Single-photon level ultrafast time-resolved measurement using two-color dual-comb-based asynchronous linear optical sampling

We demonstrated an ultrafast time-resolved measurement method operating at the single-photon level and employing a two-color comb-based asynchronous optical sampling (ASOPS) setup. We harnessed the two-color ASOPS photon counting approach to achieve long-term averaging of the ultralow intensity signal with a synchronized optical trigger signal, which minimizes residual timing jitter between the two combs. A pulse-width limited picosecond cross-correlation signal was successfully obtained with a power level of <1 photon/pulse. This approach enables the thorough study of ultrafast time-resolved detection of entangled photon pairs, quantum mechanical correlations in the time-frequency domain and finds wide use in optical quantum technology.

T he nonclassical nature of light plays an essential role in many quantum optics applications to demonstrate fundamental concepts of quantum mechanics, quantum information protocols, and quantum measurements.In particular, frequency-time entangled photons are anticipated to offer notable benefits for emerging quantum optical sensing or spectroscopic measurements.To fully exploit frequency-time entangled photons, it is necessary to understand their detailed properties on ultrafast time scales. 1)owever, the limited time resolution of photon-counting detectors 2) makes time-domain characterization methods challenging.Therefore, the development of time-resolved optical experiments at the single-photon level plays a crucial role in future applications of quantum optics.In addition, ultrafast single-photon measurements will enable a wide range of applications, such as fluorescence lifetime imaging in biological samples 3) or 3D depth imaging. 4)n the past, there have been investigations on fast gating methods to resolve single photons temporally.Optical gating with sum-frequency generation (SFG), followed by singlephoton detection with Si avalanche photodiodes (APDs), demonstrated efficient up-conversion 5) with sub picosecond 1,6) down to a few hundred femtoseconds 7) time-resolution, limited by the duration of the gate pulse.The highest temporal resolution to date has been achieved via the optical Kerr gating technique, which enabled a timing resolution of 224 ± 9 fs. 8)owever, these methods rely on mechanical translational stages to adjust the time delay between pump and probe pulses similar to traditional pump-probe ultrafast time-domain measurements.However, the speed of the motorized stages does not allow for rapid scan rates and poses a risk to introduce measurement uncertainties due to mechanical vibrations or backlash, beampointing instabilities, and possible wavefront deformations.Moreover, using a degenerate setup, i.e. single-color pulses for both pump and probe, induces significant background light from the strong pump pulse, which limits the signal-to-noise ratio (SNR) and could even lead to saturation of the detector.In our approach we overcome these limitations by introducing two-color asynchronous optical sampling (ASOPS), which relies on the precision and agility of dual-comb setups and avoids the large background by introducing a distinctly different color for the pump pulses.This ultimately enables single-photon sensitivities by fully eliminating the pump scatter.
Optical frequency combs have shown significant importance in various applications 9,10) such as frequency metrology, 11) dualcomb spectroscopy 12) and laser ranging. 13)Their high controllability in time and frequency domain combined with their unparalleled precision and dynamic range makes these tools ideal for such applications.Recently, optical frequency combs were utilized in single-photon counting techniques applications such as dual-comb spectroscopy, 14) laser ranging, 15) and imaging 16) at the single-photon level were demonstrated.In this paper, we employ the controllability and precision of optical frequency combs with ultrafast time-resolved measurements at the single-photon level through ASOPS.
The ASOPS approach has played an important role in terahertz (THz) time-domain spectroscopy, [17][18][19] in subpicosecond molecular dynamics investigations, 20) and in semiconductor metrology.21,22) The ASOPS technique eliminates the need for mechanical scanning and allows for rapid scan rates. By ntroducing two optical frequency combs with slightly different repetition rates f r , precise linear delay time scanning with high temporal resolution over long ranges is achieved.For this to work the two combs need to be phase locked to provide a low residual timing jitter between the two pulse trains. 22) Th difference in repetition rate, Δf r , determines the speed of the scan rate within a temporal scanning range of the pulse-to-pulse spacing (1/f r ).The ASOPS effectively down-samples the ultrafast dynamics into electronically resolvable signals by a factor of f r /Δf r and facilitates sub-picosecond to femtosecond level temporal resolutions.There is a high degree of freedom in the combination of the two light sources, and it is also possible to use light sources with two different colors.[23][24][25] In this work, we experimentally demonstrate an ultrafast time-resolved measurement method operating at the single-photon level.In this approach we investigate the temporal characteristics of single-photon level Er comb pulses using pulses from a high power Yb comb that serves as the ultrafast gate pulses in a nonlinear up-conversion in a sum-frequency periodically poled lithium niobate (PPLN) crystal.Using pulses with distinct wavelengths, the strong background light from the pump is effectively suppressed by spectral filtering enabling high SNR detection.Moreover, ASOPS electronically provides rapid optical waveform reflecting ultrafast response of the target signal.
