Mid-infrared coincidence measurements on twin photons at room temperature

Quantum measurements using single-photon detectors are opening interesting new perspectives in diverse fields such as remote sensing, quantum cryptography and quantum computing. A particularly demanding class of applications relies on the simultaneous detection of correlated single photons. In the visible and near infrared wavelength ranges suitable single-photon detectors do exist. However, low detector quantum efficiency or excessive noise has hampered their mid-infrared (MIR) counterpart. Fast and highly efficient single-photon detectors are thus highly sought after for MIR applications. Here we pave the way to quantum measurements in the MIR by the demonstration of a room temperature coincidence measurement with non-degenerate twin photons at about 3.1 μm. The experiment is based on the spectral translation of MIR radiation into the visible region, by means of efficient up-converter modules. The up-converted pairs are then detected with low-noise silicon avalanche photodiodes without the need for cryogenic cooling.


Supplementary Figure 2. Spectra at the output of the up-converter module.
The measure was taken for the 21.5 μm poled region, at a temperature of 100°C. The currents, which label the different curves, are the injected currents to the Broad Area diode Laser (BAL). The black box highlight the spectral region where the black body up-conversion may occur. The measure was taken with only a filter to cut off the pump at 1064 nm placed in front of a visible monochromator.
To reduce all these sources of dark counts when the up-converter module is coupled to the SPAD, a pinhole has been used to spatially filter out the noise. Moreover, since the up-converted photon pairs are actually generated in a very narrow band, bandpass filters have been used at the output of the up-converter module. In this way the noise is spectrally filtered, reducing the associated system background rate and increasing the signal to noise ratio. The filter transmittance for each set of filters is reported in Supplementary Figure 3. More details about the filters used after the module are discussed in the Methods section in the main text.
In Supplementary Figure 4 an experimental characterization of the CAR, which can be thought as the signal to noise ratio for a coincidence measurement, is reported. This measurement supports the choice of working with an injected current value of 3.6 A, as it gives the best CAR. Note that In Supplementary Figure 4, thermal effects within the module limits the conversion efficiency, which determine a CAR drop instead of a saturating behaviour for injected current values higher than 3.6 A.

Supplementary Figure 4. Coincidence to accidental ratio (CAR) characterization.
CAR is reported as a function of the injected current to the BAL, within the up-converter module. The data were collected for 50 s of integration time. Error bars are derived from the standard deviation of the coincidence peak and the standard error of the mean accidental background rate.
Starting from the experimental parameters, it is possible to estimate the coincidence peak due to the generated correlated pairs, versus the background of accidental coincidences [1,2]. In particular, knowing the incident photon flux on the detector and the losses from the generation stage, one is able to estimate how many correlated photon pairs arrive at the two detectors. Indeed, the probability that both the photons of the pair are detected and not lost along the way, scales as the square of the losses. Instead, the probability that only one photon of the pair is detected, scales linearly with the losses. Actually, it is more likely to have mismatched couples at the detector, with respect to photon pairs. These single photons are not correlated in time and so, they may contribute to accidental coincidences at random delay between the two detectors, represented by the baseline in Fig. 4b. In addition, the accidental coincidences are also influenced by the dark counts of the detectors. Therefore, if we call T the transmission amplitude from the generation to the detection stage, the experimental count rate subtracted for the dark count rate at each detector, C exp , is given by where N is the rate of generated pairs of photons. The correlated photons that arrive at each detector are NT 2 and the mismatched photons (NT -NT 2 ). T is a coefficient that ranges from 0 to 1 (in our case T = 0.0032, which corresponds to -25 dB of losses). Note that the description presented here is simplified for the sake of clarity. It does note take into account multi-pair emission and consider the coefficient T equal for the signal and the idler path. The simulation of the random arrival on each detector is based on a Poissonian distribution. To generate random timings, it is enough to invert the cumulative distribution function for the well known Poissonian exponential distribution. If λ is the average flux of photons on the detector and we want to know the delay between one click and the next one at the detector, this is given by where u is a random number, uniformly distributed between 0 and 1. Thus, given an average flux, we build random time arrivals within the observation window.
The simulated coincidence plot reported in Fig. 4b is obtained by performing the cross correlation between the time sequences of the two detectors, generated thanks to the relation in Supplementary Eq. 2. In the simulation the experimental electronic delay is not taken into account, therefore the simulated coincidence peak in Fig. 4b appears at zero time delay, instead of the 8 ns observed for the experimental measurement.
[2] Azzini, S., et al. Ultra-low power generation of twin photons in a compact silicon ring resonator.