1. Introduction

An important goal of modern quantum optics research is the development of scalable processing of quantum information. Photons are often used to connect parts of a quantum circuit. While coherent coupling between photons with various matter-qubit systems such as atomic ensembles [1], trapped ions [2] or quantum dots (QD) [3, 4] has been realized, these systems favor photons of incompatible spectral characteristics. In each case, scaling a quantum system up to meet the demands of a practical quantum circuit consisting of disparate components requires a major technological tour-de-force. Because any particular material system that supports quantum information processing generally has a narrow optimization range of its physical properties specific to that material, one can expect that it will be necessary to convert one frequency to another while maintaining the fidelity of the quantum state. Therefore, coherent frequency conversion is an essential enabling tool for realizing scalable quantum systems. To this aim, parametric frequency conversion is being actively researched. The properties of down-converters have been widely studied [5–9], and a recent demonstration showed that the single-photon purity, indistinguishability and phase are preserved during frequency up-conversion [10, 11]. It was also shown that the degree of coherence of up-converted faint light states does not significantly degrade after the frequency conversion [12, 13]. This property has been used to make an interferometer with independent upconversion in both arms, where fringe visibilities of 0.97(1) or better have been observed [11, 14]. For faithful frequency conversion of a quantum state, single-photon purity and phase information must be transferred to the output state. Therefore, it is of critical importance to achieve low background rates from the parametric process. An upconverter with a low background can in addition be used for a more efficient detection of telecom-band or (near)infrared quantum states [12]. Because the energy per photon in the telecom-band is considerably lower than in the visible, infrared detectors are often less efficient and suffer higher dark count rates (DCR)s than detectors of visible photons.

A significant issue with parametric upconverters however, is spontaneous generation of background photons in the output channel due to the strong pump necessary to achieve high-efficiency frequency conversion. Much attention has been devoted to reducing this background. A spectrally-broad background can be partially reduced via elaborate passive filtering arrangements, with band pass filters (BPF)s as narrow as ≈0.01 nm full width at half maximum (FWHM) [15]. In addition, the background is intrinsically suppressed by avoiding cascaded parametric processes [16]. Our group has recently demonstrated an upconverter that has an extremely low rate of background photons produced. This low background is achieved by avoiding both cascaded parametric processes and Raman sidebands via a large spectral separation between the pump, input, and output signal fields [11]. Measuring such a low rate of background events was a challenge, even using silicon single-photon avalanche diodes (SPAD)s, which have the lowest dark count rates among commonly available photon-counting detectors (<100 counts per second in our case).

Here we report a technique capable of measuring the brightness of a very faint light source and apply that technique to the problem of measuring the background of our frequency conversion system. Our measurements show that our highly-efficient upconverter generates just ≈100 background photons per hour, comparable to the photon flux of the dimmest continuous sources of visible/NIR light reported (astrophysical objects of 30 AB magnitude or lower) [17]. Those astronomical measurements of 0.025(5) cts/s compare to our measurements of 0.028(4) cts/s, while reducing data collection time by more than two orders of magnitude. To reach accuracy required for this measurement, we employed an optical transition edge sensor (TES) [18] and introduced a dark count reduction algorithm for its readout.

