Stroboscopic Space Tag for Optical Time Resolved measurements

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Stroboscopic Space Tag for Optical Time Resolved measurements with Charge Coupled Device detector Josep Canet-Ferrer, Raul Garcia-Calzada, Juan P. Martínez-Pastor, and Guillermo Muñoz-Matutano ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.8b01376 • Publication Date (Web): 10 Dec 2018 Downloaded from http://pubs.acs.org on December 14, 2018

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Stroboscopic Space Tag for Optical Time Resolved measurements with Charge Coupled Device detector Josep Canet-Ferrer,†,‡ Raúl García-Calzada,‡ Juan Martínez-Pastor,‡ and Guillermo Muñoz-Matutano∗,¶,‡ †ICFO-The Institute of Photonic Sciences. The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain ‡Unidad de Materiales y Dispositivos Optoelectronics (UMDO) Instituto de Ciencias de los Materiales de la Universidad de Valencia (ICMUV) ¶Department of Physics and Astronomy, Macquarie University, Sydney, New South Wales, Australia & ARC Centre for Engineered Quantum Systems, Macquarie University, NSW 2109, Australia E-mail: [email protected]

Abstract Time resolved measurements are extensively employed in the study of light-matter interaction at the nanoscale such as the exciton dynamics in semiconductors or the ultra-fast intraband transitions in metals. Importantly, single photon correlation, quantum state tomography and other techniques devoted to the characterization of quantum optics systems rely on time resolved experiments which resolution is bound to the time response of the detector and related electronics. For this reason, multiplexing or beam deflection techniques have been recently

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proposed to overcome the detector resolution and thus measure the final photon distribution characteristics. Taking advantage of both strategies, in this work we present a simple method to obtain time resolved light transients independently on the detector response. The method is based on the stroboscopic synchronization of a given optical signal after spatial tag of its time response. To illustrate the potential of the approach we present a simple setup able to measure time resolved optical signals with time interval per pixel < 1 ns, using conventional CCD camera optical detection with large integration times. The system response depends on the stroboscopic synchronisation parameters but not on the detector time resolution. We illustrate the operation of our proposed set-up in time resolved experiments and discuss and simulate how the proposed scheme could be used in photon correlation experiments.

keywords: Time Resolved Photoluminescence, Instrumentation, Time to Space Synchronization, Charge Coupled Device, Photon distribution

The temporal analysis of light emission (Fluorescence or Photoluminescence) 1,2 is a widely used experimental technique with great influence in many of the fundamental research fields, like organic and inorganic chemistry, biochemistry, molecular biology 3 or material science and solidstate physics. 4 The study of the time response in light emission experiments reveals radiative decay rates from different electronic transitions and the optical coherence of particular light states, among other properties. 5 This makes time resolved techniques essential tools for studying the quantum nature of light. Photon auto and cross-correlation with Hanbury-Brown & Twiss (HBT) interferometry, Hong-Ou-Mandel photon indistinguishability set-ups, Bell inequality tests or Quantum State Tomography analysis would be some examples of their strong potential. 6 Current approaches to develop time resolved light analysis could be classified into analogical techniques such as boxcar or gated integrators, or photon counting experiments as Time Correlated Single Photon Counting (TCSPC). Methods based on the Boxcar Integrator result more friendly and allow processing transient signals produced with moderate time resolution limited by photodetector response. 7 Streak Camera is the most sensitive analogical approach to perform time resolved

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light analysis with very high time resolution, pico- to femto-second. Streak camera stroboscopic synchronisation has been used to measure the photon time of flight with the impressive result of imaging the travelling of a laser pulse through the medium. 8 Other successful strategies based on stroboscopic synchronisation can be found, such as the study of the variability of the repetition rate of a pulsed optical signal 8 or the use of deflecting optics to control optical beams. These are called optically deflected streaking cameras. 9 Synchronised versions of these Optical Streak Cameras lead to intermediate temporal resolution measurements (nanoseconds) with relatively low cost equipment. On the other hand, TCSPC method requires to correlate the detection of single photons (at stop channel) with respect to a trigger signal (at start channel). This occurs into a short time window which is discretized into a range of labelled time channels. 10 In the best case scenario, the resolution of the technique is limited by the time bin width. In practice, the detector response is the main constraint. For this reason, it is possible to find in literature proposals to overcome these limitations. For example, time-resolved up-conversion schemes 11 have been proposed to reach femto-second resolution. All the approaches above mentioned rely on the performance of modern photo-detectors and related electronics, which have been considerably improved with the advent of fast and efficient single photon avalanche photodiodes (APDs) and superconducting single photon detectors (SSPD). 12 Recent progress in these technologies have influenced photon correlation experimental schemes. As a result, during the last decade new experimental approaches to study the statistical fluctuations of light have been proposed. This is the case of the two photon absorption method, where the improvement on detection has allowed the study of super-poissonian photon statistics, 13 or the measurement of non-classical photon correlations with single SSPD and InGaAs APDs detector experimental schemes. 14,15 Alternatively, Streak camera set-up has been implemented to directly analyse photon statistics and study multiple n-photon coincidences, 16 higher order photon bunching 17 and bundle correlations, 18 revealing arrival times of individual photons from a light beam. The analysis of n-photon correlation effects is essential for advancing in quantum optics research,

