High-sensitivity quantum sensing with pump-enhanced spontaneous parametric down-conversion

The interference effects of correlated photon pairs allow measurements with undetected photons.¹ Hereby, information on the transmission of one photon path can be detected in the interference pattern of their correlated partner photons. A common source for correlated photons is spontaneous parametric down-conversion (SPDC), which can be described as the spontaneous decay of pump photons into two photons of lower energy, called signal and idler. These correlated photons can have vastly different frequencies. In a nonlinear interferometer^2,3 (see Fig. 1), two of these sources can be superimposed so that the signal photons (and also the idler photons) from the first and second sources become indistinguishable. In this case, both the signal and idler photons will show interference modulation due to an effect called induced coherence.⁴ Due to the low emission rates of SPDC sources, no induced emission takes place.

Since the photons are correlated, the interference contrast of signal and idler photons is mutually dependent. If the idler photons are absorbed by a sample (with an amplitude transmission τ), the two correlated photon sources become distinguishable, and the signal light will show a decreased interference contrast. This way, information on the idler photon path is imprinted on the signal light. Since there is no induced emission of signal or idler light, the interference contrast depends linearly on the transmission of the sample.⁵ 

Using correlated photon pairs with mid-infrared idler and visible or near-infrared signal wavelengths allows us to acquire mid-infrared information with silicon-based detection of the signal light. Silicon-based detectors operate without cooling and offer lower detector noise as well as higher bandwidths than typical mid-infrared detectors. This measurement concept has been demonstrated for various applications such as imaging,^1,6 optical coherence tomography,⁷ and spectroscopy with undetected photons.^8–10 Nonlinear interferometers are maturing as tools for precise measurements with low light exposure to the sample. However, due to the low number of photons per spectral element emitted by the SPDC process, the signal-to-noise ratio of measurements based on induced coherence is typically limited by shot noise,¹⁰ which affects their sensitivity.

Several approaches have been pursued for increasing the emission rates of SPDC sources in the context of various applications. The brightness of SPDC sources can be enhanced by placing the light source inside an optical cavity that is resonant for signal or idler light.¹¹ According to the spectral profile of the resonator, the bandwidth of the correlated photons is drastically decreased, which can be desirable for many applications, such as those that involve coupling to specific transitions of atomic systems.¹¹ Recently, however, non-resonant SPDC sources with large instantaneous signal and idler bandwidths¹² have been demonstrated, which, considering sensing applications such as spectroscopy and optical coherence tomography, is an advantage that should be retained.

The emission rates can also be increased in a straightforward manner by using intense (often pulsed) pump lasers, which results in high-gain parametric down-conversion (PDC).¹³ This type of emission is characterized by its non-spontaneous nature based on induced emission. However, in contrast to nonlinear interferometers based on spontaneously emitting sources, approaches based on high-gain PDC receive a nonlinear response from the interference contrast to the sample transmission.^5,14 In addition, reaching the high-gain regime often requires short-pulse pump lasers, which limit the frequency-anti-correlation of the signal and idler light for applications where spectral information is of interest.

Another option for increased emission rates is waveguide-based SPDC sources, which offer higher efficiencies than macroscopic (bulk) nonlinear crystals due to improved mode overlap.¹⁵ For sensing experiments, however, coupling losses and the narrow mode aperture discourage the multi-pass operation of a waveguide-based nonlinear interferometer with free-space coupling to a sample.

In a different approach, a bulk crystal SPDC source is placed inside an optical cavity, which is resonant only for the pump light and does not provide any feedback for the signal or idler light. This allows us to increase the emission rate of SPDC without any modification of the spectral properties of signal and idler light or any induced emission. So far, several concepts for pump-enhanced SPDC sources have been investigated: Volz et al. have realized a pump-enhanced SPDC-based source for polarization entangled photon pairs with a low-finesse cavity in a semi-monolithic design.¹⁶ Thomas et al. have realized a similar concept with a symmetric cavity.¹⁷ Katamadze et al. have presented an SPDC source with higher pump enhancement by placing the nonlinear crystal within the cavity of the pump laser.¹⁸ This approach, however, complicates possible applications and requires adapting the cavity to the losses of the nonlinear crystal for stable laser operation.

