WO2023275738A1 - Method and device for performing spectrally and temporally resolved spectroscopy of single photon emission in a quantum device - Google Patents

Abstract

A light spectrometer including a laser configured to provide for a laser pulse (12), a quantum dot (30), an objective (21) configured to focus the laser pulse (12) onto the quantum dot (30) such that a fluorescent light beam is emitted from the quantum dot (30), a blazed grating (40) arranged in a light path of the fluorescent light beam to generate a plurality of fluorescent light beams of different wavelengths, an imaging lens (26) configured to generate a plurality of images from the fluorescent light beams of different wavelengths, respectively, a single photon avalanche diode (SPAD) array (50) having a plurality of pixels arranged at the imaging plane of the images, a circuit interfaced with the SPAD array, the circuit configured to detect a first photon and a second photon of an entangled photon pair emitted by the fluorescent light beam of the quantum dot in response to the laser pulse (12), wherein each pixel of the SPAD array is arranged to be aligned with a respective one of the plurality of images.

Description

METHOD AND DEVICE FOR PERFORMING SPECTRALLY AND TEMPORALLY RESOLVED SPECTROSCOPY OF SINGLE PHOTON EMISSION IN A QUANTUM DEVICE

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present patent application claims priority to International Patent

Application Number PCT/IB2021/055760 that was filed on June 28, 2021, the entire contents thereof herewith incorporated by reference in its entirety.

FIELD OF THE INVENTION

[0002] The present invention is directed to the field of spectroscopy with quantum light sources, for example single particle spectroscopy of multiply exited states, and a method for using single-photon avalanche diode (SPAD) arrays for quantum spectroscopy. BACKGROUND

[0003] Over the past three decades, numerous types of semiconductor nanocrystals of various compositions, shapes, sizes and structures have been fabricated and studied^1-3 with some even making their way into mass produced consumer products⁴. Since the energy of a charge carrier in a nano-confined solid is quantized, nanocrystals are often referred to as artificial atoms. In a further analogy to atomic physics, photo-exciting such a quantum dot (QD) generates a Hydrogen-like electron-hole state, an exciton, which is typically bound even at room temperature due to the increased Coulomb interaction. However, unlike atoms and molecules, semiconductor nanocrystals include another readily-excited manifold of states, multiexcitons, multiple electron-hole pair states⁵. In the lowest energy multi -excitonic state, the biexciton (BX), a strong exciton-exciton interaction is imposed by the confining potential of the nanoparticle. In the resulting energy ladder of ground, single exciton (IX) and BX states, shown in FIG. 1A, the BX state energy is somewhat offset fromtwice the energy of the IX state, by the BX binding energy (¾)⁵. This binding energy is considered positive (attractive interaction) w hen En_.\ < E_\x , where E_k is the energy difference between state k and state right beneath it in the ladder.

[0004] A cascaded relaxation from the top to the bottom of this ladder can yield a pair of photons; the first around A/;v and the second around Ev . Such an emissionfrom self- assembled Indium Arsenide (InAs) QDs, for example, is one of the leading candidates for efficiently generating on-demand entangled photon pairs as carriers of quantum information⁶. On the other hand, avoiding the excitation of the BX state is key for using the same type of QDs as high-purity single-photon sources⁶. More conventional light-based applications that stand to vastlybenefit from the incorporation of colloidally synthesized QDs, such as light emitting diodes (LEDs)^7,8, lasers^{9 10}, displays⁴ and photo voltaics¹¹, also require characterization and control of the energy and dynamics of the BX state. For instance, non- radiative Auger recombination often dominates the BX relaxation dynamics¹². Therefore, to achieve low threshold lasing from QDs, sophisticated heterostructures have been designed to either increase the BX energy via Coulomb repulsion (avoiding its occupation)¹³, or to reduce the Auger recombination rate¹⁴. Furthermore, the Auger induced low BX quantumyield sets a saturation boundary for the achievable light fluence of nanocrystal-based FEDs¹⁵.

[0005] The above-mentioned interest in the BX- IX ladder inspired substantial spectroscopic efforts to characterize the BX binding energy in multiple material systems suchas 111 -V ^{16 l x}. II-IV¹⁹·²" and lead halide perovskite^{21 22} semiconductor nanocrystals as well as atomically thin films of transition metal dichalcogenides (TMDC)²³. However, conditions under which the BX-1X ladder can be directly probed are restrictive. While at cryogenic temperatures the very stable and narrow IX and BX emission lines of a single self-assembled InAs or colloidal cadmium chalcogenide QDs can be discerned^{17 18}’²⁴, in most other cases this was not achieved due to several fundamental limitations. First, at room temperature, both emission lines are thermally broadened well-beyond typical BX binding energies, as shown in FIG. IB. Spectral features are further broadened in ensemble measurements due to in homogeneity of nanoparticles in the ensemble, as shown in FIG. 1C. Additional inhomogeneous broadening is caused by spectral diffusion, as shown in FIG. ID. In many nanocrystals, this includes not only the effect of spurious electric fields but also of spectral jumps due to other states contributing to fluorescence interm ittency^{25 26}. see FIG. ID.

