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Abstract
Infrared quantum absorption spectroscopy is one of the quantum sensing techniques, by which the infrared optical properties of a sample can be estimated through visible or near infrared photon detection without need for infrared optical source or detector, which has been an obstacle for higher sensitivity and spectrometer miniaturization. However, experimental demonstrations have been limited to wavelengths shorter than 5 µm or in the terahertz region, and have not been realized in the so-called fingerprint region of 1500–500 cm−1 (6.6 to 20 µm), which is commonly used to identify chemical compounds or molecules. Here we report the experimental demonstration of quantum Fourier-transform infrared (QFTIR) spectroscopy in the fingerprint region, by which both absorption and phase spectra (complex spectra) can be obtained from Fourier transformed quantum interferograms obtained with a single pixel visible-light detector. As demonstrations, we obtained the transmittance spectrum of a silicon wafer at around 10 µm (1000 cm−1) and complex transmittance spectrum of a synthetic fluoropolymer sheet, polytetrafluoroethylene, in the wavelength range of 8 to 10.5 µm (1250 to 950 cm−1), where absorption due to stretching modes of C-F bonds is clearly observed. These results open the way for new forms of spectroscopic devices based on quantum technologies.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Spectroscopy is a versatile tool in a broad range of sciences from astronomy to life sciences. Spectroscopy in the far infrared (FIR) region, in particular in the so-called “fingerprint region” in the wavelength range of approximately 1500–500 cm−1 (6.6 to 20 µm) [1], where complex patterns of absorptions are found that are unique to the chemical compounds or molecules, is of particular importance and is an essential tool for material science, chemistry, pharmaceutical sciences, and life sciences. As the most popular technique, Fourier-transform infrared (FTIR) spectrometers have been widely used [2–4]. However, far-infrared light sources using a heating element and the lack of a highly sensitive detector with a wide dynamic range in the FIR region are obstacles for improving sensitivity and miniaturizing spectrometers.
Remarkable progress has been made in photonic quantum technologies [5], namely the applications of quantum entangled photons for quantum information [6–8], quantum communications [9–12], and quantum sensing [13–21]. Infrared quantum absorption spectroscopy (IRQAS), which harnesses the quantum interference of photon pair generation processes, enables spectroscopy in the infrared wavelength region using a visible light source to generate frequency entangled photon pairs in the infrared region and the visible and near-infrared (VNIR) region (0.4–1.1 µm, which can be detected by commonly used silicon photodetectors). The first demonstration of such quantum spectroscopy was performed by Korystov et al. in the mid infrared wavelength region around 3 µm [22]. Prompted by the recent demonstration of the IRQAS of CO2 in the wavelength region around 4.2–4.5 µm [23], many important experiments [24–29] including the application of infrared microscopy [30,31] have been reported. However, these demonstrations were performed for wavelengths below 5 µm or in the terahertz region with wavelengths of 300 µm [25] and 600 µm [29]; IRQAS in the fingerprint region has not yet been demonstrated. A possible reason for this is that the nonlinear crystals (e.g., LiNbO3, LiTaO3, BaB2O4) used for entangled photon-pair generation are not transparent in the fingerprint region.