In this letter, we report the first utilization of a pump-enhanced SPDC source in a nonlinear interferometer for sensing with undetected photons at enhanced sensitivity. To this end, the nonlinear crystal is placed within a passive optical cavity that is resonant for the pump light. With an enhancement factor of about 55, the SPDC emission rate is increased accordingly while retaining the unique features of a nonlinear interferometer based on induced coherence without induced emission. We demonstrate the advantages of this concept for experiments and applications based on sensing with undetected photons in the exemplary case of mid-infrared Fourier-transform spectroscopy with near-infrared detection.

In our experiment (Fig. 2), we use a single-frequency pump laser with a 775 nm emission wavelength and up to 250 mW of output power. The pump laser is coupled into a cavity (formed by the concave end mirrors M_p1 and M_p2) , which is piezo-tuned and locked to the laser. The dichroic intra-cavity mirrors (DM₁ and DM₂) are highly reflective for the pump light only and anti-reflection coated for the involved signal and idler wavelengths. The resonator has a finesse of about 290, which results in an enhancement factor of about 55 (taking coupling losses into account).

As an SPDC source, a 4 mm-long periodically poled lithium niobate crystal (PPLN) is placed at the center of the cavity. The pump wavelength and type-0 quasi phase matching configuration are designed for broadband mid-infrared idler light emission around 3.6 µm wavelength. A large bandwidth of SPDC emission can be achieved by choosing a group-index-matched signal wavelength.¹² For our target idler wavelength, the group-index-matched signal wavelength in lithium niobate results in about 1 µm, which is still measurable with a silicon-based detector. The signal and idler wavelength pair is addressed by the pump wavelength of 775 nm. This results in broadband idler emission ranging from wavelengths of about 3.1 µm (about 3200 cm⁻¹) to 4.1 µm (about 2400 cm⁻¹) and corresponding signal wavelengths ranging from about 1030 nm to 950 nm.

The power of the near-infrared signal light emitted by the SPDC source as a function of the pump laser power is shown in Fig. 3(a). The linear dependence confirms that despite the high cavity-enhanced pump power, the SPDC source still emits in the spontaneous, low-gain regime without induced emission.

The SPDC emission to the left-hand side passes the dichroic mirror DM₂ and is collimated using an off-axis parabolic mirror (OAPM). The signal light is reflected on a third dichroic mirror (DM₃), while the idler light is transmitted and passes through the transmission cell, which can be flushed with sample gas. Both signal and idler beams are reflected on plane mirrors (M_s and M_i) and imaged back to the SPDC source. Due to induced coherence, the superposition of reflected and direct emission on the right-hand side of the PPLN crystal shows interference modulation when the phase difference of the interferometer is varied by moving mirror M_i. Additional technical details on the nonlinear interferometer setup are given in the supplementary material.

In most nonlinear interferometers, the optical path difference of the interferometer arms is varied by a few wavelengths (typically <10 µm) only to determine the interference contrast.⁸ Recently, it has been shown that the interferometer itself can be used to determine the spectrum of the idler light, in analogy to the measurement principle of a classical Fourier-transform infrared spectrometer (FTIR).^9,10,19 In this measurement setup, the optical path difference between the signal and idler interferometer arm is varied, not only to determine the interference contrast but also to sample the auto-correlation function of the SPDC source. To this end, the idler mirror M_i is mounted on a high-precision linear stage with a maximum travel range of ±20 mm. As the optical path difference between the signal and idler interferometer arms varies, a single-pixel silicon-based photodiode (PD_sig) detects the interferogram of the signal light. A detailed view of the central part of the interferogram is shown in Fig. 3(b). The interferogram is broadened due to the dispersion of the nonlinear crystal.¹⁰ A Fourier-transform analysis then reveals the broad mid-infrared spectrum of the SPDC source [shown in Fig. 3(c)]. As in classical Fourier-transform spectroscopy, the spectral resolution is only limited by the maximum optical path difference between the interferometer arms.

