Mid-infrared single-photon upconversion spectroscopy enabled by nonlocal wavelength-to-time mapping

Abstract

Ultrasensitive spectroscopy is an essential component in mid-infrared (MIR) technology. However, the drawbacks of MIR detectors pose challenges to robust MIR spectroscopy at the single-photon level. We propose an MIR single-photon frequency upconversion spectroscopy nonlocally mapping the MIR information to the time domain. Broadband MIR photons from spontaneous parametric downconversion are frequency-upconverted to the near-infrared band with quantum correlation preservation. Via the group delay of fiber, the MIR spectral information within a 1.18-micrometer bandwidth of 2.76 to 3.94 micrometers is then successfully projected to arrival times of correlated photon pairs. Under the conditions of 6.4 × 10⁶ photons per second illumination, the transmission spectra of polymers with single-photon sensitivity are demonstrated using single-pixel detectors. The developed approach circumvents scanning and frequency selection instability, which stands out for its inherent compatibility for evolving environments and scalability for various wavelengths. Because of its high sensitivity and robustness, characterization of biochemical samples and weak measurement of quantum systems are possible to foresee.

A high-sensitive and scalable mid-infrared spectroscopy is provided without moving parts or array detectors in noisy conditions.

INTRODUCTION

Mid-infrared (MIR) spectroscopy plays a crucial role in biological (1, 2) and materials research (3), pharmaceutical sciences (4), molecular dynamics (5), art conservation (6), and environmental monitoring (7, 8) as a vital instrument for investigating the structure of substances. The most common method of analyzing MIR spectra is Fourier transform infrared (FTIR) spectroscopy (9–11). FTIR spectroscopy consists of an interferometer system with moving parts to capture the interferogram. In addition to structural complexity and bulky size, FTIR spectroscopy is much affected by the low efficiency and excessive noise of the existing MIR detectors. MIR semiconductor detectors commonly require cryogenic cooling, and their performance is still inferior to that of visible sensors. Quartz tuning forks can detect photons from the visible to terahertz region, although it has the disadvantages of slow response speed (12, 13). With respect to standard FTIR spectrometer, common-path birefringent interferometer in the MIR is more compact and stable since it avoids the use of Michelson or Mach-Zehnder interferometers, which is thus promising for handheld devices (14, 15). On the basis of the birefringent crystal mercurous chloride (Hg₂Cl₂), the MIR spectrum is tunable in the range from 3 to 10 μm (16). Nevertheless, birefringent interferometers remain restricted to modest measurement speeds and detection sensitivity, which is, to a great extent, due to the limited availability MIR array detectors. To overcome these main limitations, MIR spectroscopic measurement based on nonlinear effects emerges as a promising option. The nonlinear interferometry based on the phenomenon of induced coherence has received much attention in the realm of MIR spectroscopy (17–20). Correlated photons are proposed to circumvent the need for MIR detectors since MIR idler photons from spontaneous parametric downconversion (SPDC) do not need to be monitored in this technique. However, the technique also necessitates an interferometer where two pairs of downconversion photons must be carefully superimposed to erase “which-way” information, which inhibits its potential commercial usage.

Because of its faster response speed, higher sensitivity, and simpler operability, the frequency upconversion technology is experiencing a renaissance as an alternative detection approach in the MIR band (21–24). MIR frequency upconversion is to convert MIR photons into the near-infrared (NIR)/visible range by applying a strong pump field to a nonlinear medium. In the upconversion process based on sum frequency generation (SFG), the frequency of NIR/visible upconverted photons is the sum of the frequencies of the MIR and pump photons, ω_up = ω_MIR + ω_p. In general, the upconverted photons are able to be detected efficiently by Si-based single-photon detectors at room temperature. This method has the advantage of eliminating the requirement for both MIR detectors and interferometers, which results in a stable and compact structure. MIR frequency upconversion has been a key technique for MIR spectrometer (25), imaging (26–29), optical coherence tomography (30), etc. However, in ultrasensitive MIR frequency upconversion, effective signal extraction in complicated and noisy environments remains a pressing concern. A high-power pump laser combined with bright MIR illumination is the straightforward approach to extracting spectrum information with a high signal-to-noise ratio (SNR) at present, while it is certain that high-power pumping with short wavelengths generates nonnegligible parametric fluorescence noise of the same frequency as the MIR signal. Since the inevitable noise of the pump laser is extremely difficult to filter out, advancing the identification of MIR frequency upconversion spectra to the few-photon and single-photon levels becomes a challenging task. Moreover, since photosensitive samples and quantum coherence phenomena impose restrictions on the intensity of optical probes, bright MIR illumination used in previous MIR upconversion spectroscopy is not appropriate in some scenarios.