Here we report the experimental demonstration of quantum Fourier-transform infrared (QFTIR) spectroscopy [26–28] in the fingerprint region. In this method, a spectrum in the IR region can be obtained by a Fourier transformation of an interferogram obtained with a single pixel silicon detector. Note that the interference in the entangled photon-pair generation process occurs in a so-called “low gain regime”, where the average photon flux is below one photon pair per correlation time for the biphotons, which cannot be described by classical theory [32–35]. In addition to the ordinal transmittance spectra, QFTIR spectroscopy can provide the dispersion (refractive index spectra) of the sample [26]. To extend the operating wavelength of IRQAS to the fingerprint region, we newly developed a VNIR-FIR photon-pair source based on a spontaneous down-conversion (SPDC) process in an AgGaS2 (AGS) crystal, which has a high transparency over a wide spectral range of 0.5 to 12 µm (20000 to 833 cm−1). Very recently, Kumar et al. reported highly nondegenerate photon-pair generation with AGS crystal [36], confirming the infrared photon generation up to around 6 µm. In this work, we succeeded in extending the SPDC wavelength to the fingerprint region by angle tuning with a proper pump wavelength. Using this photon-pair source, we successfully obtained the transmittance spectrum of a silicon wafer at around 10 µm (1000 cm−1) and complex transmittance spectrum of polytetrafluoroethylene (PTFE) sheet in the wavelength range of 8 to 10.5 µm (1250 to 950 cm−1), where absorption due to symmetric and asymmetric stretching modes of C-F bonds is clearly observed. Harnessing the quantum correlation of the photon pairs, these measurements were performed with probe light intensities much lower than the thermal background radiation, which is a significant background noise source for conventional spectroscopy in the finger print region. These results not only prove the applicability of IRQAS in the fingerprint region, but pave the way to new compact devices and technologies for molecular/chemical contents recognition on the silicon-based integrated circuit platform [37,38] and also IR spectroscopy unencumbered by the thermal background photons [39].
2. Methods
In this section, we briefly review the theoretical basis for photon-pair generation via the SPDC process and the measurement procedures for QFTIR spectroscopy.
2.1 Wavelength-tunable photon-pair generation via SPDC process
In an IRQAS system, the entangled photon-pair source is a key component because the photon-pair generation band and flux determine the operating wavelength range and measurement precision, respectively. In this work, we use a type-I (e → oo) collinear SPDC process in a negative uniaxial nonlinear crystal for photon-pair generation, where a pump light with extraordinary polarization (e) is down-converted into signal and idler photons with ordinary polarizations (o). The energy conservation and phase matching conditions for this SPDC process can be represented as follows:
Fig. 1. Schematics of photon-pair generation via collinear SPDC process. (a) Normal incidence and (b) oblique incidence of the pump light on a nonlinear crystal. $\varphi $ is the cut angle, i.e., relative angle of the optic axis (OA) and the crystal surface normal. ${\theta _{{\rm{in}}}}$ and ${\theta _{\rm{p}}}$ are the incidence and propagation angles of the pump light, respectively.
To construct a VNIR–FIR photon-pair source, we chose an AgGaS2 (AGS) crystal as the nonlinear crystal since it has high transparency over a wide spectral range of 0.5 to 12 µm and a large second-order nonlinear coefficient [41]. The refractive indices of AGS, ${n_{\rm{o}}}(k )$ and ${n_{\rm{e}}}(k )$, are modeled by the following Sellmeier dispersion equation [42]:
2.2 Principle of QFTIR spectroscopy
QFTIR is a method of IRQAS where Fourier analysis is performed for the quantum interferogram and the complex transmittance of the sample is extracted [26]. Figure 2 schematically illustrates the operation of QFTIR. Figure 2(a) depicts a Mach-Zehnder type nonlinear quantum interferometer, where VNIR-FIR photon pairs are generated in the two identical nonlinear crystals via SPDC processes driven by a common cw pump laser. When the photon pairs generated from the two crystals are indistinguishable, as a result of the quantum interference between the two SPDC processes, the photon-pair generation rate varies depending on the relative phase acquired by the pump, signal, and idler photons during the passages between the two crystals. By adjusting the idler path length, one can observe the periodic modulation of the VNIR photon flux as a function of the optical path length difference $\Delta L$, so called quantum interferogram (Fig. 2(b)). If a sample is inserted in the FIR idler path, optical loss and phase retardance cause the distortion of the quantum interferogram. In QFTIR spectroscopy, the complex transmittance spectrum of the sample is extracted from the ratio of complex Fourier spectra of the quantum interferograms measured with and without the sample (Fig. 2(c)). Note that, in the actual implementation of the QFTIR system, we employ a Michelson-type nonlinear quantum interferometer (Fig. 3) as explained in the next section.
