9]. For backward-wave spontaneous parametric downconversion (BW SPDC), there have been several theoretical studies [10–16] highlighting the unique features of BW SPDC, which include having a highly narrowband idler [10,13] and separable joint spectral amplitude [11,15]. However, only a few experimental studies have utilized third-order [17] and fifth-order [18–20] QPM gratings, which have low conversion efficiencies. Thanks to the progress in ultrashort-period, periodically poled Rb-doped KTiOPO$_4$ (PPKTP) [9,21,22], we can now report on the first demonstration of BW SPDC in a first-order, PPKTP grating having 500 nm period and direct measurement of the SPDC spectra. We further show that BW SPDC can be used to generate spectral shaped, heralded single photons, which are useful for quantum networking [23,24], quantum interconnects [25], and quantum information processing [26].
One key application of BW SPDC is in producing spectrally shaped, single photons. These are useful for optical quantum computing where the qubits are encoded in frequency bins [26]. Also, spectrally shaped single photons will be needed in the quantum interconnects between different quantum nodes in a quantum network. These nodes may be based on different technologies such as atomic ensembles [23,27], trapped ions [28], or nitrogen-vacancy centers [29]. The operating wavelengths, linewidths, and other spectral requirements of these nodes may be different, which will require quantum frequency conversion [30], filtering [31], or spectral engineering of entangled photons [32] to connect the nodes. BW SPDC represents a new way to generate spectrally tailored photons.
Spectral shaping of single photons using BW SPDC has advantages over existing techniques. SPDC photons are typically shaped after they are generated using programmable filters or spatial light modulators [32,33]. These techniques cause some loss of the downconverted photons, break apart photon pairs, and reduce the SPDC pair generation efficiency. In contrast for BW SPDC, spectral shaping is applied to the pump and then transferred to the downconverted single photons through the process of frequency translation [7,34]. Losses due to spectral shaping of the pump beam can be compensated by increasing the pump power without degrading the SPDC pair generation efficiency. The improvement in generation efficiency and avoidance of losses are very attractive features for quantum networking and quantum computing. Another method for spectrally shaping SPDC photons is to engineer the nonlinear optical medium by incorporating an optical cavity [35] or by aperiodic-domain-engineering of the nonlinear crystal [36–38], but the spectral shape is fixed during fabrication and does not offer reconfigurability.
In BW three-wave mixing, the pump and signal are co-propagating while the idler is counter-propagating. The phase-mismatch, $\Delta k$, is given by
The unique tuning behaviors of BW three-wave-mixing devices arising from their $k$-vector constraints have been previously noted [4,6–8,10,14,34,39]. These unique tuning behaviors include having highly narrowband backward-propagating idler wave and weak dependence of the idler frequency with respect to the pump frequency ($\partial \omega _\textrm { i}/ \partial \omega _\textrm { p} \approx -0.01$ [7], where $\omega _j$ refers to the angular frequency of wave $j$), which is illustrated in Fig. 1. Another tuning behavior of BW three-wave mixing is that the forward-propagating signal wave has a frequency response that mimics that of the pump wave. This observation led to the proposal that BW devices can be used as frequency translators between the pump and signal wavelengths [7,34]. This frequency-translation property follows from having a highly narrowband idler that is insensitive to pump tuning; by energy conservation, the spectral information of the pump wave is translated onto the forward-propagating signal wave. In this work, we experimentally investigate frequency translation using BW SPDC.
Fig. 1. Using the same pump, signal and idler that are all $z$-polarized, theoretical idler tuning for (a) BW and (b) forward-wave (FW) downconversion as the pump is varied near 800 nm in a 6 mm long PPKTP crystal. The BW case shows highly narrowband idler that is nearly insensitive to pump tuning. The poling periods are 0.5 µm for the BW case and 26.3 µm for the FW case.