[0006] More indirect methods to probe the BX state rely on power-dependent measurement of photoluminescence (PL), either in a time-resolved or quasi-continuous-wave manner^20,22,23’²⁷ or of transient absorption²¹’²⁸. While careful modeling and analysis of these measurements provided important spectroscopic information, it has often led to large variance in BX binding energies measuredin different studies. For example, while some works found very high BX binding energies in CsPbX, (X = Cl, Br, 1) nanocrystals²¹, recently a substantially more stringent bound on its magnitude has been reported²²’²⁹. Such discrepancies are mainly due to the difficulty in modeling the different mechanisms that affect PL and ab-sorption at high excitation powers, such as charging, oxidation, blinking and photo-induced damage²².

[0007] While isolating the BX state in the spectral domain alone is a convoluted task, isolating the BX state in the time domainis conceptually simple. A detection of a photon pair emitted from a single nanocrystal of the QD following a short excitation pulse by a laser pinpoints a relaxation cascade^{17 18}: First from the BX to the IX state and then from the IX to the ground state, see FIG. 1A. Separating the two energies facilitates a direct measurement of EBX and E\x for a single nanoparticle. However, currently available instrumentation does not enable practical implementation of this simple scheme to measure spectro-temporal photon correlations. Namely, a standard spectrometer cannot provide the required temporal resolution since it relies on a charge-coupled device (CCD) or a complementary metal-oxide- semiconductor (CMOS) camera with a maximal frame rate of - 10³ fps. [0008] Accordingly, in light of these deficiencies of the state of the art in detection of different multi -exciton states, more advanced solutions are desired.

SUMMARY

[0009] According to one aspect of the present invention, a light spectrometer is provided, preferable configured to detect correlated photons emitted from a quantum emitter. Preferably, the light spectrometer includes a laser configured to provide for a laser pulse, a quantum emitter excited by the laser pulse, an objective configured to focus the laser pulse onto the quantum emitter such that a fluorescence is emitted from the quantum emitter, a blazed grating arranged in a light path of the fluorescent light beam to generate a plurality of fluorescent light beams of different wavelengths, an imaging lens configured to generate a plurality of images from the fluorescent light beams of different wavelengths, respectively, a single photon avalanche diode (SPAD) array having a plurality of pixels arranged at the imaging plane of the images, and a circuit interfaced with the SPAD array, the circuit configured to detect a first photon and a second photon of a correlated photon pair emitted by the fluorescent light beam of the quantum emitter in response to the laser pulse, wherein each pixel of the SPAD array is arranged to be aligned with a respective one of the plurality of images.

[0010] According to another aspect of the present invention, corresponding a method and device is provided, to perform a detection of cascaded emission of photons from a quantum emitter under study. For example, according to another aspect, an analysis method for a spectroscopic analysis of groups of photons is provided, preferably including the step of post-selecting groups of emitted photons for a spectroscopic analysis based on their relative arrival times and relative spectral positions. Moreover, the groups of emitted photons can comprise pairs of photons or triplets of photons emitted following a single excitation pulse. [0011] According to some aspects of the present invention, of performing time-based detections of light emitted from multiexciton states, for example the biexciton state of a semiconductor nanocrystal, which leads to correlated photon pairs being emitted, classical camera technology with CCD and CMOS is replaced by a monolithic single-photon avalanche diode (SPAD) array, a technology that presented an immense performance boost over the past decade^30,31. In such a novel spectrometer, for example a system 100 or device, hereinafter referred to as the spectra SPAD, the spectral information of single photons can be measured and correlated with sub-nanosecond temporal resolution.

[0012] According to some aspects of the present invention, the herein presented spectroSPAD system can be configured to measure spectral correlations in photon cascades from the BX state of single CdSe/CdS/ZnS core/shell/shell quantum dots QD with meV precision. Thanks to the temporal resolution and high sensitivity of the spectroSPAD, the measurements overcomes aforementioned obstacles, for example thermal broadening, spectral diffusion, blinking and low BX yield, and in particularit separates the signal from the misleadingly similar “trion” (‘grey’) charged state. While for the particular sample under study the average value of the binding energy is ~ 6 meV, it could be shown that its value in individual QDs correlates with the IX band edge transition energy. Furthermore, the temporal fluctuations of the BX binding energy is followed for a single nanocrystal and find that those correlate with the spectral fluctuations (“spectral diffusion”) of the IX transition.

[0013] The above and other objects, features and advantages of the present invention and the manner of realizing them will become more apparent, and the invention itself will best be understood from a study of the following description with reference to the attached drawings showing some preferred embodiments of the invention.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS [0014] The accompanying drawings, which are incorporated herein and constitute part of this specification, illustrate the presently preferred embodiments of the invention, and together with the general description given above and the detailed description given below, serve to explain features of the invention.

