We report the high-flux and broadband generation of biphotons with controlled frequency entanglement. For the generation of the entangled state consisting of frequency-anticorrelated photons, we use PPMgSLT pumped by a continuous-wave (cw) laser. Meanwhile, the state consisting of frequency-correlated photons is produced from PPKTP under the extended phase-matching condition. Both states exhibited interference patterns with over 90% visibilities in two-photon interference experiments.
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The nonclassical nature of a multi-photon wave packet is a key resource for overcoming the limitations of the present optical technologies governed by classical wave optics. Specifically, quantum entanglement of photons, which is the most striking nonclcassical feature of the multi-photon wave packet, plays a pivotal role in quantum optical technologies, including quantum information and communication , quantum imaging  and quantum metrology . One of the goals of this study was to clarify the role of quantum entanglement in light-matter interactions at the single-photon level. Although there have been some reports on nonlinear light-matter interactions under extremely weak light conditions [4,5], almost all of these works focus on nonlinear optical phenomena caused by the differences in photon statistics between classical and nonclassical lights. However, it is predicted that optical nonlinear effects are sensitive to the temporal correlations of a multi-photon wave packet in a fully quantum mechanical treatment of nonlinear light-matter interactions , and that frequency correlation, or frequency entanglement, strongly affects the temporal correlation among the constituent photons in a multi-photon wave packet as a result of Fourier duality. We recently reported a nonlinear light-matter interaction at the single-photon level in a photonic crystal fiber . However, attenuated coherent light, which does not show the nonclassical nature of light, was used to investigate the interaction. Therefore, the phenomena induced in the fiber can be explained by the conventional theory of light-matter interactions. In order to further develop experiments on light-matter interactions at the single-photon level, we are constructing high-flux biphoton sources with controlled frequency entanglement. In this letter, we present the spectroscopic and interferometric properties of biphoton sources with controlled frequency entanglement.
2. Generation schemes for frequency-entangled states
Experimental demonstrations of the spectral control of biphotons have recently been reported [8–10]. In the following, however, we focus on the control method of frequency entanglement in spontaneous parametric down-conversion. In addition, we employ the type-II phase-matching condition, which generates two photons with orthogonal polarizations, because it allows us to independently manipulate the constituent photons of a two-photon wave packet.
Let us consider the generation scheme for the state consisting of frequency-anticorrelated photons with a broadband spectrum. As is well-known, the frequency-anticorrelated biphoton state can be obtained from conventional phase-matching conditions with narrow-band, cw pumping in the spontaneous parametric down-conversion process. While we can achieve the high-flux generation of photon pairs by the use of a long nonlinear crystal, the spectrum of the photon pairs becomes narrower as the interaction length of the crystal increases. For instance, periodically poled KTiOPO4 (PPKTP) crystals with the type-II phase-matching condition yield signal and idler photons with a narrow spectral bandwidth (<1 nm) in an interaction length longer than 10 mm . The relationship between the group velocities of the signal and idler photons determines the temporal distribution in the type-II phase-matching condition. We can qualitatively understand this temporal distribution affects the frequency distribution of the constituent photons as a result of Fourier duality. Therefore, the spectral bandwidth of parametric emissions is strongly related to the group velocities of the constituent photons . The weak birefringence of LiTaO3 crystals results in a small difference in group velocities, which allows us to create spectral broadening of parametric emissions even under type-II phase-matching conditions. Therefore, we employed periodically poled MgO-doped stoichiometric LiTaO3 (PPMgSLT) to generate broadband frequency-anticorrelated photon pairs under the type-II phase-matching condition. In this study, we used a 40-mm-long PPMgSLT crystal with a poling period of 21.5 μm, constructing a high-flux biphoton source.
We also consider the generation scheme for the state consisting of frequency-correlated photons. Several schemes to control the frequency correlation of biphotons generated via spontaneous parametric down-conversion have been proposed to date [13,14] and have been successfully demonstrated [15,16]. In particular, the method utilizing the extended phase-matching (EPM) condition [17,18] promises to construct a high-flux biphoton source with the frequency-correlated state and lacking wavelength tunability. To exploit a high-flux biphoton source with coincident frequencies, we used a 30-mm-long PPKTP with a poling period of 46.1 μm, which satisfies the EPM condition around a pumping wavelength of 792 nm.
