Fig. 1 Schematic representation of QSUP experimental setup. Yb fiber optical frequency-comb laser (λ_f = 1060 nm) is used for second-harmonic generation (SHG) of optical frequency-comb at λ_p = 530 nm (a). The SHG field is then split into two paths by a polarizing beam splitter (PBS) to pump the two spatially separate but identical PPLN crystals. The parametric down-conversion processes, PDC1 and PDC2, are stimulated by injected seed beams from a CW laser at 1542 nm with a linewidth of <1 Hz (c). Each StPDC produces a stream of path-entangled pairs of signal and idler photons. In the radiation source module, a 50:50 beam splitter (BS) is used to divide the coherent CW light into two paths. The lower path CW light interacts with an FP cavity whose cavity length is 7.5 mm and free spectral range is 10 GHz (d), which is a model optical sample. In (a), a variable neutral density (VND) filter is used to adjust or attenuate the CW beam intensity at the PDC1 crystal, to enhance the measured visibility. The signal beam is separated from the collinearly propagating idler beam using a dichroic mirror (DM) placed after each periodically poled lithium niobate (PPLN) crystal. Only the signal beams from the two PPLN crystals are combined by a 50:50 BS and the one-photon interference of the band-pass-filtered (BPF) signal field is recorded by spectrometer and EMCCD (b). The phase modulation is introduced by periodically changing the difference in the two pump (530 nm) pathlengths in (a). Here, the FP cavity with a finesse of 135 exhibits a resonant peak with a linewidth of 74 MHz.

Fig. 2 One-photon interference and FP cavity transmission spectrum. (a), Experimentally measured single photon counting rate of signal field in Fig. 1(b) is plotted with respect to the detuning frequency, which is changed by scanning the FP cavity length with PZT. Here, the voltage applied to the PZT attached to one of the cavity mirrors is also shown. Each scan time is 10 s. By assuming that the frequency was adjusted linearly with the voltage scan time, the frequency was calibrated with a time interval between the two resonant peaks (10 GHz). In a, the coherent CW seed laser frequency is fixed. The pump pathlength difference (Δx_p) is modulated by a 0.5 Hz triangle wave between 0 to 6 μm (11 oscillations per second), to obtain interference fringes. The SNR (the ratio of peak amplitude to standard deviation of noise) is about 20. (b) The measured (normalized) transmission (blue square) is plotted with respect to the detuning frequency. In this figure, open black circles are the transmission obtained by directly measuring the transmitted 1540 nm laser with a near-IR photodiode detector. The red solid line in (b) is the fitted Airy function that is known to describe the transmission spectrum of the FP resonator, i.e., |T_FP (ν_FP ,ν_i )|² = |T₀|² /{1 + (2F/ π)² sin² [δ/2]}(with δ = 2πν_i /ν_FSR, T₀ is the characteristic constant depending on each FP cavity, ν_FSR = c /4L for a confocal cavity, and L the cavity length. The resonant transmission peaks appear at δ = 2πq (q = integer), i.e., ν_i = ν_FP = qν_FSR, with a peak width Δν = ν _FSR /F and a Finesse $F=\pi \sqrt{R}/(1-R)$ with R being the mirror reflectance of the FP cavity. Two resonant peaks appear in (b) and the linewidth of each peak is estimated to be 74 MHz. The blue squares represent the QSUP results (averages over 5 independent measurements), which are extracted from the signal field interference fringe analyses, where the EMCCD detection window is ± 5 nm around 807 nm. (c) One-photon interference of signal photons is modulated by idler transmission. Here, the FP cavity length (resonance frequency) is fixed, but the CW laser frequency is scanned in the frequency window of ± 150 MHz around the FP cavity resonance frequency with scan time 2 s by applying FM voltage to WGM micro-resonator of the laser. The frequency is calibrated by the full width at half maximum (FWHM) to 74 MHz based on the assumption of a linear relation between the FM voltage scan time and frequency shift. The applied FM voltage scan rate is 10 V/s and the frequency-voltage relationship is 15 MHz/V. The pump pathlength difference (Δx_p) is modulated by a 0.5 Hz triangle wave between 0 to 6 μm (11 oscillations per second). (d) The retrieved QSUP spectrum (blue squares) of the FP cavity. The black dots represent transmission data obtained by directly measuring the transmitted idler photon intensity with a near-IR photodiode and the solid red line is a fitted Airy function. The sign of the detuning frequency refers to the opposite sign to the detuning around the resonant frequency.