[0015] FIG. 1A to ID show representations to visualize obstacles in measuring the

1X-BX energy ladder, with FIG. 1A showing the energy diagram of the ground, single exciton (IX) and biexciton (BX) states in a nanoparti- cle. The energy difference between the BX and IX states (EBX) is smaller than the difference between the IX and ground states (E1X ) by the biexciton binding energy (eb). FIG. IB showing a schematic of the thermal broadening of spectral lines (intensity normalized for clarity). At room temperature the IX- ground (blue) and BX-1X (red) transitions emission lines are broadened to approximately KBT = 26 mev > eb. As a result the two emission spectra substantially overlap. FIG. 1C showing the schematic dependence of the IX energy on nanoparticle size. An ensemble mea surement (with a ± 5% size variance) at room temperature roughly includes a mixture of the depicted spectra, and FIG. ID showing a scheme of spectral drift in the emission lines of a single nanocrystal throughout the measurement time. Apart from the stochastic random walk of the spectral lines (diffusion), discrete spectral jumps typically accompany blinking events; [0016] FIGs. 2A and 2B shows a simplified representation of the spectroscopic SPAD device or system 100 where a microscope objective 20 is used to focus a pulsed laser beam 12 of a laser 10 on a single QD 30 and collect the emitted fluorescence beam 14. At the microscope output, light is passed througha spectrometer setup with a linear SPAD array detector 50. Inset (i) is an optical image of part of the SPAD detector array 50. Each blue circle represents a single pixel. Scale bar is 30 uni. Insets (ii) and (iii) show two possible analyses of a single nanocrystal spectroSPAD measurement by circuit 60. In (ii), detections are binned according to detection time in the millisecond scale (horizontal) and photon energy (vertical) whereas in (iii) the horizontal axis represents the delay time of detection from the excitation laser pulse in nanosecond scale . Color-scale corresponds to the number of countsin each temporal-energy bin. The optical elements include, an objective 20 with objective lens 21 and tube lens 22, collimating lens 24 and one or more imaging lenses 26, and a blazed grating (BG) 40;

[0017] FIGs. 3 A to 3D show different representations of the spectral dynamics of a single quantum dot, with FIG. 3A showing a fluorescence intensity collected over all detectors vs. time in a 4-second period (1 ms time-bins), FIG. 3B showing a histogram of intensity values over a five (5) minute measurement. Intensity states are marked by colored shading: ‘off, ‘grey’, ‘mixed’ and ‘on’, FIG. 3C showing spectrum by intensity state, showing the ‘grey’ state’s red-shift with respect to the ‘on’ state, and FIG. 3D showing the On’ state spectral peak evolution overtime. Each point is the mean photonenergy for a 1 ms time-bin of the ‘on’ state ({E)\_ms), colored according to the local density of data-points for clarity. The red line, (E)w_s, presents a moving Gaussian weighted average (s = 10 s);

[0018] FIGs. 4A to 4C show different aspects of the heralded spectroscopy, with FIG.

4A showing a 2D histogram of photon pairs following the same excitation pulse, according to the energy of the first (EBX ) and second (Ev ) photons (vertical and horizontal axes respectively), over a five (5) minute measurement. Dashed green line serves as a guide to the eye, marking same energy for both photons (undetectable by the system), FIG. 4B show spectrum of the BX (red line), IX (blue line), and all “on” state detections (grey area, normalized). Binding energy, estimated as the difference between BX and IX spectral peaks, is ¾ = 9.3 1.6 meV, and FIG. 4C shows binding energy as a function of IX spectral peak for thirty (30) QDs 30. Error bars are 90% confidence intervals;

[0019] FIG. 5 A and 5D show representations of the BX binding energy fluctuations are correlated with IX spectral diffusion, with FIG. 5 A showing the estimated binding energy (_<¾) as a function of the momentary IX spectral shift ( \//i v ) for a single QD 30. Each point represents one post-selected BX event, colored according to the local density of data-points for clarity. As a guide to the eye, red crosses and line mark median binding energy for each 2 meV window of AEi and a linear fit to these medians (slope +0.59), respectively, and FIG. 5B shows a histogram of the ;-;i, medianslope (red line in FIG. 5 A) for 30 QDs;

[0020] FIG. 6 shows a graph that illustrates the fluorescence decay by intensity state. Histogram of detection delays from the excitation pulse for the intensity states seen in FIG. 2A. Note the different lifetime scales of the “on” and the “grey” state;

[0021] FIG. 7 shows a two-dimensional spectrum-lifetime data and fit, with the top curve showing a 2D histogram of photon detections according to their energy (pixel) and arrival time with respect to the excitation laser pulse 12 for the same measurement analyzed in FIGs. 2A-5D. In this figure, we include only detections during the “on” intensity state. The middle graph shows a fit of the spectrum-lifetime data. Data in all energies (rows) is fit with the same two exponential terms, allowing the amplitudes to be different for every energy. The bottom curve shows residuals between the experimental data and the fit. The missing band of time delays in all data sets were deducted from the fit in order to mitigate the effect of the irregular IRF;

[0022] FIG. 8 show the spectra of different lifetime components. Following the fit procedure described herein, a spectrum for each lifetime component separately is obtained. The blue and green dots show the long and short lifetime spectral contributions to the “on” intensity state data, respectively. The purple dots show the spectrum of the charged state obtained through the fit of the ‘grey’ intensity state spectrum-lifetime data. The matching color lines present Cauchy-Forentz fits for each spectrum; [0023] FIG. 9 show the spectral peak fit. Cauchy-Lorentz fit for the two spectra seen in FIG. 4B. Red (blue) dots and solid (dashed) line are the BX (IX) measured spectrum and fit to a Cauchy-Lorentz distribution, respectively. The BX spectrum is vertically shifted for clarity. The fitted spectral peaks are 1.994 eY for the BX, and 2.004 eY for the IX;