We used a mode-locked Ti:sapphire laser operated in cw mode as a pump source for the PPMgSLT, and in pulsed mode with a full width at half maximum (FWHM) of 6 nm, corresponding to the pulse duration of 120 fs, and a repetition rate of 90 MHz for the PPKPT crystal. These pump beam were focused into the crystals with the waist size of 45 μm. To compare the characteristics of these biphoton sources, we tuned the pump at the same center wavelength (792 nm), which was determined by the EPM condition for the PPKTP. The pump beam with its polarization along the crystallographic y axis propagated each crystal along the x axis. Since biphotons generated via the type-II phase-matching condition have orthogonal polarizations, the constituent photons of a biphoton were aligned along either the y or z axis. To obtain the degenerate parametric emission spectra in the collinear propagation direction of the pump beam, the crystal temperatures were controlled by a heater with an accuracy of 0.1°C because the phase-matching conditions are sensitive to crystal temperatures.
Characterizing biphotons with controlled frequency entanglement, we made both spectroscopic and interferometric measurements. In the spectroscopy of biphotons, we employed two detection schemes: conventional spectroscopy using a linear-arrayed InGaAs detector through a grating spectrometer, and measurement of the frequency correlation of biphotons using two tunable bandpass filters with a coincidence counting technique, as shown in Fig. 1(a) . The transmission FWHMs of these filters were 0.5 nm each and the center wavelength can be changed from 1560 to 1620 nm. In addition, the filters have the transmittance over 90% at the center wavelength. In the coincidence counting measurements, we used two fiber-coupled single-photon detectors (id Quantique id201), followed by a time interval analyzer. We recorded the number of coincident events within the time window determined by the gate pulse width (100 ns). We observed photons from spontaneous parametric down-conversion through a single-mode fiber in all measurements and did not use any spectral filters to restrict the spectralbandwidth of the biphotons in the interferometric measurements. We carried out two-photon interference experiments utilizing probabilistic generation of polarization entanglement by a single-beam arrangement , and evaluating the quantum coherence of the biphotons. Figure 1(b) shows a schematic diagram of the experimental setup. Unlike in the setup in Reference , we used a polarization Michelson interferometer instead of a timing compensator crystal because we needed to continuously change the delay time between the constituent photons to measure the temporal profiles of the two-photon interference.
4. Results and discussion
We first show the spectroscopic properties of biphotons obtained by conventional spectroscopy. Figure 2 presents the parametric emission spectra generated from the (a) PPMgSLT and (b) PPKTP crystals. In all figures, polarization aligned along the y (z) axis is represented by E // y (z). In this measeuremnt, the pump power was tuned at 1.0 W for the PPMgSLT and 1.2 W for the PPKTP. Spectral degeneracy was achieved at a crystal temperature of 41.3°C for the PPMgSLT and 31.5 °C for the PPKTP. Thanks to the weak birefringence of the MgO-doped LiTaO3 crystal, we successfully generated broadband parametric emissions whose FWHM was approximately 30 nm, even under the type-II phase-matching condition with a 40-mm-long crystal. On the other hand, we can see that the FWHM of the parametric emission from the PPKTP is approximately 13 nm. The bandwidth of 13 nm, which is almost twice as broad as that of the pump laser, is quite reasonable because we can understand the EPM as a condition that allows broadband second-harmonic generation in terms of the up-conversion process . We also confirmed that the spectral bandwidth of the emission from the PPKTP becomes narrower as the pump spectrum narrows. Therefore, the bandwidth of the parametric emission from the PPKTP is controllable within the EPM condition.
An emission peak was observed around 1460 nm in the lower graph of Fig. 2(a). We identified the origin of this peak as the other phase-matching condition of parametric down-conversion because, by changing the PPMgSLT temperature, the center wavelength of the emission spectrum was shifted in conjunction with that of the parametric emission observed around 1584 nm. To clarify the temperature dependence of the emission spectra, we present the tuning curves of the parametric emissions constructed from the emission spectra at several crystal temperatures (Fig. 3 ). In the tuning curve for z-polarized emissions, two emission peaks appear when the crystal temperature is below 41°C, and these peaks merge into a single peak around a crystal temperature of 42°C. In addition, no emissions were observed at temperatures higher than 43°C. A similar tendency is expected to be observed in the case of y-polarized emissions, however, due to the lack of detection efficiency of the InGaAs detector in the region of wavelengths longer than 1600 nm, we were unable to observe the conjugate emission spectrum that should appear around 1730 nm in the upper graph of Fig. 2(a).