2. Experimental setup

The frequency converter used here is detailed elsewhere [11]. A magnesium-oxide-doped periodically poled lithium niobate (MgO:PPLN) crystal is phase-matched for type-0 sum frequency generation (SFG) of 919.5 nm and 1550 nm. Typically, a wavelength of 1550 nm is used as a pump and 919.5 nm is the signal input. In this configuration the crystal is pumped with a continuous wave (CW) 1550 nm beam from a wavelength-stabilized diode laser, amplified with an optical fiber amplifier. We also studied the conjugated process, with the strong pump at 919.5 nm and the signal at 1550 nm. For that, a home-built tunable external cavity diode laser in Littrow configuration at 919.5 nm was used as the pump. In the experiment (Fig. 1), both the signal and pump beams are combined on a dichroic mirror (DM) before the up-converting crystal. Both lasers are used simultaneously for alignment and to characterize the quantum efficiency of the up-conversion setup. To measure the background of the up-converter, only the pump laser is used, while the input signal laser is blocked. The pump and input beams are focused into the PPLN waveguide through an achromatic objective lens (numerical aperture ≈ 0.25). The waveguide temperature is maintained at ≈25.3°C for maximum conversion efficiency. After wavelength conversion, the up-converted 577 nm yellow light is collimated by an aspheric lens (numerical aperture ≈ 0.5). Then the 919.5 nm signal beam and residual background counts due to the strong pump are removed using a broad band-pass filter (BPF). The BPF is centered at 572 nm with a bandwidth of 28 nm, with a nominal 0.98 transmittance at 577 nm and a blocking optical density (OD) >7 at 919.5 nm. Because of limited performance of the commercial BPF in the telecom-band, we also added a low-pass filter with an additional OD >7 to ensure that pump photons are not seen at the output of the converter. Attenuation from the other optical components, such as dielectric mirrors, add up to more than 5 additional orders of magnitude for the pump light. The output is then coupled to a single-mode fiber for further analysis. Note that the only requirement for a BPF is to block pump wavelengths (1550 nm or 919.5 nm, depending on a configuration) and also their second harmonics (775 nm or 460 nm, respectively), [11]. We characterized the background with two different PPLN crystals to show that the low-background feature of this up-conversion process is repeatable.

 

Fig. 1 Experimental setup. HWP - half-wave plate; DM - dichroic mirror; BPF - band-pass filter; SMF - single-mode fiber, TES - transition edge sensor.

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A custom-built TES (optimized for signal at 780 nm wavelength) is used for our high accuracy characterization of the background. The TES is maintained at a temperature below 0.1K with help of adiabatic demagnetization refrigerator. The temperature is monitored and data acquisition is suspended each time the temperature exceeds 0.1K. The output of the TES is read by a superconducting quantum interference device (SQUID), amplified and processed by digitizing hardware. Each time the output voltage exceeded a chosen threshold, an associated waveform was recorded by a computer for further analysis. Using a threshold significantly reduced the amount of data recorded, but that threshold requires calibration. For a measurement of upconversion quantum efficiency, we detected the upconverted signal with a conventional Si-photodiode-based power meter.

3. Experimental results

3.1. Quantum efficiency characterization

To characterize the conversion efficiency of our upconverters, we measured the upconverted power as a function of pump power. The measured coupling ratios of the lasers to the two PPLN waveguides, 28%/37% and 27%/34% for the wavelengths 919.5/1550 nm respectively, were used to determine the internal quantum conversion efficiencies (defined as the number of up-converted photons divided by that of signal photons) of the PPLN waveguides (Fig. 2). The nearly linear trends, particularly at the maximum observed efficiency (above ≈50%) show that, for the power range investigated in our setup, the efficiency of the QPM SFG process is limited only by the optical power of the pump.

 

Fig. 2 Internal quantum efficiencies of up-conversion versus coupled pump power for two PPLN crystals.

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3.2. TES calibration and dark count reduction