[0024] FIG. 10 shows the quantum dot 40 excitation saturation, with the upper graph showing the saturation measurement. A single QD illuminated at increasing intensities from 28 W/cm2 to 280 W/cm2 and then back down ( 10 s, 25 W/cm2 steps). Each point represents the detected intensity at a 5 ms time-bin, colored according to the local density of data-points for clarity. The lower graph shows the peak occurring “on” state intensity for each illumination power with the circles and a fit to a saturation curve with the solid line. The excitation power used is marked by a dashed line;

[0025] FIGs. 11A and 1 IB show the aspects of linear SPAD array 50 and electrical circuit for pixels 52, with FIG. 11A showing the electrical circuit of a SPAD array pixel 52, and FIG. 1 IB showing an optical image of the detector array 50, mounted with microlenses. Each blue square represents a single pixel 52. Scale bar is 100 pm; and

[0026] FIG. 12 shows a temporal response function of a typical pixel. A pixel of the array is illuminated directly with the synchronized excitation laser (laser pulses are <160 ps FWHM), and recorded through the TDC.

[0027] Herein, identical reference numerals are used, where possible, to designate identical elements that are common to the figures. Also, the images are simplified for illustration purposes and may not be depicted to scale.

DETAILLED DESCRIPTION OF THE INVENTION [0028] According to one aspect of the present invention, a spectroscopy system or device 100 is provided, herein referred to as the spectroSPAD, as exemplarily showed in FIGs. 2A and 2B, using a SPAD array 50 for photon detection. In recent years, considerable effort was invested in the design of time-resolved light spectrometers with high sensitivity^{32 36}. As a replacement for the standard CCD camera, different research groups adopted photo multiplier tube (PMT) arrays³³, superconducting nanowire single photon detectors (SNSPDs)^{35 37} or SPADarrays^{32 34 3339}. While these implementations harbor great potential for applications such as Raman spectroscopy and on-chip quantum communications, none was able to provide the combination of high overall detection efficiency, low dark counts, and parallel time and spectrum detection at the single-photon level. The herein presented spectroSPAD spectrometer system 100 and the method of operating the same, see FIGs. 2A and 2B, achieves precisely that by employing a high-performance linear SPAD array 50 as a detector. While a more detailed description of the spectroSPAD system 100 is given below, a brief description thereof is herewith provided.

[0029] A microscope serving as an objective 20 with a high numerical aperture objective can be used to focus pulsed laser illumination 12 from a laser source 10 on a single quantum dot (QD), and to collect epi-detected fluorescence. This signal is spectrally fdtered from the excitation laser with a dichroic mirror and a dielectric filter (not shown), and imaged by a second lens. This image serves as the input for a spectrometer setup - a 4f system with a blazed grating 40 at the Fourier plane. At the output image plane IP of the spectrometer system 100, a monolithic linear SPAD array 50 is placed, such that each pixel 52.1, 52.2,

52.3 is aligned with the image 18.1, 18.2, 18.3 ofa different wavelength range. In the variant shown, only three pixels are labelled for illustration purposes, with exemplary fluorescent images 18.1, 18.2, and 18.3 impinging thereon. The photon detection efficiency (PDE) of the SPAD array 50 can be at least 11% or more at 530 nm and the median darkcount rate (DCR) is ~ 33 counts per second per pixel. The signal of 40 out of the 512 pixels available in SPAD array 50 were analyzed, thereby spanning approximately 80 nm around a center wavelength of 620 nm, resulting in a spectral resolution of ~2 nm (6-7 meV). Single-photon detections are time-tagged by an array of field-programmable gate array (FPGA) based time-to-digital converters (TDCs) synchronized with the excitation laser. Finally, time and wavelength tagged datais analyzed with a dedicated MATLAB™ script.

[0030] Inserts (ii) and (iii) of FIG. 2A show possible and exemplary visualizations of fluorescence data collected by the system 100 from a quantum dot (QD), in this variant a single CdSe/CdS/ZnS core/shell/shell QD, as two-dimensional detection histograms. The spectrum over time is seen in (ii), where the time of detection spans the horizontal axis (10 ms time-bins) and energy the vertical axis (6 meV to 7 meV energy-bins). The effects of thermal broadening, spectral diffusion and blinking, discussed above, can be clearly observed through the width of the spectral peak at each time-bin (35 meV to 50 meV FWHM), the temporal jitter of the spectral peak position and the variation of emitted intensity, respectively. To achieve spectral dependent fluorescence decay curves, shown in (iii), the same dataset is analyzed by binning the detections according to their temporal delay from the preceding excitation pulse. Note that a full horizontal binning (FHB) of either histogram is equivalent to a standard spectrometer measurement, and a full vertical binning is equivalent to a full spectral measurement by a single SPAD.