Fig. 2. (a) Schematic of QFTIR system. NLC: nonlinear crystal. (b) Schematics of quantum interferograms measured with and without a sample. (c) Schematic of complex transmittance spectrum, the phase retardance (upper panel) and magnitude of the transmittance (lower panel), can be determined from the ratio between the complex Fourier amplitude spectra of the quantum interferograms (Fig. 2(b)).
To obtain the theoretical basis for the QFTIR analysis, we follow the descriptions in Ref. [26]. The quantum interferogram ${P_{\rm{s}}}({\Delta L} )$, i.e., the signal photon count rate recorded as a function of the optical path length difference $\Delta L$, can be given as
The Fourier transform of the quantum interferogram, ${A_{\rm{s}}}\left( k \right) = \left( {{1 \mathord{\left/ {\vphantom {1 {2\pi }}} \right. } {2\pi }}} \right)\int {d\Delta L{P_{\rm{s}}}\left( {\Delta L} \right){\rm{ }}} {e^{ik\Delta L}}$, gives information about the spectral intensity of the idler photons and the transmittance of the sample:
The transmittance spectrum (including the dephasing parameter) can be extracted by taking the ratio of ${A_{\rm{s}}}(k )$ to a reference spectrum $A_{\textrm s}^0(k )$ taken without a sample $({\gamma (k )= 0{\rm \;{ and }}\; {\tau_k}(k )= 1} )$,
As discussed in Ref. [26], this analysis gives the complex transmittance spectrum, that is, both the magnitude of the transmittance and the phase spectrum of the sample. The dephasing in the sample, $\gamma $, can be evaluated when the transmittance at a certain wavenumber is known. Also note that identification of the chemical compounds or molecules can be performed without the information about $\gamma $.
3. Experimental setup
Figure 3 shows a schematic of the experimental setup for QFTIR spectroscopy with a Michelson-type nonlinear quantum interferometer. The pump source is a monochromatic continuous-wave (cw) laser diode with a center wavelength of 785 nm (output power: 100 mW, linewidth: < 100 MHz). The pump laser is focused by a lens L1 (f = 200 mm) into an AGS crystal (thickness: 0.5 mm, cut angle: 50°) where type-I SPDC generates VNIR–FIR photon pairs. The pump beam diameter is 1.2 mm before L1. The idler photons emitted from the AGS crystal are reflected by the dichroic mirror DM2 and spatially separated from the pump and signal photons. After collimation by an off-axis parabolic mirror OAPM (f = 150 mm), the idler photons pass through a germanium window G, where residual pump light and signal photons partially reflected by DM2 are filtered out. An end mirror Mi in the idler path is placed on a high-precision translational stage (FS-1050UPX, Sigma Koki) to adjust the idler path length. The reflected idler photons are refocused onto the AGS crystal. A sample of interest is placed between G and Mi in the idler path and the idler photons pass through the sample twice. The pump and signal photons are transmitted by DM2 and reflected by a concave mirror CM, and they are also refocused onto the AGS crystal. All the optical paths are aligned such that the spatial modes of the first SPDC photons perfectly match those of the second SPDC photons, to generate quantum interference between the photon-pair generation processes.
Fig. 3. Schematic of experimental setup. HWP: half wave plate, L1: focusing lens for the pump (f = 200 mm), L2: collimation lens for the signal (f = 200 mm), OAPM: off-axis parabolic mirror (f = 150 mm), DM1: long pass dichroic mirror (edge wavelength 800 nm), DM2: short pass dichroic mirror (edge wavelength 2000 nm), AGS: AgGaS2 crystal, CM: concave end mirror, Mi: end mirror, LPF: long-pass filter (edge wavelength 800 nm), SPF: short-pass filter (edge wavelength 1000 nm), MMF: multi-mode fiber, APD: Si avalanche photodiode, G: germanium window, I: Iris. A continuous-wave (cw) laser with a wavelength of 785 nm (power 100 mW, linewidth < 100 MHz) is used as a pump.