In order to test the performance of the pump-enhanced interferometer, we measured the transmission spectrum of a multi-gas sample. At first, a reference measurement is taken, in which the sample cell is filled with pure nitrogen. For the sample measurement, a mixture of 0.90(3)% N₂O and 0.30(8)% CH₄ in nitrogen is filled into the cell. Each interferogram is averaged from 50 measurement scans, which were recorded with an acquisition time of 7.6 s each (resulting in a total measurement time of 380 s). For these measurements, we chose a reduced pump laser power of 100 mW in order to demonstrate which level of performance can be reached with pump powers available even from cost-efficient single-frequency diode lasers. In order to obtain a well-defined and smooth instrument line function, the interferograms are apodized (cf. Lindner et al.¹⁰ and supplementary material), as in classical Fourier-transform spectroscopy. With a Gaussian window function with a width of 3.4 mm full width at half maximum (FWHM), the theoretical spectral resolution is limited to about 0.5 cm⁻¹ (FWHM of the instrument line function).

The transmission spectrum is calculated from the quotient of the sample and reference spectrum and shown in Fig. 4. The spectrum spans a bandwidth of more than 800 cm⁻¹. The transmission spectrum can be used to quantify the signal-to-noise ratio (SNR) and, therefore, the advantage of pump enhancement. The inset of Fig. 4 shows a detailed view of a spectral range without absorption features of the sample gases. The variance of the measured values around the 100%-line allows estimating the SNR (cf. Lindner et al.¹⁰) to about 570. This corresponds to a transmission change of about 0.5% (3σ-width) that can be distinguished from noise.

An earlier experiment without pump enhancement demonstrated an SNR of 390 in a comparable spectral range (cf. Lindner et al.¹⁰). Taking the increased spectral resolution, reduced measurement time, shorter nonlinear crystal (improving bandwidth), and reduced pump power (easier accessibility) of the present experiment into account, the SNR is increased in agreement with the pump enhancement factor (see supplementary material for a detailed calculation). For the shot-noise limited measurement, the SNR increases as the square root of the enhancement factor. The cavity pump enhancement as a strong lever for the increase of SPDC power by orders of magnitude is, therefore, an important tool for the path toward faster or more sensitive measurements.

The multi-gas sensing experiment demonstrates the high quality and sensitivity of spectroscopic measurements with the pump-enhanced nonlinear interferometer. The high spectral resolution allows clearly resolving the rotational lines of the gaseous samples and is only achievable due to the high degree of frequency-anti-correlation of the signal and idler light (which, in turn, is due to the low bandwidth of the CW pump laser). For example, a typical PDC source pumped with a laser with a 10 ps pulse length has a Fourier-limited pump bandwidth of about 1.5 cm⁻¹ (the ideal Gaussian pulse), preventing the recording of spectra with sub-wavenumber spectral resolution.

The large bandwidth of the SPDC source allows differentiating multiple gases, which demonstrates the benefit of a cavity that is only resonant for the pump light and therefore does not restrict the bandwidth of the signal/idler light.

The pump enhancement concept requires a narrow-linewidth pump laser for efficient coupling to the cavity and active stabilization. With these investments in instrumentation, the pump enhancement allows for a higher signal-to-noise ratio, which results in improved sensitivity of the transmission measurements. This is a key benefit for quantitative quantum sensing measurements. Considering the high spectral resolution, the SNR per measurement time becomes comparable to that of classical FTIR devices²¹ while using a much lower light exposure of only about 60 nW to the sample. In future realizations, the SPDC rates may be enhanced until a significant level of parametric gain is reached.

We believe that the concept of pump-enhanced sensing will be beneficial to a multitude of measurement concepts with undetected photons based on the induced coherence effect. The results prove that the single-pass pump laser beam of previous experiments can be substituted by an enhanced intra-cavity field while retaining the unique properties of the SPDC source and the nonlinear interferometer. Pump enhancement allows for achieving higher SPDC emission rates at readily available diode laser pump power levels while preserving the benefits of quantum sensing experiments based on induced coherence. This is a crucial step toward allowing these novel quantum measurement concepts to outperform classical measurement techniques in a wide range of applications.