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where spatial and time multiplexing have been implemented in time resolved and photon correlation set-ups to improve their capabilities and performances. A clear example is the demonstration of the increase of the heralded photon rate of non-deterministic single photon sources by means of multiplexing strategies to reduce their multiphoton probability with high degree of photon indistinguishability. 19,20 High speed temporal and spatial multiplexing has been proposed to develop single-photon counters with photon number resolving capabilities, 21 or to actively reduce detector dead-time to allow photon counting at higher rates. 22 These multiplexing approaches could be implemented to develop more complex scenarios, as for example the proposal of a sensing method for studying n-photon correlations, 23 or to enhance the capabilities of quantum repeater networks. 24 Keeping all these challenges in mind, in the present work we propose a reliable time resolved experimental technique based in the stroboscopic spatial tag of pulsed optical signals. 25 In the first part of the work, the technique is validated through time resolved photoluminescence (TRPL) measurement of the Donor-Acceptor recombination in a GaAs wafer exhibiting a double exponential decay time well below the resolution of the proposed set-up. As an advantage, our method allows to reach time resolution of about 10 ns by means of a conventional CCD camera and friendly opto-mechanics instead of fast photodetectors and electronics. We also discuss how hardware improvements of the experiment could lead to unprecedented time resolution in the future. In the second part of the work, we describe a numerical simulation to demonstrate the potential of the system in the study of photon statistics.

Experimental Methods and Set-Up Based in the particular description of CCD imaging with stroboscopic conditions (see Supp Info) here we propose a basic scheme to perform time resolved light analysis using a simple space tag procedure. Figure 1.a shows the required elements: periodic light under study, with its characteristic time period between pulses (T L ); time to space converter, characterised by its deflection modulation period (T d ), where here we have used an hexagonal rotating mirror; and a wide pho-

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Figure 1: Stroboscopic Spatial Multiplexing. a) This technique is based on the periodic deflection (with period T d ) of a time modulated optical signal (with period T L ) which is converted to spatial modulated light pattern, with the help of a Time to Space converter. Here the Time to Space converter is an hexagonal polygonal rotating mirror (used for conventional laser scanning). The periodic light impinging on the mirror is imaged by a CCD placed at a distance dCCD . When stroboscopic spatial tag synchronisation conditions are satisfied (see main text and supp info), CCD acquisition return time resolved analysis of the pulsed light under study. b) Comparison between CCD acquisition of deflected laser with single periodic (gray) and 3-burst (red) triggering modes operated at 0.5 MHz when positioned at dCCD = 0.6 m away from the rotating mirror. c) CCD acquisition of the deflected laser signal when positioned at dCCD = 6 m away from the rotating mirror. The spot size time resolution have been extracted from Gaussian fitting. Black line with greyish shadow shows 400 vertical pixels CCD binning, where red line corresponds to two Gaussian cumulative fitting. In order to record two consecutive pulses in the CCD and calibrate the measurement, here we have used slightly higher laser triggering period (2.5 MHz) and a second CCD with an array of 1024 x 1024 pixel (ImagEM X2-1K EM-CCD camera from Hamamatsu)

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todetector (being here a CCD) at a distance dCCD from the mirror. With the aim to properly calibrate the system, we have analysed the direct deflection of a pulsed laser with single periodic and burst trigger modes, as it is shown in Figure 1.b. With a greyish shadow it is shown CCD acquisition of the laser deflection when a diode laser is triggered at 500 KHz and using a distance of dCCD = 0.6 m between the deflecting mirror and the CCD. The mirror vertical axis is coupled to an electrical motor feed by an external function generator operating at a frequency νd = 2.000000856 KHz, with µHz resolution. With these parameters, the stroboscopic synchronisation condition is satisfied by two different spinning harmonics of the hexagonal mirror, with frequencies of 2 KHz (synchronisation with one single mirror side) and 4 KHz (synchronisation with two opposite mirror sides). With a reddish shadow it is shown CCD acquisition of the same laser triggered at 500 KHz with 3-burst operation and same deflection frequency. We have selected a burst period of 0.5 µs. This measurement returns the proper time calibration of the CCD pixel, with ∼ 12.5 ns/CCD-pixel. At the same time, this calibration can be used to check the possible coexistence of multiple deflection harmonics. However, as it is shown in figure 1.b, there is only one repetition pattern that suits the time scale for both conventional and burst trigger modes, thus being a consequence of the lower frequency in the harmonic single laser deflection, i.e. synchronisation with one single mirror side. The last condition represents a lower bound of the instrument performance, as higher speed rotation will enhance the time resolution and the optical contrast of the CCD acquisition by the use of the rest of the side mirrors. However, in the actual case, the use of the hexagonal mirror reduces the sources of mechanical jitter. The motor used here provides enough resolution for many demanded temporal chemical analysis, with an exceptional commercial low cost. In principle, once the stroboscopic condition is established, the space tag pattern could be propagated up to reaching the required τ/px value. In figure 1.c we have achieved τ/px ∼ 0.6 ns, when using a distance of dCCD = 6 m between the deflecting mirror and the CCD. However, the final time resolution of the device is limited by the laser spot size in the CCD detector (dS ) (∼ 200 ns both in fig. 1.b & 1.c). Hence, the spot size is an important optical figure of merit of the set-up.