The signal photons from the quantum interferometer are transmitted by DM1 and collimated by a lens L2 (f = 200 mm). An iris I is placed after L2 and its aperture is set to 1.5 mm to spatially select only the center-most part of the signal beam where the SPDC emission angle is close to perfect collinear geometry. The signal photons are transmitted by a long-pass filter LPF and a short-pass filter SPF, while the residual pump light is filtered out. Then, the signal photons are coupled to a multi-mode fiber and sent to a detection system for quantum interferogram measurement. The flux of the signal photons is measured by a single photon counting silicon avalanche photodiode APD (SPCM-AQRH-14FC, Excelitas Tech., detection efficiency: >70% at 650 nm, detectable wavelength range: VNIR (400 to 1060 nm)) and a photon counter (SR400, Stanford Research Systems). In this work, we define the quantum interferogram as the signal photon count rate ${P_{\rm{s}}}$ recorded as a function of the optical path length difference between the signal and idler paths $\Delta L$. The signal photons are also sent to a spectrometer with a charge-coupled device image sensor (SR500i + DU416A-LDC-DD, Andor, wavelength resolution: 0.1 nm) to measure the signal photon emission spectrum in the VNIR region.
Note that in this experiment, quantum interferometric measurements were performed in the low gain regime. The number of generated photon pairs from the crystal is estimated to be at most 5×107 pairs/s, considering the count rate of the signal photons <1×106 counts/s and the effective total detection efficiency of 2% (the quantum efficiency of the APD is more than 20% over the signal photon generation band and the coupling efficiency of photons to the multimode fiber including optical loss in the system is at least 10%). As a result, the estimated number of photon pairs per the biphotons’ correlation time, which is estimated to be about 100 fs from the spectral width of the signal emission (Fig. 4(a)), is 5×10−6 and much less than 1. Thus, we can conclude that our experiment shown in the next section is performed in the low gain regime.
Fig. 4. (a) Signal emission spectra measured for several incident angles, plotted in 5° increments from 10° to −20°. The upper horizontal axis shows the corresponding idler wavelength. The incidence angle was changed by rotating the AGS crystal. (b) Center wavelengths of the signal emission spectra (red open circles) plotted as a function of the propagation angle of the pump light inside the AGS crystal against the optic axis. The right-side vertical axis shows the corresponding idler wavelength. The black line is the theoretical prediction of the phase-matched SPDC wavelength.
4. Results and discussion
4.1 Tunable VNIR-FIR photon-pair source
First, we confirmed that the idler photons are generated in the FIR region by measuring the emission spectra of the signal photons in the VNIR region. As the pump source is a monochromatic cw laser, the generation band of the idler photons can be uniquely determined from the wavelength of the signal photons, using energy conservation in the SPDC process (Eq. (1)). As explained in the previous section, the SPDC wavelengths can be selectively tuned by mechanical adjustment of the incidence angle of the pump beam to the nonlinear crystal θin. Figure 4(a) shows signal photon spectra measured by the spectrometer with several different incidence angles θin by tilting the AGS crystal against the pump beam. For normal incidence, the wavelength of the signal photons is around 883 nm, suggesting idler photon generation around 7 µm (1430 cm−1). The signal wavelength can be tuned from 845 to 900 nm by changing θin from −20° to 10° This corresponds to the generation of idler photons in the FIR range of 6 to 11 µm (1670–910 cm−1). The spectral intensities at θin of 5° and −10° are larger than the others but the spectral intensity at each angle is enough stable for a long period of time to perform spectroscopy measurement. In Fig. 4(b), the center wavelength for the signal photons is extracted by fitting a Gaussian curve to the spectral data in Fig. 4(a), and plotted as a function of the propagation angle of the pump light relative to the optic axis of the AGS crystal θp, which can be calculated from θin using Snell’s law as explained in Sec. 2.1. The figure also shows the theoretical prediction of the SPDC wavelengths calculated from Eqs. (1)–(4). The experimental results show fair agreement with the theoretical calculation and suggest that our photon-pair source covers a wide FIR spectral range.