2. Experimental Setup
We demonstrated BW SPDC using a first-order PPKTP crystal having 500 nm QPM period. The fabrication of this PPKTP crystal was performed via coercive field engineering and is described in Refs. [9,22]. The crystal was designed to have all waves $z$-polarized (type-0) with wavelengths 800 nm $\longrightarrow$ 1.4 µm + 1.87 µm, and it was uncoated and operated at room temperature. The PPTKP grating was 6 mm long, 3 mm wide, and 1 mm thick. Figure 2 sketches the experimental setups. The pump was a mode-locked Ti:sapphire laser with transform-limited 1.6 ps pulse duration, and 76 MHz repetition rate focused to 44 µm beam waist. A Glan–Taylor polarizer was placed before the PPKTP crystal to ensure the pump was polarized along the crystal $z$-direction. Dichroic mirrors (DM) that reflect the pump and transmit the signal and idler were used to direct the pump to the crystal and reject it afterwards. The forward-going signal and backward-going idler were coupled into SMF28 fibers and sent to superconducting nanowire single-photon detectors (SNSPD$_1$ and SNSPD$_2$ for the signal and idler, respectively). Long-pass filters (LPFs) were placed before the fiber couplers to remove any residual pump photons.
Fig. 2. Experimental setups for measuring (a) coincidences and (b) spectra using a fiber-coupled monochromator. The 1.6 ps duration Ti:sapphire laser pumps the PPKTP crystal. The signal and idler are collected into fibers and sent to SNSPD$_1$ and SPSND$_2$, respectively. The collection fibers are alternately connected to the monochromator to record the spectra. HWP, half-wave plate; PBS, polarizing beam splitter; DM, dichroic mirror; pol., polarizer; LPF, long-pass filter.
To detect the infrared photons, we used SNSPDs with broadband infrared sensitivity coupled to SMF28 single-mode fibers. The fibers connected to SNSPD$_1$ (signal) and SNSPD$_2$ (idler) were coiled with 40 mm and 60 mm diameters, respectively, to reduce dark counts caused by blackbody radiation while transmitting the wavelengths of interest [40]. The tighter coils for SNSPD$_1$ resulted in lower dark count rates but excess attenuation at the 1.87 µm idler. We estimated the system detection efficiency of SNSPD$_1$ to be 88% at 1400 nm, and SNSPD$_2$ to be 85% at 1875 nm. Using these SNSPDs, we detected SPDC from the PPKTP and also analyzed the spectra of the downconverted photons by passing them through a grating monochromator [Fig. 2(b)].
To observe the frequency translation of spectral properties from the pump to the signal, we used self-phase modulation (SPM) [41] to create a spectrally modulated pump. A 3.2-meter-long section of HI780 fiber was inserted in the experimental setup between the PBS and focusing lens before the PPKTP crystal. The coupling efficiency into the HI780 fiber was approximately 56%. The polarization from the fiber was adjusted using a fiber polarization controller to maximize the transmission through the polarizer placed before the PPKTP crystal. We measured the power before the polarizer, and after the PPKTP crystal (the latter, at the pump block in Fig. 2). We held the ratio of these powers constant (at 70% $\pm$ 1%) while changing the Ti:sapphire laser power using the half-wave plate (HWP in Fig. 2), thereby changing the amount of self-phase modulation on the pump.
3. Results
Figure 3 shows the measured signal and idler count rates, and coincidence rates for BW SPDC. Using 60 mW incident average power from the mode-locked Ti:sapphire laser, we observed $2.5 \times 10^5$ counts/s at the signal and $7.6 \times 10^4$ counts/s at the idler (with background count rates of $1.7 \times 10^3$ counts/s and $3.8 \times 10^3$ counts/s at the respective detectors). The coincidence rate was $5.7 \times 10^3$ coincidences/s and the coincidences-to-accidentals ratio (CAR) was $330 \pm 26$ (where the uncertainty is calculated by assuming Poisson statistics for the observed counts). We estimated the signal and idler collection efficiencies [42] to be 8.5% and 2.7%, respectively, which include detector efficiencies and losses in the paths between the crystal and the detectors (i.e., losses from the uncoated crystal, optical elements, fiber coupler, etc.). From these data, we calculated the internal pair production rate to be $4.0 \times 10^4$ pairs/s/mW. As a comparison, BW SPDC in a type-0, fifth-order QPM, periodically poled LiNbO$_3$ (PPLN) waveguide exhibited internal pair production rate of 5 pairs/s/mW [20] using similar pulsed pumping. Table 1 presents a comparison of our result with other BW SPDC experiments. The internal pair generation rate is expressed in terms of the average pump power, so we also include the pump duration ($\tau _{\textrm {pump}}$) and pump repetition rate in the table for clarity.
Fig. 3. Measured (a) single-channel and (b) coincidences count rates. (c) CAR as a function of incident average pump power.