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After we have set the synchronisation parameters, we have analysed TRPL emission from bulk n-doped GaAs semiconductor sample, grown by Molecular Beam Epitaxy (MBE). Light excitation was carried out by a pulsed laser diode at 785 nm (Pico-Quan LDH), externally triggered with a delay generator (SRS-DG645) and fixing the laser repetition frequency to fL = 500 KHz (T L = 2µs). Photoluminescence (PL) signal was post-selected by band pass filtering and collected by a free optics microscope that was coupled into a single mode optical fibre. Light from the opposite fibre end was sent to the time to space setup depicted in figure 1.a, being focused with conventional lens to the CCD (iDUS 401 from ANDOR: 1024 x 127 pixels). Conventional TRPL was carried out to compare our stroboscopic measurements with a traditional TCSPC method, which is based on a Silicon APD (Perking Elmer SPCM-AQRH-14) connected to a time correlated single photon counting card (TCC 900 from Edinburgh Instruments). The steady state PL spectrum was measured by a CCD attached to a monochromator (double monochromator Acton SP-300i from Princeton Instruments).

Lifetime Measurement and Simulation Figure 2.a shows conventional photoluminescence (PL) measurement of the different optical emission bands present in the sample under study, corresponding to: i) GaAs exciton, ii) GaAs acceptor impurities band, iii) LO-Phonon replica from ii), iv) InAs Wetting Layer and v) InAs QDs optical emission. Inset in figure 2.a shows the TRPL trace of the B-band (black continuous line) recorded with monochromator filtering and APD single photon detector connected to our TCSPC electronic card. The recorded TRPL trace is fitted through a bi-exponential decay function (red continuous line), which returns fast and slow decay times τ f = 75 ns and τS = 488 ns, respectively. In order to measure TRPL spectra of the B-Band optical recombination using our time to space stroboscopic synchronisation technique we have placed a 830 ± 10 nm band pass filter before the light is coupled to a single mode optical fibre (filtering the reddish shadow region indicated in figure 2.a). The PL signal is re-directed to the deflection set-up and measured by the CCD under

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Figure 2: Time Resolved Photoluminescence Measurement & Simulation. a) Continuous wave measurements of the sample PL to identify the different emission bands of the spectra that are labelled as: i) GaAs, ii) GaAs acceptor impurities, iii) Phonon replica from ii), iv) Wetting Layer emission and v) InAs Quantum Dot optical emission; The PL transient of the GaAs acceptor impurities measured by conventional TCSPC is shown in the inset. b) PL transients of the laser (shadowed) and B-band PL using the time to space stroboscopic spatial tag technique with the laser triggered at 500 (upper panel) and 250 KHz (lower panel). c) Numerical simulation of the measurements of the synchronised laser (upper panel), the B-band signal with synchronised conditions (middle panel) and the B-band signal with unsynchronised conditions (lower panel). d) Comparison of the simulated and the experimental CCD integrated intensity with full vertical binning.

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synchronisation conditions. Figure 2.b show the CCD acquired TRPL spectra of the B-Band (black continuous lines) by triggering the laser with repetition rates of 500 (upper panel) and 250 KHz (lower panel). System time response is measured deflecting the laser into the CCD (grayish shaded area) returning Gaussian FWHM of ' 0.2 µ. Time decays are extracted from a bi-exponential decay fitting function convoluted with the system time response:

−

IPL (t) =[I0 + I1 e

(t−t0 ) τf

+ I2 e−

(t−t0 ) τs

(t−t )2 −2 02 ω

1 ⊗ q e

]+ (1)

2ω2 π

where ω = 2σ = 0.85 × Gaussian-FWHM. The fitting analysis returns τ f = 67 ± 5 ns and τS = 423 ± 40 ns (500 KHz triggering) and τ f = 50 ± 10 ns and τS = 570 ± 30 ns (250 KHz triggering), which are in good agreement with the TRPL analysis carried out by the conventional TCSPC + APD detection. We tentatively associate the small discrepancy between these numbers to a non-linear deviation of the time scale in the CCD array, originated by the circular aberration that will depend upon the CCD-length over 2π × dCCD . With the aim to demonstrate the operational principles of the time to space stroboscopic synchronisation technique presented here, we have modelled the photon deflection time analysis as described in the supporting information. Each laser pulse triggers a single photon emission following bi-exponential decay probability distribution. This produces a pulsed train of incoming photons characterised by the laser repetition period T L = 2µs and the bi-exponential decay time, producing a single array of time distributed photons. We included a randomly distributed photon population along the entire array to be aware of the noise arriving to the CCD. Then we simulate the time to space modulation defined by its characteristic optical deflection period T d . This is executed dividing the first single array in sub-arrays of length T d . All these sub-arrays are added together to simulate the single spatial CCD recording of the multiple deflection cycles. Next step is to produce the appropriate integration bin defined by the corresponding CCD pixel width. Here

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time to space conversion produces an equivalence of 12.5 ns/CCD-pixel, and hence we would integrate the required number of time slots until reaching 12.5 ns. In our particular case, we included only the first 1024 pixels, to simulate the signal over our specific CCD model. Finally, the resulting array is convoluted with a 2D Gaussian to simulate the spot size of the optical beam focused into the CCD, and thus producing the final time resolved optical signal. The entire process is repeated m times, to include the possibility to perform multiple acquisition simulations. Figure 2.c shows three different simulations following the above described procedure. In the upper panel it is shown the laser pulse train reconstruction, without including any PL simulation, and using T d = 499.79 µs. With this parameter the stroboscopic synchronisation is accomplished, showing a series of circular spots separated between them by 2 µs, as it is expected. In the middle panel it is simulated TRPL spectra with the same synchronisation parameters. As we have included the bi-exponential emission probability, the final output consist of the fast (central circular spots) and slow (tail) decays. In the lower panel it is simulated the same TRPL signal with a slightly mismatched deflection period (499.81 µs). As it is shown, the small perturbation of T d (corresponding to 0.08 Hz detuning) lead to the breakdown of the synchronisation condition, producing a flat pattern along the entire CCD array. Upper panel in figure 2.d shows the simulation of the full vertical binning of the synchronised TRPL CCD acquisition in figure 2.c. The actual simulation of the process reconstructs the real TRPL spectra (lower panel in figure 2.d). To give better insights about the potential of the Stroboscopic Spatial Tag method, we conclude this section discussing its limits and different strategies to improve time resolution. The picture is considerably simplified when the ultimate time resolution is estimated in units of time per pixel, e.g. ns/pixel. The pixel size, the number of pixels in the CCD, the light spot size in the CCD, the deflection angle (here determined by the number of mirror sides) and deflection angular frequency or the distance between the camera and the mirror will be the parameters to be considered. The transients shown in figure 2.b have been acquired using a maximum laser rate of 500 kHz and a mirror angular velocity of 2 KHz. The result is an optical signal modulated in 125 pulses and spread over an angle of 60◦ . For example, if the detection plane was 23 mm far from the mirror,