4.2 Quantum interferogram in the fingerprint region
Utilizing this photon-pair source, we performed QFTIR spectroscopy in the fingerprint region. First, we measured a quantum interferogram without a sample. Here, the incidence angle of the pump light to the AGS crystal was adjusted to θin = −18° such that the signal and idler wavelengths were phase-matched at around 850 nm and 10 µm, respectively. The signal photon count rate measured by APD is shown in Fig. 5(a) as a function of $\Delta L$. We translated Mi with step sizes of 500 nm (equivalent to a change in $\Delta L$ of 1000 nm) up to a total scanning length W of 400 µm. The wavenumber resolution $\Delta k$ of the QFTIR measurement is determined by the inverse of the width of the transform window, that is, $\Delta k( = {1 \mathord{\left/ {\vphantom {1 W}} \right. } W}) = 25\;{\rm{ c}}{{\rm{m}}^{ - 1}}$. The origin of the optical path length difference is defined as the position where the interference fringe takes the maximum value. The photon count is integrated over 10 s for each step. The periodicity of the interferogram is estimated to be around 10 µm, as shown in the inset, being coincident with the expected generation wavelength of the idler photons. The visibility of the interferometric signal, $V = {{\left( {{P_{\max }} - {P_{\min }}} \right)} \mathord{\left/ {\vphantom {{\left( {{P_{\max }} - {P_{\min }}} \right)} {\left( {{P_{\max }} + {P_{\min }}} \right)}}} \right. } {\left( {{P_{\max }} + {P_{\min }}} \right)}}$, was 11%, where ${P_{\max }}$ and ${P_{\min }}$ are the maximum and minimum photon count rates observed in the quantum interferogram. A discrete Fourier transform (DFT) of the interferogram was performed with a fast Fourier transform algorithm. The obtained Fourier amplitude spectrum is shown in Fig. 5(b). The spectral peak is located around 1000 cm−1, corresponding to an idler wavelength of 10 µm, as expected, and the full-width of half maximum is about 100 cm−1.
Fig. 5. (a) Quantum interferogram with signal and idler wavelengths of 850 nm and 10 µm, respectively. The inset shows an expanded plot around $\Delta L = 0\;{\rm{ \mu m}}$. (b) Fourier amplitude spectrum of the interferogram.
4.3 QFTIR spectroscopy for a silicon wafer in the fingerprint region
Next, as a demonstration of QFTIR spectroscopy in the FIR region, we measured the transmittance spectrum of a silicon wafer (thickness 1 mm) around 10 µm (1000 cm−1). In this measurement, the total scanning length W was set to 800 µm and the photon count was integrated over 500 ms for each step. The quantum interferograms were measured with and without the sample (Fig. 6(a)). Because of the high refractive index of silicon, a shift of about 5000 µm in the peak position was observed, along with a decrease in signal amplitude due to Fresnel reflection loss. Figure 6(b) shows the Fourier amplitude spectra of the interferograms in Fig. 6(a). The wavenumber resolution $\Delta k$ is 12.5 cm−1. Taking the ratio of these spectra, the transmittance spectrum of the silicon wafer is obtained as shown in Fig. 6(c). Here, the measurements were repeated 10 times and the average data for the transmittance spectra are plotted. In this spectral range, the obtained result shows an almost flat transmittance spectrum near 0.5. Since we used a polished optical-grade silicon wafer as the sample, we assumed the dephasing parameter $\gamma = 0$. For comparison, we also plot a transmittance spectrum measured by conventional FTIR spectroscopy (IRTracer-100, Shimadzu Corp.) with a wavenumber resolution of 4 cm−1 in the same figure. The results of the QFTIR measurements are in good agreement with the data obtained from the conventional measurements.