Quantum correlation has been introduced for ultrasensitive MIR upconversion spectroscopy (31). SPDC photon pairs are used to achieve nonlocal spectral measurement (32, 33), effectively suppressing the noise uncorrelated to the upconverted MIR photons. On the basis of the notions of nondegenerate temporal-spectral correlation, broadband MIR upconversion spectroscopy with MIR probe intensities as low as 0.09 photons per pulse has been demonstrated previously (34). Nevertheless, spectrometers/monochromators or interferometers are required for all of the aforementioned MIR spectroscopy investigations. Especially in sensitive MIR spectroscopy, scanning of mechanical structure is so far indispensable to accomplish MIR spectral acquisition with single-pixel detectors if costly electron-multiplying charge-coupled devices (EMCCDs) are to be avoided. For future advancements in various quantum spectrum analyses using a low-intensity beam at a sample, mechanical scanning is expected to be avoided, and a shorter acquisition time is necessary.

Here, we demonstrate an MIR single-photon upconversion spectroscopy scheme with nonlocal wavelength-to-time mapping. In our scheme, the broadband MIR signal photons, as a branch of SPDC photon pairs, are translated to the NIR region based on a chirped-poling nonlinear crystal and subsequently detected by a Si single-photon detector. In the frequency upconversion process, the quantum-correlated properties of MIR photons are well maintained. The conjugated NIR heralding photons from photon pairs are routed via a 10-km single-mode fiber (SMF) to acquire group velocity dispersion (GVD), enabling wavelength-to-time mapping (35–39). Because of the quantum correlation inherited by the upconverted photons, we successfully implement correlation measurement that nonlocally maps the spectral information contained by the MIR signal photons into the time domain. As a result, we are able to retrieve the weak MIR signals in the noisy environment by quantum correlation between upconverted MIR signal photons and NIR heralding photons with an illumination intensity of 0.21 photons per pulse on samples. This scheme enables broadband MIR single-photon upconversion spectroscopy without the requirement for spectrometers, monochromators, or interferometers, as well as MIR detectors. While the quantum correlation retains the ultrahigh detection sensitivity, the wavelength-to-time mapping technique in upconversion spectroscopy markedly reduces the total exposure time of broadband MIR spectra at the single-photon level. In conventional wavelength-to-time mapping, the repetition rate of the laser limits the width of the time-domain spread and the detected spectral range. We propose the scheme to solve the problem via the time-correlated nature of photon pairs and therefore achieve wavelength-to-time mapping independent of the repetition rate. We demonstrate MIR transmission spectra of polymer compounds and unknown environmental samples from tidal flats to verify the scheme.

RESULTS

Figure 1 shows the sketch of MIR upconversion spectroscopy at the single-photon level based on the nonlocal wavelength-to-time mapping. The system is driven by a mode-locked picosecond laser of a narrow line width at 1033 nm. A low intensity of 2 mW from the pulsed laser source is picked off to pump a broadband MIR heralded single-photon source. A 25-mm-long chirped poled LiNbO₃ (CPLN) crystal is implemented to satisfy the quasi–phase-matching (QPM) condition of linear chirp (see Materials and Methods for detailed parameters). While one photon from the pump is annihilated, a pair of correlated photons that are nondegenerated in frequency is produced via the type 0 SPDC process. The spectrum of one photon from each pair (called “heralding” photon) is in the telecom wavelength, whereas its conjugate photon (called “signal” photon) is centered at the MIR region. A variety of functional groups can be found in the wavelength region of MIR signal photons. According to the photon-pair generation rate (see details in the Supplementary Materials), the SPDC source produces 0.21 photon pairs per pulse with a repetition rate of 30 MHz.

Fig. 1. Schematic diagram of MIR single-photon upconversion spectroscopy via nonlocal wavelength-to-time mapping.

The SPDC process is used to obtain correlated photon pairs, of which the red sphere represents MIR signal photons and the orange sphere represents NIR heralding photons. The MIR photons transmitted from the sample are upconverted to the NIR band (purple sphere) for straightforward detection with a mature Si-based single-photon detector. In addition, the heralding photons are coupled into the 10-km SMF with large dispersion. The broadband spectrum of a narrow optical pulse (colored pulse) is mapped into a time-stretched temporal waveform using the dispersive Fourier transformation (DFT) technique. The heralding photons are detected by a superconducting nanowire single-photon detector (SNSPD).