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the time interval per pixel (τ/px) will be around 250 ns. In our actual measurements (Figure 2.b), we have moved the camera backwards about 600 mm to improve τ/px ∼ 10 ns. At this distance the angular size of the camera is reduced to 2-3◦ corresponding to a time span to about 11 µs to be divided by 1024 pixels. Finally, when we moved the camera until dCCD = 6 m (Figure 1.c), the final temporal resolution was not finally improved, as the focused spot size on the CCD was very large, which does not profit the enhancement of the time interval per pixel. However, the optical spot size can be independently adjusted with appropriate free optics beam expanders and collimators, and thus it does not represent any fundamental limitation of the device. Another parameter that can be considerably improved is the CCD pixel discretization, since the onset on the telecom market is continuously pushing the performance of imaging systems and the number of pixels of commercial cameras. Indeed, currently there are few manufacturers providing spectroscopic CCDs of 21360x6 pixels, namely the TCD2964BFG chip from Toshiba (pixel size 2 × 4 µm), which would increase τ/px by a factor 20 for a given modulator-CCD distance. Finally, time resolution of the system can be drastically enhanced when using more sophisticated optical deflection systems, with the important penalty of increasing costs. As a first upgrade it is possible to increase the number of facets of the polygonal mirror (up to 72 of the Road Runner from Precision Laser Scanning). With optical phase array devices the light steering frequency can reach MHz, 26 or even GHz operation. 27 Nowadays these optical devices are receiving much attention due to the popularity of LIDAR and autonomous processes, 28 and hence it is expected a fast device development and product cost to drop in the near future. In summary, the main advantage of our technique comes from the enhanced configuration versatility, where the required time resolution is dependent on the specific set-up parameters selected for each application.

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Light Intensity Fluctuation Simulation The proposed setup presented in last sections is not just a light analysis imitation of streak camera schemes, with slower operational performance. It also allows to think of complementary and alternative applications, which it brings an interesting modularity property of the setup. With the advent of modern EMCCDs 29 and SPADs cameras, 30,31 readout noise has been decreased until sub-electron/pixel while maintaining fast frame rates. The recent progress in the development of ultra-low noise electronics enables the quantized measurement of charge in CCD pixels. 32 Recently it has been shown high quality imaging with intensities in the order of single photon per pixel. 33 As an example in this direction, here we study a possible application of our time to space stroboscopic space tag technique: the measurement of the second order correlation function (g(2) (τ)). Due to the absence of detector deadtime and the setup parameter tunability, it is possible to measure a sample of consecutive photons in a single CCD acquisition synchronised with a single mirror deflection, and extract from there the g(2) (τ) value. In order to explain the g(2) (0) measurement details, here we present the protocol demonstration for a Fock state with photon mean number = 1. Figure 3.a shows a simulation of 100 consecutive pulses deflected in the CCD without any source of photon losses and noise. In this ideal situation, the CCD readout consist in uniformly distributed single photon detection through a single CCD row. Figure 3.b shows the resulting photon state distribution after a single mirror deflection (grey bars) and after 20 deflections (blue bars), returning well-defined = 1. We have simulated the same measurement with the influence of 70% random photon losses (Figure 3.c and d) and 70% random losses + 20% of Poisson noise (Figure 3.e and f). The random losses are simulated photon by photon and take into account for the finite efficiency of the detectors and the shot noise due to the discrete nature of the photons. When losses and noise are included in the simulation, is reduced, as the photon stream contains either CCD space tagged pixels with photon gaps or with more than 1 single photon (see Figure 3.d and f). The measurement of the photon coincidences can be carried out performing simple two photon threshold statistical counting along the CCD array (red lines in Figure 3.e), and normalising to 12


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Figure 3: Protocol demonstration of the g(2) (0) measurement for a Fock state with mean photon number = 1. a) CCD capture of the arrival of 100 consecutive photons without any source of losses. b) Photon state counting for a single deflection (gray bar and bottom horizontal axis) and 20 deflections (blue bar and top horizontal axis). c) Same CCD capture when it is included 70 % of random photon losses, and d) equivalent photon state counting. e) & f) equivalent plots when it is included 70 % of random photon losses and 20 % of Poisson noise. At the bottom it is shown same CCD capture than e) but when it is included a 50/50 beam splitter before the deflecting optics, and thus producing Left (g) and Right (h) CCD arrays.