Fig. 6. (a) Reference quantum interferogram (red) and interferogram for silicon sample (blue). (b) Fourier amplitude spectra of signals in Fig. 6(a). (c) Transmittance spectrum of silicon wafer measured by QFTIR (red circles) and conventional FTIR (black line) spectroscopy. The error bars indicate standard deviations estimated from 10 measurements.
4.4 QFTIR spectroscopy of a synthetic fluoropolymer sheet
Finally, we measured the complex transmittance spectrum of a polytetrafluoroethylene (PTFE) sheet, which has a steep spectral structure due to strong absorption lines in the FIR region. Note that the thickness of the sheet is estimated to be less than 10 µm. To cover a wide spectral range, QFTIR measurements were performed under several SPDC generation conditions by setting the incidence angle of the pump light θin to −8, −13, and −18°. The total scanning length W was set to 800 µm (wavenumber resolution $\Delta k$ of 12.5 cm−1) and the photon count was integrated over 500 ms for each step. The reference and sample data for the quantum interferograms were taken at each crystal angle and the results are shown in Fig. 7(a). Figure 7(b) shows the reference spectra taken at each angle to clarify the spectral coverage of these measurements, showing that the Fourier spectra covered a wide spectral range from 950 to 1250 cm−1 (corresponding to an FIR wavelength range of 8 to 10.5 µm).
Fig. 7. (a) Reference quantum interferogram (red) and interferogram for PTFE sheet (blue) measured for different SPDC generation conditions. (b) Fourier amplitude spectra of reference signals in Fig. 7(a). (c) Transmittance spectrum of PTFE sheet measured by QFTIR (red, blue, and green circles) and conventional FTIR (black line) spectroscopy. (d) Phase retardance spectrum. The error bars in (b), (c), and (d) indicate standard deviations estimated from 10 measurements.
The obtained QFTIR spectrum is shown in Fig. 7(c), where measurements were repeated 10 times for each SPDC generation condition and the average data for the transmittance spectra are plotted. In contrast to the previous sample (silicon wafer), the effect of the surface roughness of the PTFE sheet on the signal is non-negligible and we need to set an appropriate value of the dephasing parameter $\gamma $. Here we adapted $\gamma = 0.2$ so that the transmittance at 1000 cm−1 obtained by the QFTIR coincides with that measured by the conventional FTIR. We also plot the transmittance spectrum measured with conventional FTIR spectroscopy for comparison. The transmittance spectrum obtained by QFTIR spectroscopy reproduces the spectral features of the PTFE sheet well, such as the sharp absorption dips around 1150 and 1200 cm−1, which are assigned to symmetric and asymmetric stretching modes of the C-F bond [43]. Figure 7(d) shows the phase retardance spectrum, $\arg \left( {{{{A_\textrm s}\left( k \right)} \mathord{\left/ {\vphantom {{{A_s}\left( k \right)} {A_\textrm s^0\left( k \right)}}} \right. } {A_\textrm s^0\left( k \right)}}} \right)$, which gives information about the dispersion of the sample. The phase spectrum is plotted in the rage of $\pm \pi $. The obtained result clearly exhibits a non-monotonic change in the phase spectrum, suggesting a large variation of the refractive index in this spectral range, which is expected from the strong optical absorption shown in Fig. 7(c). Note that Kramers-Kronig analysis is sometimes used to evaluate the dispersion of the material, however, generally we need to make strong assumptions regarding the optical response of the sample. In contrast, QFTIR spectroscopy can provide the dispersion of the sample directly from the experimental result without any assumptions.