The frequency upconversion scheme serves to transduce the nonclassical states of MIR photons from one wavelength to another. Experimentally, the MIR signal photons are sent to a target, followed by a frequency upconversion module. The MIR signal photons are upconverted to the NIR wavelength using the same pulsed laser source pumping a 50-mm-long CPLN crystal. The poling period of the CPLN crystal for SFG varies continuously from 18 to 23 μm according to the QPM condition Λ(z) = 2π/(k_MIR + k_p − k_up). Each frequency component of MIR photons achieves QPM at a particular position along the propagation axis in the crystal. Therefore, the CPLN crystal with step modulation periods can overcome the acceptable bandwidth constraint of typical periodically poled lithium niobate crystals and provide an ultrabroadband MIR detection window. Similar to the single-pass pump configuration reported earlier (40), synchronous pulsed upconversion with 311-mW pump power allows for high upconversion efficiency and low average noise. The Si single-photon counting module (Excelitas, SPCM-780-14) is quite suitable for the detection of the SFG photons around 750 to 820 nm with ideal detection efficiency. Since the pump frequency is constant, the frequencies of SFG photons and MIR signal photons are related through energy conservation. Intrinsically, the frequency upconversion process is capable of preserving the quantum state of the input signal photons (41). Hence, the correlation also exists between the upconverted photons and the conjugated telecom-wavelength heralding photons. It is proved that the measurement of the quantum correlation is fully justified to obtain the information carried by MIR photons, although the MIR photons are not directly detected. The second-order Glauber correlation function G⁽²⁾(t_h, t_up) is defined as

$$G^{\left(2\right)}(t_{\mathrm{h}},t_{\text{up}})={\mid \langle 0\mid {{\widehat{E}}_{\text{up}}}^{(+)}\left(t_{\text{up}}\right){{\widehat{E}}_{\mathrm{h}}}^{(+)}\left(t_{\mathrm{h}}\right)\mid \mathrm{\psi }\rangle \mid }^2$$ (1)

where ${E_j}^{(+)}(t_j)=\int \mathrm{d}{\mathrm{\omega }}_{j}a({\mathrm{\omega }}_j)\text{exp}(-i{\mathrm{\omega }}_j{t}_j)$ , (j = up, h) is the positive frequency components of the field at the single-photon detector for upconverted photons and heralding photons, respectively, and a(ω_j) is the annihilation operators at the frequency ω_j.

In the branch of the SPDC source, dispersive Fourier transformation (DFT; also known as time stretching) of heralding photons could be achieved, relying on the large GVD of a long-distance fiber. NIR heralding photons of SPDC emission with different frequencies originally have a narrow temporal distribution. The finite SPDC pulse duration is mainly inherited by the pump pulse duration and affected by the temporal walk-off caused by the dispersion of the downconversion crystal. Experimentally, telecom-wavelength heralding photons are coupled into the single-mode optical fiber (YOFC Ltd., G.652.D). The selected dispersive medium is extensively available in optical communication. Low attenuation of the SMF from 1260 to 1625 nm enables enough propagation to satisfy the far-field conditions of the DFT. After propagation in the 10-km SMF, different spectral components of the heralding photons arrive at the superconducting nanowire single-photon detector (SNSPD; Photon Technology Co. Ltd.) in sequence to trigger coincidence measurement with the upconverted MIR signal photons. Although the time stretching discussed here is not physically interpreted by the concept of wavepacket broadening for either heralding or signal path individually, the first-order correlation function G⁽¹⁾(τ) remains unchanged as the dispersion is introduced, and the G⁽²⁾(τ) function does represent being broadened by the group dispersion medium in the temporal domain (42, 43). Let S(ω) be the spectral function of the sample; the existing quantum correlation between the upconverted MIR photons and the time-stretched heralding photons can then be evaluated with

$$\begin{array}{c}{G}^{(2)}(\mathrm{\nu })\sim \mid \int \mathit{d}\mathrm{\nu }{T}_{\text{UPC}}({\mathrm{\omega }}_{\text{MIR}}+{{\mathrm{\omega }}_{\mathrm{p}}}^0,{\mathrm{\omega }}_{\text{MIR}})\hfill \\ T_{\text{SMF}}({\mathrm{\omega }}_{\mathrm{h}})\mathrm{\Phi }(\mathrm{\nu })S({\mathrm{\omega }}_{\text{MIR}}) \text{exp}(i\mathrm{\nu }\mathrm{\tau }+i\frac{k_{\mathrm{h}}^{″}{\mathrm{\nu }}^2}{2}L)\mid 2\hfill \end{array}$$ (2)

where ${\mathrm{\omega }}_{\mathrm{h}}={{\mathrm{\omega }}_{\mathrm{h}}}^0-\mathrm{\nu }$ , ${\mathrm{\omega }}_{\text{MIR}}={{\mathrm{\omega }}_{\text{MIR}}}^0+\mathrm{\nu }$ , ${{\mathrm{\omega }}_{\mathrm{p}}}^0={{\mathrm{\omega }}_{\mathrm{h}}}^0+{{\mathrm{\omega }}_{\text{MIR}}}^0$ , and $\mathrm{\tau }=(t_{\mathrm{h}}-t_{\text{MIR}})-(k_{\mathrm{h}}^{\prime }{r}_{\mathrm{h}}-k_{\text{MIR}}^{\prime }{r}_{\text{MIR}})$ . T_UPC is the transmission function of upconversion process. T_SMF is the transmission amplitude for SMF and losses other than upconversion process and sample, and Φ(ν) is the phase-matching function of the SPDC crystal. Here, the first-order dispersion derivatives $k_{\mathit{j}}^{\prime }$ are considered, while higher-order dispersions in the MIR path are small enough to be neglected. The term of $k_{\mathit{h}}^{″}$ is related to the GVD of the long-distance fiber, where L is the propagation distance. Under the far-field circumstance, the shape of the second-order correlation function displays the biphoton spectrum modulated by the transmittance of the sample (44)