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the photon rate. This protocol is equivalent to a post-processing fast oscilloscope counting. 14,15 However, g(2) (0) measurement could be directly provided by the CCD row electronic processing if the beam is divided in two optical paths (namely, Right and Left) with a 50/50 beam splitter placed before the optical deflection takes place. Figures 3.g and h show the photon stream divided in L and R paths, with red lines indicating the presence of a coincidence. When the zero-delay path between L and R channels is calibrated, the g(2) (0) value can be calculated by the direct dot product between both L and R CCD arrays (see supp information). Finally, if photon losses are large enough it would be necessary to repeat this measurement M times. The final g(2) (0) value will be calculated as the mean value of these M different measurements. Following the entire protocol, we simulated the g(2) (τ) measurement for Bose-Einstein, Poisson and Fock states with = 1. We build the initial photon train following the selected probability distribution and projecting the expected photon number in each time slot. Then we include the 50/50 beam splitter to divide the photon train into R and L beams with the possibility to include a relative time delay (τ) between them. Then it is included the simulation of the deflection and finally the CCD measurement. We have included simulation without any photon losses (Figure 4.a, b and c) and with 50 % losses and 20 % Poisson noise (Figure 4.d, e and f). As it is shown, the super-Poisson, Poisson and sub-Poisson photon statistics is correctly simulated for each photon distribution under study. The principal advantage of our setup when measuring g(2) (τ) comes from its parameter tunabilty. Due to our setup design it is possible to configure its parameter space (laser repetition period (T L ), light deflection period (T d ) and CCD distance (dC CD)) for the specific conditions of the light under study, and hence build the required photon sample size in a single mirror deflection. Additionally, as the time to space conversion is performed through the horizontal CCD axis (namely, X axis), this configuration makes possible the study of the spatial correlations through the CCD vertical axis (namely, Y axis). Furthermore, if the size of the photon ensemble and the detection efficiency are large enough, the expected integration time to measure g(2) (0) could reach the ms time scale.

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The minimum number of CCD acquisitions (M Min ) to produce a large enough photon ensemble and be able to measure the g(2) (0) value accurately is affected by a list of factors: 1) The maximum number of light pulses (NP ) arriving to the CCD array. If N increases, the statistical photon sample size increases, and hence M Min decreases. This parameter will be controlled by the laser repetition period (T L ). 2) The total amount of photon losses affecting the measurement, including the finite light collection, the detector efficiency and the probabilistic nature of the photodetection process. As the photon losses increases, M Min increases too. 3) The desired error in the g(2) (0). Measurements with smaller errors need larger M Min values. 4) The magnitude of the g(2) (0) value under study, i.e. g(2) (0) = 0 or g(2) (0) = 2 will be faster to measure than g(2) (0) = 0.8 or 1.1, as in the last case it is needed bigger statistical ensembles to provide the required statistical sigma distance from g(2) (0) = 1. 5) Finally, M Min will be limited by the maximum CCD frame rate and light deflection frequency. In order to provide an example of the setup tunability, here we have analysed the g(2) (0) measurement process with our current setup limitations. The two principal setup parameters that affects NP and the final integration time are the highest CCD frame rate and mirror frequency. Our maximum hexagonal mirror frequency is ∼ 2 KHz. Here we have selected as an example of single photon camera the commercial available Andor iXon3 Ultra 888 (1024 x 1024 pixels) CCD. The hexagonal mirror operated at its maximal deflection frequency would produce a single light deflection onto the CCD capture when the camera is operating with the chip in 1024 x 1 configuration (1 x 1 binning) in standard mode operation (0.8 ms per frame). Here, we used as maximum number of allowed light pulses (NP ) impinging on the CCD the number of horizontal pixels divided by 3, i.e ∼ 340 pulses. With this 3 pixel separation between pulses, each photon impinging on the CCD will not overlap between each other. To generate the synchronisation of this maximal NP , we need to tune the laser period (T L ) and the CCD separation (dCCD ) accordingly. With our example setup parameters this condition is satisfied for a laser repetition in the range of MHz and dCCD in centimeters (see bottom panel in Figure 4.g). However, the maximal CCD separation is limited to the distance where the CCD spot size (dS ) is equal to 3 pixels, and thus it becomes the same size than

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Figure 4: Simulation of the second order correlation function (¯g(2) (τ)) experiment for the three photon distributions and the analysis of the total integration time. g(2) (τ) measurement simulation for a) Bose-Einstein b) Poisson & c) Fock state photon distributions with mean photon number = 1, for ideal conditions. d), e), f) shows same photon statistics analysis considering the effect of detector dark noise (20%) and optical losses (50%). g) Example of our setup parameter tunability, simulated with an hexagonal mirror rotating a 2KHz and using a commercial available single photon camera (described in the main text). Upper panel: (blacksquares) light spot size impinging on the CCD (dS ) and (open red circles) inter-pulse separation in the CCD array, both in units of CCD pixels as a function of the distance between the deflection optics and the CCD detector (dCCD ). Bottom panel: laser repetition as a function of dCCD maximising the number of pulses synchronized onto the CCD array (NP ). h) Integrated time analysis for a Fock state with = 1 and a measurement error of 10 % when using the suggested CCD camera (see main text). Upper panel: Minimum number of acquisitions (M) as a function of photon losses. Bottom panel: Expected total integration time as a function of photon losses. Horizontal discontinuous lines points towards 1s total integration time.