[0031] FIG. 3D shows the spectral evolution of the neutral IX emission (‘on’ state) over time. Each dot rep- resents the mean photon energy over a 1 ms time-bin( Ev \ms), colored according to the local density of data-points for clarity. The red line represents a Gaussian weighted (s = 10 s) moving average of these values ( Eix \ 0_,y). This smoothed trend shows a gradual wavelength change, predominantly towards shorter wavelengths, possibly due to oxidation⁴². The fast spectral diffusion dynamics are evident in the of (Eve ) \ms around this moving average, AEix, ( Eix ) \_ms - ( Ev ) lOs· These faster dynamics are typically attributed to rapid fluctuations in the local electro-static potential, leading to a shift in emission energy according to the quantum confined Stark effect⁴³.

[0032] An exemplary and non-limiting system 100 was built with a commercial inverted microscope (Eclipse Ti-U, Nikon). A pulsed diode laser (470 nm, 5 MHz, LDH-P- C-470B, PicoQuant) as laser 10 was focused through an oil immersion objective 20 (xlOO,

1.3 NA, Nikon) on a single QD 30. Illumination power density at the sample plane of the QD 30 is 140 W/cm2 leading to 66% probability to excite at least one (1) exciton per laser pulse 12, see below. The same objective 20 is used to collect the emitted fluorescence with fluorescence beam 14, while back-scattered laser light is filtered by a dichroic mirror 28 (505 LP, Chroma) and along-pass dielectric filter (488 LP, Semrock). At the output of the microscope objective 20, the spectrometer system 100 includes a collimating lens 24, a blazed grating 40 (235 g/mm, 5.06° blaze, 53-*-790R, Richardson) and an imaging lens 26, resulting in 3.9 ^c 10-5 reciprocal linear dispersion and ~6 A° spectral resolution (FWHM). At the spectrometer output image plane IP, an exemplary 512 pixel linear SPAD array 50 was employed, being an upgraded version of the sensor described in reference 52, see below, is placed such that the active pixel pitch is 2 nm in wavelength (every second pixel is active).

As a non-limiting example, circuit 60 for reading out the SPAD array 50 includes an FPGA with an implemented time-to digital converter (TDC) array, a timing circuit, and is synchronized with the laser 10 via synchronization signal of signal path 75, is configured to assign timestamps and pixel addresses to single detections in forty (40) pixels 52 of the SPAD array 50. The trace of detections was analyzed by a dedicated MATFAB™ script, implementing temporal and intensity corrections, see below and the analysis schemes. [0033] With respect to the QD 30, colloidal CdSe/CdS/ZnS core/shell/shell QDs were synthesized and used. Samples were prepared by spin coating a glass coverslip with a solution of QDs dispersed in a 3wt% solution of poly(methylmetacrylate) (PMMA) in toluene.

[0034] The above results discussed with respect to FIG. 3D emphasize the difficulty in isolating the BX state emission. Namely, its rather weak contribution is overshadowed by spectral broadening, and especially by the “grey” state emission which overlaps it in both spectral and temporal domains. As a result, even acomprehensive analysis of the 2D lifetime- spectrum data, was unable to resolve the BX state spectrum. With the herein presented method and system 100, it has been possible to overcome these difficulties in detecting the two different emissions, more specifically to isolate the BX state emission from the neutral IX emission.

[0035] According to some aspects of the method to perform spectroscopy, to directly probe the BX emission, pairs of photon detections following the same excitation pulse from laser 10 are post-selected, to perform heralded spectroscopy. Such paired events are the result of excitation to the BX state, and two subsequent radiative relaxations. The first from the BX to the IX state, and the second from the IX to the ground state, see FIG. 1A. We note that, due to the low quantum yield of the BX, this is not the most probable route for relaxation from the BX state. Yet, its occurrence (10%)⁴⁴ provides sufficient signal for the herein presented analysis. Applying this post-selection to the single QD acquisition shown in FIG. 3, yields 1.4 10³pairs over 1.5 10⁹ excitation pulses. The two-dimensional spectrum of photon pairs, showing the distribution of the energy of the first emitted photon as a function of that of the second, is shown in FIG. 4A. The distribution is clearly centered below the diagonal, indicating BX binding. Note that events where both photons of the cascade impingeon the same pixel are not detected by the system due to pixel dead time (about 100 ns). FIG. 4B highlights the first insight that can be derived by such an approach - the BXspectrum (red line, FHB of panel a) is red-shifted with respect to the IX spectrum (blue line, FVB of panel a). The agreement of the IX spectrum with the overall spectrum of the ‘on’ state (grey area), corroborates this distinction. The BX binding energy for this particular QD, estimatedas the difference between the IX and BX spectra peaks (extracted by a fit to a Cauchy-Lorenz distribution, see Supplementary), is ;-;i, = 9.3 ± 1.6 meV (90% confidence interval).

[0036] We note that the identification of the IX and BX spectral peaks is done here without ambiguity. This is done by identifying all occurrences of pairs of photons emitted following a single excitation pulse and spectrally analyzing only the pairs for which the time difference between the arrival of the first photon and of the second photon exceeds the time resolution of the SPAD array timing circuit, for example implemented in readout circuit 60. While the state of the art required a power dependence study (even when the peaks are well separated) to correctly assignthe IX and BX states^16,20, the herein presented method for performing heralded spectroscopy obviates this requirement. More importantly, the herein presented method allows to super-resolve the few-meV separated IX and BX spectral peaks despite their 50 meV FWHM, and clearly distinguishes between the overlapping BX and “grey” state emission.