Table 1. Comparison of Several BW SPDC Experiments
We performed a direct measurement of the SPDC spectra by sending the fiber-coupled SPDC photons to a grating monochromator (with 1/3 m focal length and 600 groove/mm grating blazed at 1.5 µm) connected to SNSPD$_2$. The incident average pump power was 120 mW. Figure 4(a) shows the pump transmitted through the PPKTP crystal, while Figs. 4(b) and 4(c) show the signal and idler spectra. The signal was detected at 1400 nm and the idler at 1868 nm, which agreed well with phasematching predictions [43]. We note that the spectral scans were limited by the step size rather than by the instrument resolution. The reciprocal linear dispersion (RLD) of the monochromator was 1.16 nm/mm, and the monochromator slit size was 2 mm. However, the exit-aperture size of the monochromator was set by the collection fiber (with aperture width of the order of 10 µm). The monochromator resolution is the RLD multiplied by the aperture size or approximately 0.02 nm. In comparison, the minimum step size was approximately 0.5 nm, which is larger than the theoretically predicted BW idler bandwidth of 12 GHz (or 0.14 nm).
Fig. 4. Measured spectra for the (a) pump transmitted through the PPKTP, (b) signal, and (c) idler. For the latter, we also show the background counts (measured with the pump to the experiment blocked).
We also investigated wavelength tuning of BW SPDC. Figure 5 shows the effect of tuning the pump wavelength by 5 nm (from 800 nm to 805 nm) while keeping other parameters the same (temperature, pump power, etc.). Spectra represented by solid lines in Fig. 5 have 800 nm pump wavelength while the dashed lines have 805 nm pump wavelength. We see that the idler wavelength is nearly unchanged: $\Delta \lambda _i = -0.5$ nm, which is the step size for the monochromator scan. The change in the signal (measured in wavenumber, $\tilde {\nu }$, where $\tilde {\nu } = 1/\lambda$) is $\Delta \tilde {\nu }_s = -76$ cm$^{-1}$, which is nearly equal to the change in the pump, $\Delta \tilde {\nu }_p = -78$ cm$^{-1}$. This tuning behavior matches the behavior seen previously in BW OPOs [4], where the backward-wave frequency depends very weakly on the pump frequency.
Fig. 5. Normalized and background-subtracted BW SPDC spectra for 800 nm and 805 nm pumping. The solid curves represent results from 800 nm pump while the dashed curves have 805 nm pump. (a) Pump transmitted through the PPKTP, and generated (b) signal and (c) idler. The backward-wave idler shows very weak tuning as a function of pump tuning.
We investigated frequency translation of spectral properties from the BW SPDC pump to the signal photons. We passed the pump through a length of fiber that produced self-phase modulation to create different modulated pump spectra. Figure 6(a) shows the pump spectra measured with the monochromator at several different pump powers. The listed average powers represent the pump power after the SPM fiber and before the PPKTP and polarizer. We see that the pump spectrum becomes increasingly distorted at higher pump powers. In Fig. 6(b), we plot the measured idler spectra. We observed that the idler remains narrowband and centered at 1867.5 nm. Figures 6(c)–6(e) show the measured signal spectra and the translated pump spectra at the three power levels. The translated pump wavelengths were calculated by assuming the idler to be highly narrowband and fixed at $\lambda _{i,0} = 1867.5$ nm, and applying energy conservation such that $1/\lambda _{\mathrm {trans}} =1 /\lambda _p - 1/\lambda _{i,0}$. There is good agreement between the signal spectra and the translated pump spectra. By using the idler as the heralding photon, the signal photon can be used as a spectrally shaped, heralded single photon.
Fig. 6. Spectra of BW SPDC using a self-phase modulated pump. (a) Pump spectra with SPM and (b) BW SPDC idler spectra at different average pump powers, $P_{\textrm {avg}}$. Comparisons of SPDC signal spectra with translated pump spectra for $P_{\textrm {avg}}$ of (c) 33 mW, (d) 46 mW, and (e) 68 mW. The counts for the translated pump spectra are reduced by a factor of 10 for easy comparison.