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the distance between synchronised pulses. Upper panel in figure 4.g shows dS in pixel units (filled squares) compared to the 3 pixel pulse separation requirement (open red circles) as a function of dCCD . Following this analysis, we estimate the best parameter space to measure g(2) (0) value with the proposed setup (reddish shadow in figure 4.g). Finally, we have calculated the total integration time as a function of photon losses for a Fock state with = 1, and with a measurement error of 10 %. Upper panel in figure 4.h shows the number of CCD single acquisitions (M) as a function of photon losses. Final integration time is calculated multiplying this number to the CCD time per frame (0.8 ms with 1024 x 1 pixel configuration). Bottom panel in figure 4.h shows that total integration time remains under subsecond time interval until losses reach 95 %, where it is needed more than 1000 CCD single acquisitions to produce the targeted statistical sample. In summary, here we suggest that the measurement of light intensity fluctuations with our setup proposal is possible by the use of fast and ultra low noise readout and highly efficient single photon CCD cameras. Our setup parameter tunability and the absence of deadtime allows the direct recording of photon statistical samples with an extended multichannel detector. Both setup features enable the fast measurement of the g(2) (0) value when photon losses and measurement error are reasonably low. Moreover, our setup (Fig. 1.a) up-graded with multicore fibers 34,35 for both L and R arms, and third, fourth, ... rows for cropped mode CCD operation, would allow the analysis of higher order correlation functions. The simulation of the g(2) (τ) function provides an example of the setup capabilities for the research field of quantum optics, but the same setup could be used in more complex scenarios, like logic operation with a photonic Turing machine, Bell tests or ghost imaging.

Conclusions In this work we have presented the principles of operation of a new experimental set-up to measure time resolved optical signals. The basic principle is based on stroboscopic synchronisation conditions using a light deflection mirror. The matching between the laser and deflection frequencies

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transforms a synchronised time resolved optical signal into an spatial distribution to be analysed with a multichannel detector. Following this process we have built a prototype demonstrating 10 ns resolution in good agreement with conventional TRPL analysis. Our extended setup modularity and versatility are very interesting qualities to be included in a general laboratory time resolved device. Once the potential of this technique for conventional time resolved technique is demonstrated we discuss about further applications of the technique in the characterisation of quantum light. We demonstrate numerically that, in those cases where electronic readout noise allows the discrimination of single photon per pixel, such setup can be used as quantifier of the purity of our quantum light and the measurement of the second order correlation function. We discussed about the effects of optical losses and classical noise in this kind of measurements. Even if photon losses are strongly affecting the measurement, the expected integration times could lay below sub-second. The fast readout of the statistical nature of the light fluctuations could be very interesting for the Biophysics sector, 36 or to develop new quantum technology and computation strategies. 37

Acknowledgments Financial support from the the Spanish MINECO (TEC2014-53727-C2-1-R and TEC2017-86102C2-1-R) is gratefully acknowledged. J. C.-F. also thanks MINECO for his research grant funded by means of the program "Juan de la Cierva" (Grant No. IJCI-2015-25438).

Supporting Information Available A description of the fundamental of the method for time resolved photoluminescence and photon distribution analysis is provided.

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References (1) Demtröder, W. In Laser Spectroscopy. Vol. 2: Experimental Techniques.; Demtröder, W., Ed.; Springer-Verlag: Berlin Heidelberg, 2008; Chapter Time-Resolved Laser Spectroscopy. (2) Svanberg, S.; Demtröder, W. In Springer Handbook of Lasers and Optics; Träger, F., Ed.; Springer-Verlag: Berlin Heidelberg, 2012; Chapter Optical and Spectroscopic Techniques. (3) Lakowicz, J. R. Principles of Fluorescence Spectroscopy, 3rd Edition; Chemistry and Materials Science. Springer US.: Baltimore - Maryland - United States, 2006. (4) Prasankumar, R. P.; Taylor, A. J. Optical Techniques for Solid-State Materials Characterization; CRC Press- Taylor and Francis group: Boca Raton, London and New York, 2011. (5) Dagdigian, P. In Laser Spectroscopy for Sensing: Fundamentals, Techniques and Applications; Baudelet, M., Ed.; Elsevier Science & Technology: Woodhead publishing limited. Cambridge, UK, 2014; Chapter Fundamentals of optical spectroscopy. (6) Ahlrichs, A.; Sprenger, B.; Benson, O. In Advanced Photon Counting. Applications, Methods, Instrumentation; Hof, M., Ed.; Springer Series on Fluorescence Methods and Applications: Springer International Publishing Switzerland, 2015; Chapter Photon Counting and Timing in Quantum Optics Experiments. (7) Scheeline, A. Time-resolved measurement using commercial modular boxcar integrators. Journal of Chemical Education 1984, 61, 1110. (8) Matthews, D. R.; Summers, H. D.; Njoh, K.; Errington, R. J.; Smith, P. J.; Barber, P.; AmeerBeg, S.; Vojnovic, B. Technique for measurement of fluorescence lifetime by use of stroboscopic excitation and continuous-wave detection. Appl. Opt. 2006, 45, 2115–2123. (9) Lai, C. C. New tubeless nanosecond streak camera based on optical deflection and direct CCD imaging. Proc.SPIE 1993, 1801, 1801 – 1801 – 16.