4.5 Discussion
In this section, we discuss the background noise tolerance of the QFTIR spectroscopy. As the blackbody radiation has the spectral peak at around 10 µm, the background thermal photons can be a significant noise source for the infrared spectroscopy, especially when the probe light is small. However, as demonstrated in the previous section, the QFTIR spectroscopy can be performed with very low probe light intensity, which is much lower than the thermal background. For example, the flux of the probe idler photons used for the QFTIR measurement in the range of 9.5 to 10.5 µm (Fig. 7(c)) is estimated to be $9 \times {10^6}$ photons/s at most. Assuming that the idler photons are generated into a single spatial mode, the flux of the thermal background photon in the same mode is estimated to be $2.5 \times {10^{10}}$ photons/s in the same spectral range, which is more than three orders of magnitude larger than the probe photon flux. This result indicates that quantum spectroscopy, which utilizes quantum correlation of photon pairs, suppresses background photon noise due to the similar mechanism to the quantum illumination [44–47]. This feature of QFTIR spectroscopy allows us to perform high-SNR spectroscopy with low photon flux, being free from the thermal background radiation. We think the QFTIR is highly advantageous for the non-invasive sensing of sensitive samples such as phototoxic molecules and delicate biological tissue, or spectroscopic measurements under strong background radiation at high temperature.
It should be noted that the SNR of QFTIR measurements can be improved by increasing the flux of the entangled photon pairs using a quasi-phase-matching (QPM) device [48,49] and waveguide structures [50,51] that provide long interaction length and spatial confinement resulting in high conversion efficiency. Referring to previous studies in the VNIR region [48–50], we can expect an increase in the photon pair generation rate of more than four orders of magnitude. In addition to the above methods, an on-chip photon-pair source, which is capable of generating broadband photon pairs in the IR region [37,38], is also a promising candidate for realizing high-precision IRQAS systems that can be integrated into silicon-based circuit platforms.
5. Conclusion
In conclusion, we have developed a QFTIR spectroscopy system for the FIR wavelength region, consisting of a Michelson-type nonlinear quantum interferometer with a VNIR–FIR photon-pair source based on the SPDC process in an AGS crystal. We measured the emission spectra of VNIR signal photons by varying the incidence angle of the pump laser relative to the AGS crystal, and confirmed that the signal wavelength can be tuned from 845 to 900 nm. This corresponds to the generation of idler photons over a wide FIR region from 6 to 11 µm (1670–910 cm−1). Using this AGS-based photon-pair source, we successfully observed a quantum interferogram at an idler wavelength of 10 µm (1000 cm−1). We measured the transmittance spectrum of a silicon wafer by QFTIR spectroscopy in this FIR region, and found that the obtained transmission spectrum was in good agreement with that obtained using conventional FTIR spectroscopy. The complex transmittance spectrum of a PTFE sheet was also measured over a wider spectral range of 8–10.5 µm (1250–950 cm−1), changing the SPDC generation condition by angle tuning. The obtained results reproduced the steep absorption spectrum of this sample well and also extracted the phase retardance spectrum, which gives information about the dispersion. These results show that the operating wavelength of IRQAS can be extended to the fingerprint region, an infrared wavelength range important for spectroscopic applications, paving the way for the realization of broadband QAS systems as powerful tools for material identification and structural analysis. It has also been shown that QFTIR spectroscopy is free from the noise due to the thermal background radiation and enables clear transmittance measurements with very low probe light intensity. We note that the nonlinear quantum interferometer operated at FIR wavelengths constructed in this work can be applied not only to QAS but also other quantum sensing applications such as hyperspectral imaging [30,31] and OCT in the infrared region [21]. Recently we became aware of the relevant work, which reports the IRQAS using a spectrograph performed in the fingerprint region [52].
Funding
Ministry of Education, Culture, Sports, Science and Technology MEXT Q-LEAP (JPMXS0118067634); Japan Society for the Promotion of Science (21H04444); Precursory Research for Embryonic Science and Technology (JPMJPR15P4).
Acknowledgments
The authors would like to thank H. Takashima and K. Shimazaki for their help in preparing the manuscript, and K. Tanaka, H. Kagata, K. Tokuda, and H. Katsu for helpful comments.
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 corresponding author (S. Takeuchi) upon reasonable request.
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