Figure 4 shows the measured joint spectra of biphotons generated from (a) PPMgSLT and (b) PPKTP crystals, as a function of the frequencies of y-polarized (ω y) and z-polarized (ω z) photons. Figure 4 clearly and directly demonstrates the generation of biphotons consisting of (a) frequency-anticorrelated and (b) frequency-correlated photons. In a previous report on the EPM scheme , only the interferometric properties of a frequency-correlated state were shown. To the best of our knowledge, the present results are the first direct observation of the positive correlation in frequency between the photons generated via the EPM condition.
The spectral bandwidth along ω y = ω z (ω y = −ω z) for the anticorrelated (correlated) state reflects the degree of frequency correlation. In the following, we refer to this spectral width as the “correlation width.” The measured correlation width shown in Fig. 4(a) was determined by the resolution bandwidths (60 GHz) of the tunable bandpass filters. On the other hand, the correlation width of the PPKTP spectrum is governed by the phase-matching condition associated with the interaction length of the down-conversion process. Taking account of the resolution bandwidth of the filters, we estimated a correlation width of 120 GHz, which is almost consistent with the calculation assuming an interaction length of 30 mm. The resultant correlation width indicates that the pump pulse coherently interacts with the PPKTP along the full length of the crystal.
We also measured coincidence counts as a function of the pump power, as shown in Fig. 5 . From the fitting of the experimental data, we obtained the biphoton counting rate R exp as 11.6 and 5.7 counts/mW/sec for the PPMgSLT and PPKTP, respectively. In our measurements, there are no timing synchronizations between the gate pulse applied to the detector and the pump lasers. Thus, biphotons out of the gate pulses did not contribute to the coincidence counts. The actual production rate R act of biphotons can be estimated as the following relation:
Finally, we discuss the experimental results of the present two-photon interference experiments. The upper graphs in Fig. 6 show the coincidence counts as a function of the path-length difference ΔL of the interferometer. In this measurement, the pump power was tuned at 100 mW to suppress the multiple photon pair generation, and we set the polarization analyzer angle in path 1 (θ 1) to + 45° (open circles) or −45° (open triangles), while that in path 2 (θ 2) was fixed at + 45°. We observed constructive quantum interference fringes when θ 1 was set at + 45° and destructive interferences fringes when it was set at −45° in both frequency-correlated and frequency-anticorrelated photon pairs. All interference fringes showed visibilities over 90%, which demonstrates that the generated states are highly pure frequency-entangled states. On the other hand, the widths of the interference dips for the frequency-anticorrelated and frequency-correlated states are quite different, at 120 fs and 4.3 ps, respectively. The fringe width of the frequency-correlated state is almost 40 times broader than that of the frequency-anticorrelated state, while the spectral width of the PPMgSLT is only twice as broad as that of the PPKTP. This result is based on the fact that the difference in the frequencies between the constituent photons, which corresponds to the spectral width along ω y = −ω z in Fig. 4, determines the widths of the dips in the Hong-Ou-Mandel (HOM) type of interference experiment [21,22].
As is well-known, spectral distinguishability between the constituent photons results in the degradation of polarization entanglement . In the following, let us briefly consider the relationship between spectral distiguishability and polarization entanglement. In general, a pure two-photon state that consists of orthogonally polarized photons is given byEq. (4) leads to the following simple form:Eq. (6), we derive the condition for spectral indistinguishability:Fig. 6. These results show no difference caused by frequency correlation in the polarization correlation measurement, and the fringe patterns with high visibilities (90% for the PPMgSLT and 92% for the PPKTP) indicate that both states form polarization-entangled states. Thus, the results clearly show that the symmetric property of the two-photon spectral distribution in Eq. (6) and the resultant spectral indistinguishability in Eq. (9) play a central role in creating polarization entanglement, regardless of the frequency entanglement. One of the plausible reasons for the degraded fringe visibility is the slightly asymmetric joint spectra of the biphotons.
We have demonstrated frequency-entangled biphoton sources with high-flux and broadband spectra. The biphoton consisting of frequency-anticorrelated photons was generated from PPMgSLT with cw pumping, and the biphoton source consisting of frequency-correlated photons was constructed by PPKTP with the EPM condition, pumped by an ultrashort pulse laser. We achieved biphoton production rates of 135,000 and 67,000 pairs/mW/sec for the PPMgSLT and PPKTP crystals, respectively. The present two-photon interference experiments demonstrated that the spectral profile of the frequency-entangled states along ω y = −ω z determines the temporal profile of the fringe patterns, while spectral indistinguishability is essential in the generation of polarization entanglement. We believe that these biphoton sources with controlled frequency entanglement could be a powerful tool for metrology, including the investigation of light-matter interactions, at the single-photon level.
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