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(10) Becker, W. Advanced Time-Correlated Single Photon Counting Applications; Springer. Springer Series in Chemical Physics: —, 2015. (11) Murakami, H. Femtosecond time-resolved fluorescence up-conversion spectrometer corrected for wavelength-dependent conversion efficiency using continuous white light. Review of Scientific Instruments 2006, 77, 113105. (12) Hadfield, R. H. Single-photon detectors for optical quantum information applications. Nat. Photon. 2009, 3, 696–705. (13) Boitier, F.; Godard, A.; Rosencher, E.; Fabre, C. Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors. Nature Physics 2009, 5, 267–270. (14) Steudle, G. A.; Schietinger, S.; Höckel, D.; Dorenbos, S. N.; Zadeh, I. E.; Zwiller, V.; Benson, O. Measuring the quantum nature of light with a single source and a single detector. Phys. Rev. A 2012, 86, 053814. (15) Dixon, A. R.; Dynes, J. F.; Yuan, Z. L. è.; Sharpe, A. W.; Bennett, A. J.; Shields, A. J. Ultrashort dead time of photon-counting InGaAs avalanche photodiodes. Applied Physics Letters 2009, 94, 231113. (16) Wiersig, J.; Gies, C.; Jahnke, F.; Aßmann, M.; Berstermann, T.; Bayer, M.; Kistner, C.; Reitzenstein, S.; Schneider, C.; Hofling, ¨ S.; Forchel, A.; Kruse, C.; Kalden, J.; Hommel, D. Direct observation of correlations between individual photon emission events of a microcavity laser. Nature 2009, 460, 245–249. (17) Aßmann, M.; Veit, F.; Bayer, M.; van der Poel, M.; Hvam, J. M. Higher-Order Photon Bunching in a Semiconductor Microcavity. Science 2009, 325, 297–300. (18) Muñoz, C. S.; del Valle, E.; Tudela, A. G.; M¨uller, K.; Lichtmannecker, S.; Kaniber, M.; Tejedor, C.; Finley, J. J.; Laussy, F. P. Emitters of N-photon bundles. Nature Photonics 2014, 8, 550–555. 20


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(19) Collins, M.; Xiong, C.; Rey, I.; Vo, T.; He, J.; Shahnia, S.; Reardon, C.; Krauss, T.; Steel, M.; Clark, A.; Eggleton, B. Integrated spatial multiplexing of heralded single-photon sources. Nature Communications 2013, 4, 2582. (20) Xiong, C.; Zhang, X.; Liu, Z.; Collins, M. J.; Mahendra, A.; Helt, L. G.; Steel, M. J.; Choi, D. Y.; Chae, C. J.; Leong, P. H. W.; Eggleton, B. J. Active temporal multiplexing of indistinguishable heralded single photons. Nature Communications 10853, 7, 2582. (21) Chen, X.; Ding, C.; Pan, H.; Huang, K.; Laurat, J.; Wu, G.; Wu, E. Temporal and spatial multiplexed infrared single-photon counter based on high-speed avalanche photodiode. Scientific Reports 10853, 7, 44600. (22) Brida, G.; Degiovanni, I.; Schettini, V.; Polyakov, S.; Migdall, A. Improved implementation and modeling of deadtime reduction in an actively multiplexed detection system. Journal of Modern Optics 2009, 56, 405–412. (23) del Valle, E.; González-Tudela, A.; Laussy, F. P.; Tejedor, C.; Hartmann, M. J. Theory of Frequency-Filtered and Time-Resolved N-Photon Correlations. Phys. Rev. Lett. 2012, 109, 183601. (24) Munro, W. J.; Harrison, K. A.; Stephens, A. M.; Devitt, S. J.; Nemoto, K. From quantum multiplexing to high-performance quantum networking. Nature Photonics 2010, 4, 792–796. (25) Muñoz-Matutano, G.; Sales, S.; García-Calzada, R.; Canet-Ferrer, J.; Martínez-Pastor, J. Sistema, método y programa de ordenador para la medida y análisis de señalesluminosas temporales. 2017; https://patents.google.com/patent/ES2573955B2/es, ES Patent ES 2 573 955 B2. (26) Johnson, M. T.; Siriani, D. F.; Tan, M. P.; Choquette, K. D. High-Speed Beam Steering With Phased Vertical Cavity Laser Arrays. IEEE J. Sel. Top. Quantum Electron. 2013, 19, 1701006–1701006.

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(27) Heck, M. Highly integrated optical phased arrays: photonic integrated circuits for optical beam shaping and beam steering. Nanophotonics 2016, 6, 93–107. (28) Hecht, J. LIDAR for self driving cars. Optics & Photonics News 2018, 29, 26–33. (29) See for example Princenton Instruments PI-MAX4, Princenton Instruments ProEM, Oxford Instruments Acton IXON EMCCD. (30) Cominelli, A.; Acconcia, G.; Peronio, P.; Rech, I.; Ghioni, M. Highly efficient readout integrated circuit for dense arrays of SPAD detectors in time-correlated measurements. Proc.SPIE 2017, 10111, 10111 – 10111 – 11. (31) Bronzi, D.; Villa, F.; Tisa, S.; Tosi, A.; Zappa, F.; Durini, D.; Weyers, S.; Brockherde, W. 100 ˚ 32 Single-Photon Detector Array for 2-D Imaging and 3-D Ranging. 000 Frames/s 64 ÃU IEEE Journal of Selected Topics in Quantum Electronics 2014, 20, 354–363. (32) Tiffenberg, J.; Sofo-Haro, M.; Drlica-Wagner, A.; Essig, R.; Guardincerri, Y.; Holland, S.; Volansky, T.; Yu, T.-T. Single-Electron and Single-Photon Sensitivity with a Silicon Skipper CCD. Phys. Rev. Lett. 2017, 119, 131802. (33) Shin, D.; Xu, F.; Venkatraman, D.; Lussana, R.; Villa, F.; Zappa, F.; Goyal, V.; Wong, F.; Shapiro, J. Photon-efficient imaging with a single-photon camera. Nat. Comm. 2016, 7, 12046. (34) Muñoz-Matutano, G.; Barrera, D.; Fernández-Pousa, C. R.; Chulia-Jordan, R.; MartínezPastor, J.; Gasulla, I.; Seravalli, L.; Trevisi, G.; Frigeri, P.; Sales, S. Parallel Recording of Single Quantum Dot Optical Emission Using Multicore Fibers. IEEE Photonics Technology Letters 2016, 28, 1257–1260. (35) The Photonic TIGER: a multicore fiber-fed spectrograph. 2012; pp 8450 – 8450 – 8. (36) Wohland, T.; Rigler, R.; Vogel, H. The Standard Deviation in Fluorescence Correlation Spectroscopy. Biophysical Jour 2001, 80, 2987–2999. 22