Fig. 3 Fringe visibility at the FP cavity resonance frequency versus the intensity ratio of the two seed beams, where the latter is controlled by adjusting the transmissivity of variable neutral density (VND) filter. The intensity of the upper seed beam in Fig. 1(a) is modulated by |T_VND|², whereas that of the lower seed beam by the frequency-dependent |T_FP|². Here, the experimentally measured visibility (blue square) is at the FP cavity resonance frequency and it is plotted with respect to |T_VND |² when the pump intensity ratio I₂/I₁ is close to unity. The inset in this figure shows the sample plot when I₂/I₁ = 5.7. The solid red line is a fitted curve with the theoretical equation obtained from quantum mechanical descriptions of the coherent seed beam-cavity interaction and the single-photon interferometry, $V=2\sqrt{I_2/I_1}\left|T_{VND}{T}_{FP}\right|\left|{\alpha }_1{\alpha }_2\right|{[{\left|T_{VND}\right|}^2{\left|{\alpha }_1\right|}^2+1+(I_2/I_1)({\left|T_{FP}\right|}^2{\left|{\alpha }_2\right|}^2+1)]}^{-1}$ . Here, the experimental parameters, such as the average photon numbers of the seed (in an idler mode) beams at the PDC crystals and the degree of intensity unbalance of the pump beam, are measured independently. The dashed line corresponds to the visibility obtained from a classical mechanical description with the same parameters for the pump beam intensities. The error bars represent the standard deviation estimated from ten consecutive, independent measurements.

Fig. 4 Schematic diagrams representing conventional spectroscopy, single StPDC QSUP, and our dual StPDC QSUP. (a) The transmission spectrum of the FP cavity can be directly measured with detector D1 at 1524 nm. (b) Single StPDC QSUP can be used to indirectly measure the transmission spectrum, where the quantum entangled signal beam at a center wavelength of 807 nm is measured with detector D2. This is the ordinary frequency conversion setup with one nonlinear crystal (PDC). (c) Our dual StPDC QSUP uses two nonlinear crystals and the one-photon interference of thus generated signal fields is detected with D3 at around 807 nm.

Fig. 5 Experimentally measured transmission spectra of the FP cavity with the FP cavity length scan. The transmission spectrum of the FP cavity is obtained by tuning the resonance frequency of FP cavity, which is achieved by scanning the cavity length for 10 s. The scan rate is 1.27 GHz/s. The spectrum in the top panel is the transmission intensity (arbitrary unit) of injected seed beam, which is measured with NIR (1542 nm) photodiode (D1) in Fig. 4(a). That in the middle panel shows the frequency converted signal photons modulated by the idler beam transmission, where EMCCD (D2) in Fig. 4(b) is used. The spectrum in the bottom panel is one-photon interference fringe of signal photons modulated by idler beam transmission, which is detected by EMCCD (D3) in Fig. 4(c). To obtain the scan time-dependent signals in the middle and bottom panels, the single photon counting rates are measured for 10 ms (exposure time) and the detection wavelength window is 807.2 nm ± 0.1 nm. In this FP cavity length scanning mode, SNR improvement in our QSUP setup is significant compared to the conventional single path technique using just one nonlinear crystal.

Fig. 6 Experimentally measured transmission spectra of the FP cavity with a seed beam frequency scan. To measure the transmission spectrum of the FP cavity, we scan the seed laser frequency with a fixed FP cavity length (resonance frequency). The scan time is 2 s and the seed beam frequency scan rate is 150 MHz/s. The spectrum in the top panel corresponds to the transmission intensity (arbitrary unit) of the injected seed beam, where NIR photodiode (D1) in Fig. 4(a) is used. That in the middle panel is single-photon counting rates with respect to the seed beam frequency scan time (or equally seed beam frequency), where the used detector is EMCCD (D2) in Fig. 4(b). The spectrum in the bottom panel corresponds to the one-photon interference fringe of signal photons modulated by the seed beam transmission, where EMCCD (D3) in Fig. 4(c) is the detector. Here, the single photon counting rates are measured for 10 ms (exposure time) and the wavelength window of the EMCCD is 807.2 nm ± 0.05 nm.