$$\begin{array}{c}{G}^{(2)}(\mathrm{\tau })\sim \mid T_{\text{UPC}}({{\mathrm{\omega }}_{\text{MIR}}}^0+\mathrm{\nu }+{{\mathrm{\omega }}_{\mathrm{p}}}^0,{{\mathrm{\omega }}_{\text{MIR}}}^0+ \mathrm{\nu })\hfill \\ T_{\text{SMF}}({{\mathrm{\omega }}_{\mathrm{h}}}^0-\mathrm{\nu }) \mathrm{\Phi } (\mathrm{\nu })S({{\mathrm{\omega }}_{\text{MIR}}}^0+\mathrm{\nu }){\mid }^2{\mid }_{{\mathrm{\nu }}_{\text{st}}=\mathrm{\tau }/(k_{\mathrm{h}}^{″}L)}\hfill \end{array}$$ (3)

Coincidence measurements are performed using a time-correlated single-photon counter (TCSPC; PicoQuant HydraHarp 400) to evaluate the correlation properties between the upconverted photons and the heralding photons. The coincidence before the dispersion propagation is recorded in Fig. 2A, where a variable attenuator is inserted before SNSPD to simulate the absorption and loss of the long fiber. It is shown that the shape of G⁽²⁾(τ) function is delta function–like when the photon pairs travel through the air or the low-dispersion medium. The dominant coincidence peak at the time delay τ = 0 indicates the generation of the “true” photon pairs. The shorter peaks on either side are accidental coincidence peaks with an interval of ~33 ns, corresponding to the 30-MHz repetition rate of the pump laser source. Accidental events generally occur as a result of SPDC multi–photon pair generation, as well as contributions of parametric fluorescence noise from the frequency upconversion process. With the advent of the 10-km SMF, the broadened second-order correlation function is shown in Fig. 2B. After the long-distance fiber, both the dominant coincidence peak and accidental coincidence peaks are broadened. The brown-shaded region represents the range of the dominant coincidence peak, which is located where the time axis is less than zero because the spectrum of the heralding photons is in the region of normal dispersion of the SMF. The width of the shaded region is ~36.63 ns, which is greater than one period (~33 ns). In traditional time-stretched schemes, the laser’s repetition rate is restricted since adjacent pulses stretched more than one pulse period would overlap and become indistinguishable. Notably, in the time-stretched scheme based on coincidence measurements, the dominant coincidence peak generated by photon pair correlation occurs only once in time domain. Although accidental coincidence peaks mixed on adjacent sides after broadening, it occurs periodically and can be easily subtracted as the background. The magnified dominant coincidence peak is shown in Fig. 2C (black curve). The occurrence of both net coincidence events and accidental coincidence events is influenced by the coupling efficiencies, the absorption and the insertion losses of SMF, and the spectral response of the SNSPD. As a result, the coincidence peak and the accidental events exhibit similar envelope. The coupling efficiency could be one of primary factors affecting the modulation of the coincidence spectra as the configuration of the chirped crystal leads to spatial distribution of heralding photons. However, this modulation has no influence on the measurement of absorption spectra. The broadened accidental coincidence peak averaged over eight accidental periods is represented by the blue curve. The accidental events have no effect on the MIR spectrum measurement. Consequently, the correlation technique is not bound by the laser’s repetition rate. Even when laser’s repetition rate is set higher, the time-stretched spectrum could be fully broadened with longer fiber to achieve a great spectral resolution.

Fig. 2. Coincidence detections between NIR heralding photons and upconverted MIR signal photons in the time domain.

(A) Quantum correlation is confirmed before time stretch. Coincidence histogram between two NIR single-photon detectors (SNSPD and single-photon counting module) with (black) and without (orange) the MIR signal photons is recorded. As the black line shows, the difference between the dominant coincidence peak and recurring shorter peaks (accidental events) implies the net coincidence events. The orange line is the parasitic noise caused by pump fields in the upconversion crystal. (B) Experimental implementation of time-stretched coincidence. The coincidence peaks are broadened via the group dispersion of the fiber. The brown-shaded region highlights the dominant coincidence peak. (C) The zoom-in dominant coincidence peak (black line) and the accidental events (blue line) after broadening. The accidental coincidence peak is averaged over eight accidental periods.