One of the most powerful features of a TES is its spectral resolution of the detected photons. Photons of different wavelengths differ in energy and result in TES output waveforms of different amplitudes and FWHM [19,20]. For photons of a particular wavelength, a spread of waveforms is generated. At the same time, similar waveforms may be generated with no input light. The number of these “dark” waveforms is higher if the discrimination threshold is low. A few dark waveforms may still be distinguished from those due to photons by post-processing, while the remaining waveforms give rise to dark counts. The first step in calibrating a TES is to determine a variation in waveform parameters with photon wavelength. This information is used to select a proper threshold. In Fig. 3, the raw DCR is presented vs. the amplitude discrimination threshold. To obtain this dependence we tightly capped the optical fiber input port and recorded 10⁴ waveforms with a hardware trigger set to 14 mV and calculated the number of waveforms with peak amplitudes higher than a certain voltage level. Because the raw DCR exponentially decreases with the discrimination threshold, this dataset provides very few waveforms with high peak amplitudes. To better access these rare, high-amplitude dark count events, we recorded another 10⁴ waveforms with a hardware trigger set to 16.5 mV and computed DCR for higher discrimination thresholds. The raw DCR data is shown along with the TES response to 577 nm photons, see Fig. 3. To obtain this TES response, we attenuate the up-converted light to ≈ 10⁴ photons per second and collect 10⁴ TES waveforms. Using these measurements we select a trigger value of V₀ = 20 mV for the main data acquisition. This threshold allows for flexibility in post-processing while limiting the number of stored waveforms by excluding most of dark count events. This raw DCR data also helps us estimate what the DCR of the same detector would be with a longer-wavelength input.

 

Fig. 3 Distribution of detected TES waveforms vs. discriminating amplitude threshold level. An integrated amplitude histogram of counts above threshold value with no input light (blue dots, error bars correspond to standard deviation of measured counts, logarithmic scale); measured peak amplitude histograms of 10000 detection events for 577 nm (green circles) and 920 nm (red circles), labeled and shown with Gaussian fits on a linear scale. For each data series, a corresponding vertical scale is labeled with a matching color. The choice of the threshold V₀ defines the TES wavelength sensitivity and DCR.

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Next, we take advantage of the TES detection waveform properties to implement a DCR reduction. To use both amplitude and duration as the selection criteria in post-processing, we build a 2D histogram of amplitudes and FWHM durations of the waveforms due to 577 nm photons (Fig. 4(a)). Using this diagram we have defined waveform bounds for the up-converted photons that are subsequently applied to dark and background rate measurements. Note that these bounds results in modest reduction of the detection efficiency of about 4%, due to the high value of V₀, but significantly reduces DCR.

 

Fig. 4 TES waveform histograms of amplitudes versus FWHM durations for (a) attenuated up-converted light t_exposure ≈ 1 s, N_waveforms = 10000, (b) up-conversion background noise t_exposure = 4 × 10⁴ s, number of accepted waveforms N_waveforms = 203, (c) DCR t_exposure = 4 × 10⁴ s, number of accepted waveforms N_waveforms = 91. Pale blue background shows the bounds on duration and amplitude used in waveform post-selection. Red background represents rejected waveforms. Note: not all rejected waveforms are shown, because their amplitudes and/or durations exceed the axes limits in this plot.

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In characterizing the DCR, we obtained 0.0033(3) raw events per second. After applying constraining thresholds, the DCR is reduced to 0.0023(2) detections per second. Owing to such a low DCR, we can make measurements with record absolute accuracy in a fraction of the time heretofore required. A test of temporal variations of the DCR was made by interspersing background measurements with DCR measurements. No statistically significant deviations of the DCR were seen.

The TES used for our measurements was optimized to have nearly 100% efficiency at 780 nm and required a separate calibration for 577 nm. We calibrated it against a TRAP detector [21] using light generated by the up-converter. The TRAP detector had a detection efficiency of ≈99.5% with a spatial nonuniformity of <0.1%. We used a detector substitution calibration method with the aid of a set of pre-calibrated attenuators. Before measuring detection efficiency, discrimination thresholds on the TES output were set as described above. Our measurement yielded a detection efficiency of 60(5)% at the target wavelength on constrained TES waveforms.