[0037] With the single-nanocrystal of the QD 30 used in the herein presented system

100 and method, it is not limited to measuring the averaged properties at the ensemble level, but can also observe their distribution within the ensemble. FIG. 4C shows that the BX binding energy increases with the IX spectral peak position for thirty (30) QDs taken from the same sample. This can be explained as a result of variation in the physical size of the synthesized QDs. For the QDs investigated, a higher energy IX spectral peak is likely associatedwith a thinner CdS shell. A thinner shell also corresponds to further confinement of the electrons in the core and an increased Coulomb interaction between charge carriers, leading to a higher BX binding energy. This trend is in agreement with ensemble measurements for CdSe/CdS seeded nanorods²⁷.

[0038] With respect to the correlation between ¾ - Eix, further insight into the BX state can be obtained from comparing the temporal fluctuations of the IX and BX spectral peaks. As demonstrated in FIG. 4A to 4C, time-resolved heralded spectroscopy enables isolating the BX energy shift despite the spectral fluctuations. Alternatively, one can refer to the IX spectral positionas a sensor for the micro-environment of the nanocrystal, specifically to the fluctuating local electric field, and observe how the BX binding energy reacts to such fluctuations. FIG. 5A shows the bivariate distribution of ¾ and AEix , estimated for each post-selected BX photon event of a single QD ‘on’ state measurement. While the distribution of both variables is widened by the various spectral broadening mechanisms discussed above, one can observe a clear correlation between them. As a guide to the eye, red crosses and a red line mark the median binding energy for each 2 meV AEv window and a linear fit of these medians, respectively, emphasizing the positive cross correlation of Sb and AEix . The slope of this line is 0.59; i.e. for each 2 meV red-shift (blue- shift) of the IX emission spectral peak, the binding energy is lower (higher) by roughly 1.2 meV. FIG. 5B, a histogram of the ¾ median slope values for thirty (30) QDs, shows that this positive correlation is evident for all QDs measured. Thisresult suggests that the BX binding energy, much like IX emission, is strongly affected by the local electrostatic potential the QD is subjected to. A higher local field associated with a red-shift of the IX emission, is correlated withlower BX binding energy, or a weaker biexciton attraction, due to the spatial separation of holes and electrons induced by the external field. Notably, at high enough fields, the sign of the BX binding energy flips, indicating repulsive interaction of the excitons. This observation agrees with past results on the effect of charge separation via band engineering in type-II QD heterostructures on the BX binding energy⁴⁵. Furthermore, it strengthens the assertion that spectral diffusion indeed originates from fluctuations in the local electrostatic potential.

[0039] The mapping of photon energies to temporally correlated pixels of the SPAD array 50, makes the herein presented spectroSPAD system 100, device and method a promising tool for quantum optics and quantum communication. While transferring classical information is often performed with the time and frequency degrees of freedom, quantum information often relies on the polarization to carry information⁴⁶. This is despite the inherent robustness of energy and arrival time to imperfect transfer channels such as optical fibers⁴⁷. Partially, this is due to the limited capabilities in measuring multiple-photon energy correlations (e.g. energy entanglement) which typically require time consuming and cumbersome scanning setups⁴⁸. The spectroSPAD system 100 and corresponding method and device can be seen as a highly multiplexed version of such an experiment, timing pho ton detections at all wavelengths for multiple photons, andean act as a receiver of quantum information carried in theenergy and time degrees of freedom. Furthermore, ongoing advances in extending SPAD array detection efficiencies to the near infrared spectrum⁴⁹, may evolve this system into a powerful quantum communication tool. Specifically, it will significantly simplify spectrally multiplexed quantum communication protocols which currently rely on wavelength multiplexed sources and single wavelength receivers^50,51.

[0040] We note that the detection efficiency of SPAD arrays is complemented by the very low noise level of SPAD arrays 50 as used herein. Unlike CCD and CMOS technology, these arrays overcome readout noise altogether and feature median dark count rates of tens of counts per second per pixel⁵². A second factor to consider, common in detector arrays and specific to photon correlation analysis, is inter-pixel crosstalk. Due to the close-packing of pixels, adetection in one pixel has a small probability to lead to a false detection in a neighboring pixel, and hence a falsephoton pair. Any bias due to this effect is mitigated here by a combination of the chip design, bringing the crosstalk probability down to 10 ⁵. and of a statistical correction as described in reference [43]

[0041] In light of the results achieved with the herein presented spectroSPAD system

100 and corresponding methods and devices, it can be seen that heralded spectroscopy of BX emission cascades, leads to the direct and unambiguous identification of emission from multiply-excited states of single QDs at room temperature. Apart from avoiding the culprits of indirect and ensemble approaches, by separating the BX and IX emission in the time domain, it is possible to greatly extend the range of accessible material systems, and allow new, previously washed out insights into exciton-exciton interaction within the single nanoparticles of the QD, thereby presenting substantial advantaged over the state of the art.