The experimental setup is illustrated in Fig. 1(a).We employed a dual-laser source based on lab-made Er and Yb fiber frequency combs mode-locked by nonlinear polarization rotation, which emitted ultrashort pulses at repetition frequencies of f r,Er = 107 MHz and f r,Yb = 750 MHz, respectively.Sub-mHz level stability was achieved through a phase-locked feedback loop using piezoelectric and Peltier control referenced to a GPS-disciplined oscillator.We adopted a high repetition and high power Yb fiber comb that we had previously developed 26,27) as a pump, and performed 7 times harmonic synchronization on the Er comb source as a probe.This configuration reduced the temporal dead zone issue that has been a concern in the ASOPS measurements, and thus, it allowed us to improve the measurement efficiency.We could freely tune the repetition rate difference, defined as Δf r = f r,Yb −7f r,Er , and precisely control the relative time delay between the two comb pulses.We adjusted Δf r = 1 kHz, which determined the ASOPS scan rate as 1 kHz.
After the output of the oscillators, we amplified the optical power of the Er comb from 2 mW to 360 mW by an Er-doped fiber amplifier (EDFA).The Yb comb was amplified from 250 mW to 2.7 W by a double clad Yb-doped fiber amplifier (YDFA) (Nufern, PLMA-YDF-10/125-HI-8).The optical spectra of the amplified Er and Yb combs were centered at 1560 nm and 1040 nm, respectively.The Yb pulse was compressed into a nearly Fourier transform-limited duration of 95 fs [Fig.2(c)] using a transmittance grating pair compressor.The optical power of both, the Er and Yb combs, were split into two parts: one part each for generating a trigger pulse signal and the other for the time-resolved single-photon level measurements.
To achieve the single-photon level ASOPS measurements, we utilized an optically triggered synchronization scheme described below.As the principle illustrates in Fig. 1(b), we statistically integrated the discretely counted photons with the Δf r scan rate, and obtained the resulting histogram distribution that represents the corresponding time-resolved waveform.The jitter between the two combs and the time duration of the pump pulse limits the time resolution of the sampling system.Even though the repetition rates were stabilized to the mHz level using a slow PID servo, there was still some residual oscillator timing jitter in the system, leading to a fluctuation from the scan rate.For a single-photon level measurement, it is crucial to eliminate the timing jitter, since we need long-term averaging.Therefore, we further suppressed the influence of this residual jitter using an ASOPS   signal as an optical trigger at Δf r , which enabled continuous and synchronized data acquisition of photon counts over extended durations, which leads to highly precise and sensitive measurements.
The trigger generation was based on a two-color crosscorrelation measurement setup based on a β-barium borate (BBO) SFG crystal in which the Er and Yb combs collinearly overlapped after combining the beams on a dichroic mirror.The collinear beams were then focused into the 2-mm thick BBO crystal for SFG (1560 nm + 1040 nm → 624 nm).We optimized the optical alignment by selecting a suitable beam size to match the Rayleigh range with crystal thickness ensuring high nonlinear frequency-conversion efficiency.The input power onto the BBO crystal was 50 mW for Er and 200 mW for Yb comb, respectively.After spectral filtering, the SFG pulses were detected using a low-noise visible DCcoupled photodiode (New Focus, Model 1801) and recorded using a sampling oscilloscope (Rohde & Schwarz, MXO44).
The ASOPS scheme worked as follows: the temporal characteristics of single-photon level Er pulses are sampled using the high-powered ultrashort Yb gate pulses by generating a time-resolved cross-correlation signal.Achieving efficient nonlinear frequency up-conversion mandates the utilization of the high-power pump, 1 W.This is a type of pump-probe measurement in which the Yb pulses can be regarded as the pump light and the single-photon-level Er pulses as the extremely weak probe light.To generate the single-photon level probe light, we strongly attenuated the Er comb power to the picowatt level (with an average of less than a single photon per pulse), using a series of neutral density filters.The attenuated Er comb pulses overlapped with the high-powered femtosecond Yb pulses, and they were focused onto a multi-grating 1-mm PPLN crystal (HC Photonics) to perform highly efficient up-conversion through quasi-phase matching.At room temperature, the 11.73 μm poling period satisfied the quasi-phase matching condition for our experimental parameters.After the up-conversion, the upconverted photons were isolated from the residual mixing beams and the second harmonic components of the fundamental beams with suitable optical filters and dichroic mirrors before sending the upconverted light to the single-photon resolving detector.The detector was based on a single-mode fiber-coupled photon counting module (Excelitas, SPCM-AQRH-14-FC).It had a maximum dark count rate of 100 Hz and >70% peak photodetection efficiency at 650 nm.In the visible region, Si APDs with low dark rate and high photodetection efficiency are available, providing an excellent detection advantage for frequency up-conversion compared to NIR Avalanche Photodiode (APD) detectors.An appropriate light shield was kept around the single photon counting module (SPCM) to guard against ambient stray light.For each photon detected, the Si-APD module generated a Transistor-Transistor Logic (TTL)-level pulse.The oscilloscope started registering the single photon counts of SFG light after it got triggered by the aforementioned crosscorrelation trigger signal.We utilized Matrix Laboratory (MATLAB) to analyze the oscilloscope data for photoncounting measurement and cumulatively added the photon counts at the corresponding time-delay from the triggerpulse.A histogram representing the single-photon temporal envelope was obtained.