The wavelength-to-time encoding is based on the fiber dispersion characteristics as shown in the inset of Fig. 3A, verifying that the time difference between the arrival of correlated photon pairs uniquely related to wavelengths of the photon pairs involved in the correlation measurement (see the Supplementary Materials). The coincidence spectrum for transmittance measurement of the target is then accessible (Fig. 3A) after subtracting the effects of uncorrelated events. The projection allows a broad bandwidth of the time-stretched coincidence spectrum around 1.18 μm in the MIR frequency axis, covering 2.76 to 3.94 μm. The bandwidth is associated with the effective interaction length of the CPLN crystals and is not fundamentally restricted by the repetition rate. The main point is that the upconversion process retains quantum correlation and satisfies a large phase-matching bandwidth, enabling MIR upconversion spectroscopy to be performed through DFT. The red curve in Fig. 3A is the fitting of the coincidence spectrum, which is given by

$$\langle 0\mid {\widehat{E}}_{\mathrm{h}}^{\prime }(t_{\mathrm{h}}){\widehat{E}}_{\mathrm{\text{up}}}(t_{\mathrm{\text{up}}})\mid \mathrm{\psi }\rangle \simeq {\sum }_{\mathrm{e},c,\mathrm{\zeta }}{R}_{\mathit{ec}\mathrm{\zeta }}\text{exp}(-\frac{\mathrm{\tau }-{\mathrm{\tau }}_0}{2{\mathrm{\sigma }}_0^2})$$ (4)

where ${\widehat{E}}_{\mathrm{h}}^{\prime }$ is the quantum field operator of the heralding photons after time stretch, R_ecζ is the coefficient related to T_UPC, T_SMF, and Φ(ν), and σ₀ is the combined bandwidth of the coincidence spectrum (see the Supplementary Materials). The time-stretched coincidence spectrum is averaged over a total measurement time of 30 min. In comparison to the previous demonstration (34), the suggested scheme is able to reduce overall exposure time notablely, in the case of illuminating samples with these low magnitudes of MIR photon flux. The time-tagged time-resolved mode of the TCSPC can record individual photon events with their arrival time in all the channels. In Fig. 3A, the time delay of the heralding photons and upconverted photons is analyzed with the time resolution of 128 ps, leading to a spectral resolution of about 7.4 cm⁻¹. Higher temporal resolution of the TCSPC may improve the spectral resolution. However, considering strategic tradeoffs between the SNR and the integration time, the optimized bin width of 128 ps is selected. A satisfactory SNR is attained while ensuring a relatively continuous sampling point of various frequencies.

Fig. 3. Coincidence spectrum and SNR measurement.

(A) The coincidence spectrum over a broad spectral bandwidth of 1.18 μm appears with a high SNR even at the low MIR photon fluxes of 0.21 per pulse. The red curve represents a numerical fit to the coincidence spectrum using the model in eq. S12 in the Supplementary Materials. Inset presents the experimental data obtained by a series of bandpass filters and the fit of the fiber dispersion. (B) SNR of the system plotted as a function of the bin width of TCSPC. (C) SNR is conditioned on the overall exposure time. Averaged SNR, in the spectral range from 2.8 to 3.7 μm, plotted versus varying acquisition time for coincidence measurement.

To confirm the practical applications of the MIR single-photon upconversion spectroscopy based on time stretching, we focus the SNRs of the coincidence spectrum under various bin sizes of TCSPC (Fig. 3B) and exposure time conditions (Fig. 3C). In the range of 2.8 to 3.7 μm, SNR of different wavelengths SNR(λ) is the ratio of averaged net coincidence counting rate Mean(λ) and its SD σ(λ) in the time bin of the mapping. The SNR of the spectrum increases linearly with increasing bin size, as shown in Fig. 3B. Note that the increase in bin size will also reduce the resolution of the system, so the selection of bin size needs to be traded off. As expected, the SNR increases with the measurement time, which is presented in Fig. 3C. For a total measurement time of 30 min, averaged SNR in the limited operation bandwidth is 54.6.