3.3. Background measurements

We measure background from the up-converter in two configurations: an inherently low noise configuration when the wavelength of a pump laser is 1550 nm and the conjugated process with a pump laser at 919.5 nm. In the first experiment we use ≈150 mW of 1550 nm pump - the maximal recommended input power for our crystal. Each measurement of a background is followed by a DCR measurement. The exposure time of each measurement is 10⁴ s. This measurement sequence was repeated four times. Threshold-activated analog-to-digital recording hardware collects waveforms for further analysis. A full raw datasets obtained in a background measurement and a DCR measurement for the first waveguide are shown in Fig. 5(a) and Fig. 5(b) correspondingly. In the next step, we produce 2D histograms of the waveforms and apply pre-determined constraints to the background (Fig. 4(b)) and a DCR (4(c)) measurements. Typical raw waveforms are color-coded as accepted (blue) and rejected (red) in Fig. 5. At the TES detector, we measured the background to be just 0.0028(4) photons per second after subtracting the DCR. Then, we calculated the generated background by factoring in optical losses upstream. This method yields a background noise rate of 0.028(4) photons per second for waveguide 1 (See Table 1) for estimated efficiency of 10(1)%. Our measurement on the second waveguide resulted in a comparable value for the background noise, albeit with slightly higher absolute uncertainty (See Table 1). Thus, our up-converters in the inherently ultra-low noise configuration have an operational dynamic range of incident signal photon fluxes (at 919.5 nm) from as few as 2 photons per minute all the way to classical power (limited by ≈10% of pump power) and are linear with the input.

 

Fig. 5 Measurement of the up-converter’s background. TES waveforms collected in a 4 × 10⁴ s measurements (a) for background upconversion noise; (b) dark counts. Waveforms that are inside the bounds given in Fig 4 are shown in blue, and the others are shown in red.

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Table 1. Performance of the upconverters measured by two detectors (TES and SPAD) at the output wavelength of 577 nm. Two pump wavelengths λ_pump, 1550 nm and 920 nm, were tested. The efficiency of the SFG process is defined as the upconverted photons/incident photons. The DCR for the SPAD is the due to the detector alone. The DCR for the TES includes some amount of light leakage into the long fiber needed to reach the location of the TES system. The SFG background as measured is the photon count rate minus the DCR. This value includes losses due to optics transmission, coupling, and detection inefficiency. The inferred value is that same rate adjusted for those losses to obtain the background generated by the SFG process alone. One standard deviation statistical uncertainties are indicated.

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In the second experiment we use ≈80 mW of 919.5 nm pump - the maximum available power. We observe a significant level of background counts in this configuration. Therefore, this background was measured with a low-DCR silicon SPAD. Notice that the background in this configuration is nearly 10⁶ higher than that in an inherently noiseless configuration (see Table 1). This result confirms a clear advantage of long-wavelength-pumped upconversion (c.f. [16]), particularly important for frequency-converting quantum states of light.

We point out that this up-converter can be used to enhance the range of efficient noiseless detection. Because the energy of the output photons is significantly higher than that of the input photons, one can use single-photon detectors with a higher discrimination threshold. In this up-converter, the output wavelength matches the peak efficiency of silicon-based detectors. We evaluated the effect of using up-converted photons vs. 920 nm photons with this TES. A histogram of pulse amplitudes due to the 920 nm photons along with the measured DCR at that amplitude levels shows that the TES DCR is elevated at least 4 fold for 920 nm vs 577 nm detection (Fig. 3). Therefore, to improve signal-to noise ratio, detecting photons up-converted in this low-noise upconverter is more advantageous than a direct detection of 920 nm photons in a TES. We expect that the relative reduction in the DCR by employing a similar up-converter vs. a direct TES detection will be even more significant for input light at longer wavelengths.

4. Conclusion

We demonstrated a nearly-noiseless highly efficient up-converting frequency bridge. The background generated by the up-converter is 0.028(4) photons per second. We saw conversion efficiency as high as 53% with no signs of saturation; theoretically, conversion efficiency could reach 100% [22]. To our knowledge, these noise measurements demonstrate a new level in faint light source photon flux measurement, providing better accuracy in 100 times shorter measurement (as compared to Hubble Space Telescope extremely deep field data, [17]). Because a parametric process is phase-preserving [10,11,23,24], it can be used to faithfully convert a broad range of non-classical states including entangled states. In addition, we have demonstrated extending ultra-low-darkcount photon detection to the infrared via nearly-noiseless up-conversion.