4. Discussion
BW SPDC is a novel, unique source of photon pairs that will be useful for quantum information processing. With advances in ultra-short-period PPKTP crystals [9,22,44], higher pair-generation efficiencies through first-order phasematching can be achieved. As even shorter periods become available, shorter visible-wavelength photon pairs can be produced. BW SPDC is attractive since the output photons naturally emerge from two different ports. The BW SPDC two-photon state will have minimal spectral correlations and a nearly separable joint spectra amplitude [11,15–17,20], which is useful so that spectral filtering of the SPDC output can be avoided and higher count rates can be achieved [45].
The frequency-translation properties of BW SPDC will enable design of efficient, spectrally shaped, heralded single-photon sources. Frequency translation allows the spectral shaping to occur on the pump beam before the photon pairs are generated. This is in contrast to conventional SPDC spectral-shaping where losses due to the shaping are imposed on the downconverted photons, which reduces the pair generation efficiency.
It has been noted that frequency and phase translation using spontaneous BW three-wave mixing differs from that of optical parametric amplification (OPA) [6]. OPA acts as a perfect phase-sensitive amplifier [46], which enables processes like quantum frequency conversion (QFC) [30] or quantum frequency translation (QFT) [47], where the quantum state can be transferred from light at one frequency to another frequency. In spontaneous BW three-wave mixing, the momentum conservation condition [Eq. (1)] forces the counter-propagating idler to be nearly stationary in frequency, which gives rise to frequency translation from the pump to the signal. However, this transfer is only approximate and not perfect since the idler is not perfectly stationary and the phase of the counter-propagating idler is only approximately constant [6]. It follows that spectral shaping can be transferred between the pump and signal using BW SPDC, but BW SPDC cannot be used for transfer of the quantum state. We also note that in QFC and QFT, the stationary beam is the high-power pump, while in BW SPDC frequency translation, the stationary beam is the low-power idler.
Frequency translation using BW SPDC has similarities to group-velocity-engineered SPDC [48]. When the group velocity of the pump matches that of the signal [using asymmetric group-velocity-matching (aGVM)], the spectral shape of the signal can be programmed by the spectral shape of the pump. However, the bandwidth of the idler in aGVM SPDC is not nearly as narrow as in BW SPDC, so the spectrum of the signal will not track as closely to the pump compared with BW SPDC.
In the future, we plan to improve the spectral measurements of BW SPDC by exploring other techniques, including time-of-flight spectroscopy [49], stimulated emission tomography [50], and the use of scanning Fabry–Perot interferometers (FPIs) [51,52]. One of the challenges with first-order BW three-wave mixing is that the idler tends to have long wavelength (typically longer than 1550 nm). At these long wavelengths, fiber-based dispersion modules are not available, which makes time-of-flight spectroscopy [49] difficult to perform. Using stimulated emission tomography [50], it would be possible to seed the BW SPDC at 1400 nm and observe the output through difference frequency generation. This technique can provide detailed spectral information about the BW SPDC process, but it is not a direct observation of the SPDC. The use of scanning FPIs is also a promising technique for probing single-photon-level spectra [52], but short cavity lengths (5 mm or shorter) are needed to have sufficiently wide free-spectral range to observe the predicted 12 GHz bandwidth idler.
5. Conclusion
For the first time, we experimentally observed backward-wave SPDC in a first-order quasi-phasematched crystal. The 500 nm period PPKTP crystal produced forward-wave signal at 1400 nm and backward-wave idler at 1868 nm when pumped at 800 nm. We observed $1.1 \times 10^4$ coincidences/s using 60 mW average pump power. Using estimated signal and idler collection efficiencies, we inferred the internal pair production rate to be $4.0 \times 10^4$ pairs/s/mW. The output spectra of the BW SPDC were directly measured with a grating monochromator. We verified the phasematching wavelengths and confirmed that the backward-wave idler was nearly stationary in frequency and narrow in bandwidth. We also demonstrated for the first time frequency translation using BW SPDC where the spectral properties of the pump wave are transferred to the signal wave. BW SPDC can be used as a source of spectrally shaped, heralded single photons that can be used in quantum networks, quantum interconnects, and photonic quantum computing.
Disclosures
The authors declare no conflicts of interest. Certain commercial equipment or materials may be identified in this paper in order to specify device fabrication, the experimental procedure, and data analysis adequately. Such identification is not intended to imply endorsement by the National Institute of Standards and Technology; neither is it intended to imply that the equipment nor the material identified are necessarily the best available.
Data availability
Data underlying the results presented in this paper are available in Ref. [53].
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