A positive correlation between exciton-exciton attraction and tighter charge-carrier confinement of the single QDs have been shown. It was also possible to show a fluctuation of this attraction strength, correlated with the fast fluctuations of the local electrostatic potential, and significant enough to lead to exciton-exciton repulsion. These capabilities and insights present a new probe into QD physics, and can leadto better design of QD-based technologies where multi-excitonic states typically play a major role. This novel technique is enabled by constructing the spectroSPAD system 100 using a SPAD array 50 based correlative spectrometer extending the temporal resolution limit of standard spectrometers by several orders of magnitude. Not only is this a promising tool for probing the physics of charge-carrier dynamics invarious material systems, the energetically and temporally resolved detection can also address current challenges in quantum optics and quantum communications.

[0042] Next, apart from heralded spectroscopy, the single-particle, spectro-temporal information provided by the spectroSPAD system 100 and a corresponding method can reveal connections between the spectral and the dynamical characteristics of nanocrystal fluorescence of the QD 30. One example of such an observation is presented in the 2D histogram shown in the top panel of FIG. 7, where photon detections (here only from the ’on’ blinking state), are binned according to both their arrival time (with respect to excitation pulse) and their energy. In such a spectrum-lifetime dataset, one can differentiate the spectra of different lifetime components. While this type of data is commonly measured for an ensemble of particles (with a scanning monochromator), this is the first demonstration of such a measurement for a single QD 30.

[0043] Next, some details the heralded spectroscopy parameters and the temporal and intensity corrections are discussed. Photon pairs were time gated to support correct identification of BX and IX emission. BX emission was gated to the first 5 ns following the excitation pulse from laser 10. The short lifetime of the BX state leads to a negligible loss of signal accompanied with a significant reduction of noise. IX detections were gated to 5 ns to 60 ns delay from the BX detection. The upper bound serves to reduce noise while accommodating the longer lifetime of the IX state emission, see discussion below. The lower limit serves to filter out possible misidentification of BX and IX due to the instrument response function. The upper limits for BX and IX also assert that only photon pairs following the same laser pulse 12 are taken into account. Emission spectral peaks were then estimated by a fit to a Cauchy-Lorentz distribution. An example of this fit is seen in FIG. 9.

[0044] The time-to-digital converter (TDC) architecture assigns timestamps with a mean interval of 18 ps, and if the detector jitter is larger, scc^' bclow. However, as detailed elsewhere¹, the timestamps are not uniformly spaced but rather each span a 0 ps to 92 ps range of arrival times, with most time spans are within 18 ± 12 ps. This non -uniformity was characterized by illuminating the SPAD array 50 with temporally featureless halogen light, and recording the occurrence of each timestamp as a measure of the relative time duration it spans. The correction was then implemented as a time correction statistically by assigning to each recorded raw-timestamp a corrected-timestamp chosen at random from the respective time span. In addition, timestamps recorded for each detector pixel are differently delayed from the TDC trigger. This was characterized by illuminating the detector directly with the < 160 ps FWHM excitation laser pulse 12 from laser 10, and correcting the per-pixel timestamp delay to temporally align the recorded pulse peaks in all detectors.

[0045] Also, with respect to intensity corrections, two (2) sources of false detection and detection pairs can be considered. The first, dark count rate (DCR), was recorded and subtracted from the intensity trace (per pixel). The expected number of DCR-real detection pairs was estimated and subtracted from the photon pair signal, while the DCR-DCR pair occurrence is negligible. The second source of false photon pairs, detector crosstalk, was characterized and corrected statistically, by the protocol detailed in reference [43]

[0046] In FIG. 5A, each data-point represents a single photon pair event. Therefore, only in this figure, intensity corrections could not be implemented with this statistical approach. The number of DCR and crosstalk induced pairs in FIG. 5 A can be estimated to be 13% of the overall data-points. Hence, the use of a median estimator (the “x” in FIG 5A) mitigates the effect of noise induced outliers. Furthermore, to avoid biases where noise might be more significant than signal, the median values shown and considered for the fit were only for \/ΰ _\ energy-bins including at least 1% of the total signal. All corrections were verified to be stable over time.

[0047] With respect to the SPAD array 50 used for system 100 and corresponding method, since the creation of the first single-photon avalanche diode (SPAD) in complementary metal -oxide semiconductor (CMOS) in 2003, research in the field of SPADs and SPAD image sensors has led to the creation of the first integrated array in 2004, followed by a wide range of SPAD based image sensors with advanced functionality and continuously increasing speed. [0048] SPAD array 50 can include in an exemplary embodiment an array of 512

SPAD pixels 52. Each pixel 52 comprises a SPAD quenched and recharged passively through a poly resistor. The SPAD is interfaced to the exterior of the chip through a circuit exemplarily shown in FIG. 11A, including capacitive decoupling, a clamp to Vaa, and a low-threshold buffer. The purpose of this circuitry is to ensure low threshold of detection of the avalanche, thus optimizing jitter while controlling noise.

[0049] Quenching resistor Rq is designed to present a sufficiently high impedance to the anode of the SPAD, while minimizing the avalanche current, so as to control the overall power consumption of the chip. Yop is set to VBD + VEX , where VBD and VEX are the breakdown and excess bias voltages, respectively.