Taking advantage of the MIR spectral window, the transmission spectra of several plastic samples are demonstrated. For system verification, a piece of 50-μm-thick polyimide standard sample is placed in the path of MIR signal photons. Within the same exposure time and bin size, the transmittance is calculated directly from the ratio of net coincidence events with and without the plastic film (circles in Fig. 4A). Deconvoluted by the impulse response of the system (see the Supplementary Materials), the transmission spectrum of polyimide (blue line in Fig. 4A) is depicted by the proposed MIR upconversion spectroscopy. The presented transmission spectrum range is intercepted from 2.8 to 3.7 μm, which is adequate to highlight varied characteristic peaks of different samples. Via the approach of DFT, frequency components across the whole spectral window could be instantaneously detected and analyzed, without adjusting any mechanical devices, tuning pump wavelength, or altering the temperature of the nonlinear medium. The deconvolution is carried out for the coincidence spectra with and without samples, respectively. By deconvolution, the impacts of the pump laser’s inevitable timing jitter, intrinsic dispersion introduced by optical components, and the time jitter of single-photon detectors on the spectral resolution are eliminated. Then, the transmission spectra of the sample are obtained by the ratio of the two deconvoluted curves. Typically, the noise caused by the deconvolution shows up in the uncertainty of coincidence counting clicks. The original SNR of the coincidence spectrum is 54.6 with 30-min integration time before deconvolution. Using the Lucy-Richardson method, the deconvolution deblurs the signal roughly but increases the noise and reduces the SNR to 37.8. The SNR of the coincidence spectrum is improved to 67.2 after the smoothing with a moving average filter to remove the extra error introduced by the algorithm. More crucially, precise determination of absorption peak position is guaranteed. The results coincide well with the signatures in the FTIR spectrum of 8 cm⁻¹ of spectral resolution, showing that the absorption features of the target can be retrieved by the proposed method reliably and effectively. It is observed both in the upconversion spectrum and FTIR spectrum that there are oscillations due to the interference of the photons scattered from the sample surface. Similarly, in the upconversion spectroscopy experiment, the spectrum shows better resolved oscillations than that in the FTIR measurement due to the smaller MIR beam spot on the sample. As the beam spot becomes smaller, the spatial coherence of the scattering photons gets enhanced. As a result, the signal oscillations induced by the interference in the upconversion experiment become sharper. The spectral resolution of the system is theoretically better than 7.4 cm⁻¹ (see the Supplementary Materials). The resolution can be further improved by employing fiber with longer transmission length or higher second-order dispersion coefficient. Reducing the statistical bin width of the coincidence histogram also helps to improve spectral resolution. A simple 4f optical system is used to illuminate samples, allowing plastic debris or microplastics from real-world marine ecosystems to be placed in its focal plane. These films are typically in the size of millimeter and thickness of a few micrometers. Two unknown environmental plastic fragments are found from an international nature wetland (8) and inferred as polycarbonate ( Fig. 4B) and polyethylene (Fig. 4C), respectively, by our scheme. Inset shows images of the environment samples under a visible-light camera. Using the current configuration with weak illumination of MIR probe photons, the well-known absorption peaks at ~3431 and ~3514 nm are achieved, corresponding to asymmetric and symmetric stretching vibrations of methylene (─CH₂─) groups. Since the coincidence spectrum is assumed not strictly flattop as assumption, the SNR would get slightly enhanced at the center and is decreased at the edge of the transmission spectra than the averaged SNR. With increased bin width and the exposure time, the SNR could be improved as illustrated in Fig. 3. Besides these, there are other ways to improve the SNR, such as decreasing the system loss by replacing the long-distance fiber by the dispersive medium with distributed optical amplification or promoting the upconversion efficiency using the lithium niobate waveguide (45, 46) and higher pump laser power (47).

Fig. 4. MIR vibrational absorption spectra.

Transmission spectra of polyimide (A), polycarbonate (B), and polyethylene (C). The experimentally observed transmittance is marked with black circles, while the deduced transmission spectra are shown in blue lines after the deconvolution of the system impulse response. The FTIR spectroscopy of 8 cm⁻¹ of spectral resolution is depicted in red lines. The polyimide and polycarbonate are measured by an FTIR (Spotlight 400, PerkinElmer), and the polyethylene is measured by an FTIR microscope (Nicolet iN10, Thermo Fisher Scientific). The measured spectra via time-stretching MIR upconversion spectroscopy system based on quantum correlation are in good agreement with the results from the MIR commercial spectrometer. Inset: A visible-light camera is used to capture images of unknown samples collected from the environment.

Table 1 provides a summary of typical demonstrations in the field of broadband MIR spectroscopy. Affected by the shot noise, the SNR of sensitive detection increases by a factor of $\sqrt{N}$ as the photon number of illuminations increases by a factor of N in a unit of time. Quantum nonlinear interferometry derived from nondegenerate SPDC represents a promising strategy (17, 18). However, it typically necessitates the use of a camera or grating to detect the interference pattern with spectral resolution. So far, the waveguide-based single-photon upconversion spectrometer is achieved with a higher pump power of 0.7 W using the configuration of grating and an EMCCD camera as well (24). Although the optimized pump power and the crystal engineering could improve the conversion efficiency, the readout noise and the environmental perturbations become dominant issue in applying this scheme to lower levels of MIR photons. In comparison to conventional upconversion time stretching scheme (48), our scheme surpasses the constraint of laser repetition rate and enables a more extensive range of spectral measurements. Notably, while a variety of MIR detection techniques provide benefits of their own in overcoming disadvantages of the FTIR system (49), our system has demonstrated noteworthy noise resilience and therefore is competitive in terms of SNR and sensitivity. In the case that the background is unknown or is not correctly calibrated, it is difficult to algorithmically subtract the background. The sensitivity of our system is achieved by the preferential exclusion of uncorrelated events in the correlation measurement.