Figure 2(a) shows the result of a single shot trigger signal obtained by taking the cross-correlation between the two pulse trains.Under the condition of Δf r = 1 kHz, the ASOPS scan could sweep a time window of 1.3 ns (=1/f r,Yb ) at a 1 kHz scan rate with an effective delay step size of 12.5 fs, which is 1/f r,Er converted by a factor of Δf r /f r,Yb .This large temporal dynamic range, combined with the high scan rate is typically not accessible with motorized translation stage setups.The time delay between the two pulse trains in ASOPS (delay time) was obtained by applying a factor of Δf r /f r,Yb to the real measurement time (lab time), and both time axes were plotted accordingly.The single scan trigger measurement achieved a high SNR, and the correlation width was evaluated as FWHM = 1.58 ps.The Er (1.65 ps) and Yb (95 fs) comb pulse durations assessed by the separately measured autocorrelations shown in Figs.2(b) and 2(c).Furthermore, by tracking the residual timing jitter between the two combs, we found that the optical trigger was sufficient to achieve a timing accuracy of ∼20 fs or better at a scan rate of 1 kHz without the need for a fast feedback servo.Hence, we used this optical trigger signal to achieve the long-term cumulative accumulation of the singlephoton level ASOPS sweeps directly on the oscilloscope.Figures 3(a)-3(f) show the single-photon level timeresolved signals obtained by cumulative averaging of individual ASOPS scans.Before the up-conversion process, we attenuated the average power of the Er comb pulse to two different levels: 20.84 pW and 8.42 pW, which are equivalent to an average of 1.53 and 0.62 photons per comb pulse, respectively.Figure 3(a) is the result obtained in a single scan with 1-ms acquisition time.In the lower number of averages cases, the data appears random and discrete, however by statistically integrating them, the corresponding waveform gradually reveals the expected cross-correlation shape.At 1,000 averages (1-s acquisition time) shown in Fig. 3(d), the outline of the waveform starts to become evident.At 20,000 averages (20-s acquisition time) shown in Fig. 3(f), the SNR improved dramatically, and a clear cross-correlation waveform was obtained.
Figure 4(a) represents the temporal widths of the integrated waveforms of single-photon level pulses.It is found that with a sufficient number of averaging times, the width will converge to a constant value, which is attributed to an improvement in SNR.With 20,000 averages, the correlation width was evaluated to 1.42 ps for 1.53 photons/Er pulse.The specific origins of the discrepancy in the autocorrelation and crosscorrelation widths are not well known but are thought to be related to uncertainty in the measurement due to the limited SNR and/or to SFG crystal properties.This consistent result supports that we successfully constructed the time-resolved measurement method with an extremely low power level of <1 photon per pulse while effectively suppressing the residual temporal jitter between the two combs.
Figure 4(b) shows the SNR for the averaged waveforms as a function of averages.The SNR was defined as the signal peak value divided by the standard deviation of the noise in the tails.The SNR significantly improved with larger numbers of averages and obeying the square root of the averaging number.The improvement is realized due to the characteristics of our experimental configuration.For instance, the two-color comb configuration enables strong background suppression by spectral filtering before the detection.Furthermore, the upconverted single photons coupled into a single-mode fiber, which further suppressed the scattered light.We envision further improvements in the SNR by accumulating more photon events, by optimizing up-conversion efficiency, etc.
In conclusion, we demonstrated single-photon level ultrafast time-resolved measurements by employing a two-color combbased ASOPS approach.This method enabled kilohertz scan rates and scan intervals of the order of a nanosecond.Furthermore, the actively triggered two-color ASOPS photon counting technique facilitated the direct accumulation of successive time scans over long averaging times.Hence, without any significant degradation due to the residual temporal jitter of the two optical frequency combs without tight locking, we obtained a pulse-width limited and high SNR cross-correlation waveforms for picowatt level Er comb pulses.
Our demonstration might lead to new opportunities for time-resolved weak signal detection techniques such as fluorescence detection at the single-photon level.This new capability in essence realizes a gated detector with a much better time resolution than any commercially available singlephoton detector could provide.This might enable novel versatile and detailed time-domain characterization methods through time-resolved detection of quantum entangled photon pairs, quantum mechanical correlations in the timefrequency domain, and more.

Fig. 2 .
Fig. 2. (a) Result of the optical trigger signal generated by the ASOPS cross-correlation of Er and Yb comb pulses in the BBO crystal.Autocorrelation of (b) Er and (c) Yb comb pulses in trigger arm are shown as references.

Fig. 3 .
Fig.3.Results of (a) 1 scan, (b) 10 averages, (c) 100 averages, (d) 1,000 averages, (e) 10,000 averages, (f) 20,000 averages of consecutive single-photon level ASOPS sweeps obtained using high power Yb as a gate and low power Er comb pulses as a probe attenuated to an average of 1.53 and 0.62 photons per comb pulse.

Fig. 4 . 4 ©
Fig. 4. (a) Evaluated temporal width of the averaged waveforms versus number of averaging.Error bars are obtained as fitting error for Gaussian fit.(b) SNR dependence on the number of averaging.