[0050] SPAD array 50 can be mounted directly on a board with the SPAD outputs wire-bonded and connected to a field programmable gate array (FPGA), which hosts the TDCs that enable the time characterization of the response. The TDC array is an improved version of the earlier implementation detailed in reference [52] Pixels 52 exhibit an average jitter of 105 ps (FWHM) and a median DCR of 33 cps, their native fill factor (without microlenses) and pitch are 25.1% and 26.2pm, respectively. FIG. 1 IB shows a top view of SPAD array 50, including microlenses. Microlenses were deposited on the chip to enhance effective fill factor and thus overall photon detection efficiency (PDE).

[0051] With respect to the preparation and synthesis of the quantum dot, a cadmium oxide (CdO), n-tetradecylphosphonic acid (TDPA), and 1-octadecene (ODE) mixture was heated to 280°C in a three-neck flask under argon environment. Next, a stock solution of trioctylphosphine selenium (TOPSe) was rapidly injected. The temperature was then reduced to 250°C until the particles reached the de- sired diameter. A layer-by-layer growth technique in a one-pot synthesis method⁴ was used for shell growth of cadmium sulphide (CdS) and zinc sulphide (ZnS).

[0052] To briefly summarize, multiply-excited states in semiconductor quantum dots feature intriguing physics and play a crucial role in nanocrystal -based technologies. While photo-luminescence provides a natural probe to investigate these states, room temperature single particle spectroscopy of emission from these states has so far proved elusive due to the temporal and spectral overlap with emission from the singly excited and charged states. With the features of the herein presented method and system 100, it is possible to perform heralded spectroscopy of single quantum dots, by incorporating the rapidly developing technology of single-photon avalanche diode (SPAD) arrays in a spectrometer setup, for example the SPAD array 50 described herein with a readout circuit 60 associated thereto. This allows us to directly observe the biexciton-exciton emission cascade and measure the biexciton binding energy of single quantum dots at room temperature, even though it is well below the scale of thermal broadening and spectral diffusion. Moreover, it is possible that single particle heralded spectroscopy allows identifying correlations of the biexciton binding energy with both charge-carrier confinement and fluctuations of the local electrostatic potential, which are masked in ensemble measurements. The herein described time-resolved spectrometry, as shown with the present patent application, has the potential of greatly extending our understanding of charge carrier dynamics in multielectron systems and of parallelization of quantum optics protocols.

[0053] While the invention has been disclosed with reference to certain preferred embodiments, numerous modifications, alterations, and changes to the described embodiments, and equivalents thereof, are possible without departing from the sphere and scope of the invention. Accordingly, it is intended that the invention not be limited to the described embodiments, and be given the broadest reasonable interpretation in accordance with the language of the appended claims.

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Claims

1. A light spectrometer (100) comprising : a laser (10) configured to provide for a laser pulse (12) or a series of laser pulses; a quantum emitter under study (30); an objective (20) configured to focus the laser pulse (12) onto the quantum emitter (30) such that a fluorescent light beam (14) is emitted from the quantum emitter (30); a blazed grating (40) arranged in a light path of the fluorescent light beam (14) to generate a plurality of fluorescent lightbeams of different wavelengths (16.1, 16.2, 16.3); an imaging lens (26) configured to generate a plurality of images (18.1, 18.2, 18.3) from the fluorescent lightbeams of different wavelengths (16.1, 16.2, 16.3), respectively; a single photon avalanche diode (SPAD) array (50) having a plurality of pixels (52.1, 52.2., 52.3) arranged at the imaging plane of the images (18.1, 18.2, 18.3); and a circuit (60) interfaced with the SPAD array (50), wherein each pixel (52.1, 52.2., 52.3) of the SPAD array (50) is arranged to be aligned with a respective one of the plurality of images (18.1, 18.2, 18.3).

2. The light spectrometer (100) of claim 1, further comprising: a collimating lens (24) arranged in the light path of the fluorescent light beam

(14)

3. The light spectrometer (100) of claim 1, further comprising: a semitransparent mirror (28) arranged to redirect the pulsed laser beam (12) from the laser (10) into a direction of the fluorescent light beam (14).

4. The light spectrometer (100) of claim 1, further comprising: a synchronization link (70) between the circuit (60) and the laser (10), wherein the circuit (60) is configured to determine an arrival time of the first photon and an arrival time of the second photon.

5. The light spectrometer (100) of claim 1, wherein the circuit (60) is configured to detect a first photon and a second photon of a correlated photon pair emitted by the fluorescent light beam (14) of the quantum emitter (30) in response to the laser pulse (12).

6. A method for performing a spectroscopic analysis of groups of photons, comprising the step of: postselecting groups of emitted photons for a spectroscopic analysis based on their relative arrival times and relative spectral positions.

7. The method of claim 6, where the groups of emitted photons comprise pairs of photons or triplets of photons emitted following a single excitation pulse.

8. The method of claim 6, wherein temporal or spectral correlations are used to identify false correlations due to inter-pixel coupling within the SPAD array and/or due to background illumination.