Table 1. Performances of sensitive MIR spectroscopy.

References	Method	Spectral bandwidth (μm)	Sensitivity (photons/s)	SNR	Array detectors?	Moving parts?
This work	Quantum time-stretching scheme	1.18	6.4 × 106 (~370 fW)	54.6	No	No
(17)	Nonlinear interferometry + complementary metal-oxide semiconductor camera	0.9	3.9 × 108 (20 pW)	25*	Yes	Yes
(18)	Nonlinear interferometry + Fourier transform analysis	0.9	1.0 × 1011 (6 nW)	390	No	Yes
(24)	Upconversion + EMCCD camera	1.49	3.2 × 1010 (~2 nW)	300†	Yes	No
(48)	Classical time-stretching scheme	0.03	>1.7 × 1016 (a few milliwatts)	10	No	No
(49)	FTIR (Nicolet iN10, Thermo Fisher Scientific)	>20	-	2300‡	Yes	Yes

*Within a 7 × 7–pixel region of the 18,000-pixel camera.

†At a single absorption wavelength of 3268 nm.

‡Detected by the cooled mercury cadmium telluride (MCT) detector with a much brighter illumination.

DISCUSSION

We introduce a scheme of MIR frequency upconversion spectroscopy with ultralow MIR photon fluxes and nonlocal time-stretched measurement. The approach provides improved performance in contrast to the existing MIR low-light spectral detection. To date, most of commercial MIR detectors are based on narrow-band semiconductor materials such as HgCdTe and InSb, which still have serious dark current and thermal noise, making it a challenge to achieve ultrasensitive MIR detection at the single-photon level. The acquisition of MIR spectrum information, meanwhile, relies on a broadband MIR light source and dispersive elements at the design wavelength. Since dispersive elements including gratings and prisms, are generally used in conjunction with scanning devices, the spectral resolution and SNR of traditional MIR spectroscopy would be limited by either the number of grooves or the scanning speed. Otherwise, interferometers increase the system’s complexity and reduce its robustness.

In our proposed scheme, frequency upconversion based on a pulsed synchronous pumping setup transduces a broadband MIR spectrum to NIR bands. It has been studied that bulk crystals with chirped poling periods are advantageous for nonlinear frequency conversion across broad optical bands. Note that the spectral region of signal photons may be arbitrarily customized within the crystal’s transmission window by altering the distribution of varying periods. For instance, it is possible to generate signal photons that are suitable for developed Si/InGaAs/InP single-photon detection systems by designing a CPLN crystal with shorter poling periods and using a pump laser with a shorter wavelength. We have proven the feasibility of using the CPLN crystal as an SPDC source to produce broadband MIR photons and quantum correlation, and we confirm that the frequency upconversion of the MIR signal photons does not disrupt the temporal correlation and frequency anticorrelation of SPDC photon pairs. Spectroscopy via undetected photons based on induced coherence also illustrates its appeal in application of the MIR band (17, 50), yet in our scheme, the optical path difference between heralding photons and upconverted signal photons can be arbitrary, and there is no need for scanning delay or an array detector to analyze interference patterns. In the NIR wavelength region, we implement time stretching and correlation measurement by applying dispersive propagation to the communication-band heralding photons. To keep the GVD stable, the long optical fiber is mounted and bound in a temperature-controlled setting. Afterward, we successfully encode the spectrum information of the MIR band onto the time delay of coincidence measurement between two single-pixel single-photon detectors. Conceptually, because of quantum-state preserving of the upconversion process, DFT of MIR spectral information in the frequency domain to time-domain NIR signals is demonstrated, successfully accelerating the detection speed of the ultrasensitive MIR upconversion spectroscopy at the single-photon level and extending the operation wavelength of time-stretching schemes.