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(37) Rivas, D.; Muñoz-Matutano, G.; Canet-Ferrer, J.; García-Calzada, R.; Trevisi, G.; Seravalli, L.; Frigeri, P.; Martínez-Pastor, J. Two-Color Single-Photon Emission from InAs Quantum Dots: Toward Logic Information Management Using Quantum Light. Nano Letters 2012, 14, 456–463.

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Figure 1: Stroboscopic Spatial Multiplexing. a) This technique is based on the periodic deflection (with period Td) of a time modulated optical signal (with period TL) which is converted to spatial modulated light pattern, with the help of a time to space converter. Here the time to space converter is an hexagonal rotating mirror. The periodic light impinging on the mirror is imaged by a CCD placed at a distance dCCD. When stroboscopic spatial tag synchronisation conditions are satisfied (see main text and supp info), CCD acquisition return time resolved analysis of the pulsed light under study. b) Comparison between CCD acquisition of deflected laser with single periodic (gray) and 3-burst (red) triggering modes operated at 0.5 MHz when positioned at dCCD = 0.6 m away from the rotating mirror. c) CCD acquisition of the deflected laser signal when positioned at dCCD = 6 m away from the rotating mirror. The spot size time resolution have been extracted from Gaussian fitting. Black line with greyish shadow shows 400 vertical pixels CCD binning, where red line corresponds to two Gaussian cumulative fitting. In order to record two consecutive pulses in the CCD and calibrate the measurement, here we have used slightly higher laser triggering period (2.5 MHz) and a second CCD with an array of 1024 x 1024 pixel (ImagEM X2-1K EM-CCD camera from Hamamatsu) 189x120mm (96 x 96 DPI)


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Figure 2: Time Resolved Photoluminescence Measurement & Simulation. a) Continuous wave measurements of the sample PL to identify the different emission bands of the spectra that are labelled as: i) GaAs, ii) GaAs acceptor impurities, iii) Phonon replica from ii), iv) Wetting Layer emission and v) InAs Quantum Dot optical emission; The PL transient of the GaAs acceptor impurities measured by conventional TCSPC is shown in the inset. b) PL transients of the laser (shadowed) and B-band PL using the time to space stroboscopic spatial tag technique with the laser triggered at 500 (upper panel) and 250 KHz (lower panel). c) Numerical simulation of the measurements of the synchronised laser (upper panel), the B-band signal with synchronised conditions (middle panel) and the B-band signal with unsynchronised conditions (lower panel). d) Comparison of the simulated and the experimental CCD integrated intensity with full vertical binning 254x190mm (96 x 96 DPI)


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Figure 3: Protocol demonstration of the g(2)(0) measurement for a Fock state with mean photon number = 1. a) CCD capture of the arrival of 100 consecutive photons without any source of losses. b) Photon state counting for a single deflection (gray bar and bottom horizontal axis) and 20 deflections (blue bar and top horizontal axis). c) Same CCD capture when it is included 70 % of random photon losses, and d) equivalent photon state counting. e) & f) equivalent plots when it is included 70 % of random photon losses and 20 % of Poisson noise. At the bottom it is shown same CCD capture than e) but when it is included a 50/50 beam splitter before the deflecting optics, and thus producing Left (g) and Right (h) CCD arrays. 209x251mm (300 x 300 DPI)


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Figure 4: Simulation of the second order correlation function (g(2)(τ)) experiment for the three photon distributions and the analysis of the total integration time. g(2)(τ) measurement simulation for a) BoseEinstein b) Poisson & c) Fock state photon distributions with mean photon number = 1, for ideal conditions. d), e), f) shows same photon statistics analysis considering the effect of detector dark noise (20%) and optical losses (50%). g) Example of our setup parameter tunability, simulated with an hexagonal mirror rotating a 2KHz and using a commercial available single photon camera (described in the main text). Upper panel: (blacksquares) light spot size impinging on the CCD (dS) and (open red circles) inter-pulse separation in the CCD array, both in units of CCD pixels as a function of the distance between the deflection optics and the CCD detector (dCCD). Bottom panel: laser repetition as a function of dCCD maximising the number of pulses synchronized onto the CCD array (NP). h) Integrated time analysis for a Fock state with = 1 and a measurement error of 10 % when using the suggested CCD camera (see main text). Upper panel: Minimum number of acquisitions (M) as a function of photon losses. Bottom panel: Expected total integration time as a function of photon losses. Horizontal discontinuous lines points towards 1s total integration time. 209x116mm (300 x 300 DPI)


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250x160mm (96 x 96 DPI)


Stroboscopic Space Tag for Optical Time Resolved measurements

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