In summary, ultrasensitive MIR time-stretching upconversion spectroscopy is made possible. Several distinctive qualities strongly motivate our team to design this scheme. First, optical components in the system can operate at their optimum wavelengths individually. Frequency upconversion allows full exploitation of the excellent performance of mature NIR detectors. The remarkable technique omits the utilization of MIR detectors or array detectors. In addition, the fiber selected is of higher transmittance in the communication band. Compared to conventional wavelength-to-time mapping schemes, long-distance MIR fibers, which need special engineering, are avoided. Second, since the implementation of the system depends on GVD in principle, the structure of the system has no moving parts and is quite stable. The nonlocal temporal stretching well maintained in the broadband MIR upconversion detection fortunately precludes the necessity of grating scanning and interferometers. Not only is the quantum illumination based on correlations that are robust against uncertain noise including thermal noise, parametric noise, and electronic noise, but all the fixed structures in the system exhibited good mechanical robustness during the measurement, with few degrees of freedom that will be affected by the environment. The quantum correlation of upconverted photons and heralding photons enables the characterization of targets at remote locations with local spectral analysis, increasing the flexibility in sample selection. Besides, there is no trade-off between a high repetition rate and extended spectral bandwidths anymore. The net coincidence peak is unique along the time axis due to the correlation of true photon pairs. In the classical wavelength-to-time mapping scheme, the time interval between the laser pulse and the arriving photons is recorded. If the signal pulse is sufficiently stretched in the time domain, the signal of short-wavelength photons may overlap with that of the long-wavelength photons in the adjacent period, leading to the superposition of the spectra. Therefore, the repetition rate of the laser needs to be restricted to prevent the pulse stretching from going beyond one pulse cycle. In contrast, in our experiment, the time-stretched dominant coincidence peak is recorded uniquely in the time domain because the quantum correlated photon pairs are generated simultaneously and subsequently detected. Periodical accidental coincidence peaks would superimpose on each other, but they can be subtracted easily in the statistical analysis and do not affect the extraction of the MIR spectral information. Consequently, the quantum correlation technique is not bound by the laser’s repetition rate due to the nonlocal dispersion control (51, 52). Even if the laser repetition rate goes higher, the time-stretched spectrum could be fully broadened even with longer fiber to achieve a greater spectral resolution. Via this technique, averaged SNR achieves 54.6 in a total exposure time of 30 min, even at such a low MIR illumination of 0.21 photons per pulse. The exposure time can be further shortened to a few minutes, which is a huge step forward for correlation-based quantum spectroscopy.

It is vital that this scheme performs MIR spectroscopy of advanced performance without the need for unavailable MIR single-photon detectors. It is only reliant on a minimal setup comprising a narrow linewidth laser, two crystals, optical fiber, and two single-photon pixel detectors, eliminating the requirement for gratings, array detectors, or interferometers reducing experimental overhead. The innovative use of quantum correlation enables broadband time stretching with remarkable noise resilience in the MIR spectral range for evolving environments. In addition, the system demonstrates scalability by offering the flexibility to adjust both pump and detection wavelengths according to the requirement at room temperature. This establishes our approach as a cutting-edge solution for efficient and high-quality MIR spectroscopic measurements. We are confident that the scheme of ultrasensitive MIR upconversion spectroscopy based on nonlocal wavelength-to-time mapping is potential for nondestructive tests of photosensitive samples (53, 54), discoveries of coherence phenomena in biochemical or material systems (55, 56), as well as fields of electronic coherence dynamics (57), nanostructured metal optics (58), quantum diffraction imaging technique (33), etc. Note that redesigned SPDC waveguides or novel on-chip structures (59, 60) are expected to yield higher-purity heralding single-photon sources and optimize the photon-pair generation rate. MIR spectroscopy with much shorter exposure times on the order of milliseconds (61) is promising to be developed as a next step.

MATERIALS AND METHODS

The MIR heralded single-photon source in this experiment is pumped by a pulsed laser with an average power of 2 mW. The pump source is derived from an Yb-fiber laser together with an amplifier at a repetition rate of 30 MHz. The center wavelength of the pump laser is 1033 nm, and the full width at half maximum is 2.78 nm. The pulse duration is about 6 ps. A type 0 CPLN crystal is designed with the poling period varying linearly from 23 to 32 μm along the length of the crystal. The increment between adjacent poling periods is 0.1 μm. The bulk crystal is 25 mm in length with a rectangular aperture of 2 mm by 1 mm. Controlled at the temperature of 25°C, the CPLN crystal yields collinear photon pairs of the same polarization, with a photon-pair generation rate of 3.18 × 10⁶ counts s⁻¹ mW⁻¹. The nondegenerate photon pairs are separated by a dichroic mirror. Only the MIR signal photons that can pass through the germanium window are used for probe samples.

For the signal path, MIR photons that travel through the sample are upconverted and then detected by a Si single-photon counting module (η ≈ 70%). The other type 0 CPLN crystal at the temperature of 70°C is injected with the same 1033-nm pump as that of the heralded single-photon source. The pump beam aligns with the MIR signal. The pump intensity for upconversion is 311 mW. The poling period of the CPLN crystal covering 18 to 23 μm satisfies the first-order QPM of broadband SFG. The step of the chirped poling period is 0.01 μm. The crystal has a length of 50 mm and an incidence interface of 2 mm by 1 mm. A synchronous pulsed upconversion module is demonstrated. More details on the synchronous pulsed upconversion can be found in (40).

Supplementary Materials

This PDF file includes:

Supplementary Text

Figs. S1 to S6

References