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Which Gets the Best Reviews Photon 45 or the 65

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Abstruse

Single-photon sources accept a variety of applications. One of these is breakthrough radiometry, which is reported on in this paper in the form of an overview, specifically of the electric current state of the art in the application of deterministic single photon sources to the calibration of single photon detectors. To optimize single-photon sources for this purpose, extensive research is currently carried out at the European National Metrology Institutes (NMIs), in collaboration with partners from universities. Single-photon sources of dissimilar types are currently under investigation, including sources based on defect centres in (nano-)diamonds, on molecules and on semiconductor breakthrough dots. Nosotros will nowadays, summarise, and compare the current results obtained at European NMIs for single-photon sources in terms of photon flux, unmarried-photon purity, and spectral power distribution every bit well as the results of single-photon detector calibrations carried out with this blazon of low-cal sources.

Introduction

This paper deals with the use of unmarried-photon sources in the field of breakthrough radiometry, in particular for the calibration of unmarried-photon detectors. A perfect single-photon source is a calorie-free source that emits light every bit single photons, i.eastward., two or more photons are never emitted simultaneously. This distinguishes information technology from coherent light sources (lasers) and thermal light sources such every bit incandescent lite bulbs. Single photons can exist realized past unmarried atoms, ions, molecules, colour centres and quantum dots, i.e., in systems, where per se the organization has to be re-excited before the emission of a 2d photon. Single-photon sources based on this principle are chosen deterministic single photon sources and they could produce so-called "photons on demand" in the limit to perfect emission and drove efficiency. Another possible way to generate unmarried photons is the use of spontaneous parametric down-conversion. In this case, pairs of single photons are produced via a nonlinear procedure; the detection of i photon in ane axle path heralds a single photon in the other beam path. These sources are called "heralded single-photon sources" or "probabilistic single-photon sources". Vast literature can be establish on single-photon sources, an overview is, eastward.k., given in [1, 2]. Thus, in general, a single-photon source is a one-photon number land generator. Therefore, the field of applications for single-photon sources is wide [1]. Among the about prominent are quantum key distribution, breakthrough communication, breakthrough calculating and quantum metrology [iii]. However, so far single-photon sources compete in all these fields with highly developed light amplification by stimulated emission of radiation sources, so that a breakthrough advantage of the and so-chosen "quantum-enhancement" withal has to be proven to be applicable in real globe applications. 1 specific field, in which this advantage has been proven is quantum radiometry [iv]. Quantum radiometry ways, within the context of this newspaper, the use of unmarried-photon sources in radiometric applications. In a wider sense, radiometric applications for single-photon sources are:

Standard photon sources: as there are already the blackbody radiator and the synchrotron radiation source with their calculable photon flux, also single-photon sources have the potential to get a new type of standard photon source [5,six,7]. Consider a device (in this example a perfect single-photon source), which emits under excitation with a pulsed laser operating with a repetition rate f exactly 1 photon per excitation pulse. The optical radiant flux Φ of such a device would be exactly given by Φ =f h c/λ, where f is the repetition rate of the excitation light amplification by stimulated emission of radiation, h is the Planck constant, c is the speed of light and λ the wavelength of the emitted radiations. Since c and h accept no uncertainty, and the frequency and wavelength can exist measured with uncertainties in the 10–17 and 10–12 range, respectively, the optical radiant flux could be determined with an unprecedented accuracy, in particular far below the current country-of-the-fine art achieved using the cryogenic radiometer, which has uncertainties in the 10–5 range [eight]. Yet, this requires a perfect source, i.due east., a source with a quantum efficiency of 100% (i.e., each excitation leads to an emission of a photon), a perfect purity of the unmarried-photon emission, i.e., thou (two)(0) = 0, and a collection efficiency of the emitted radiation of 100%. On the other paw, as volition be described in detail within this paper, single-photon sources are ideal sources for the calibration of unmarried-photon detectors, because the necessary correction for the photon statistics when using a laser source is completely eliminated or at least significantly diminished for imperfect single-photon sources (meet [nine, 10]). This combined "dead fourth dimension and photon statistics effect" of, e.g., a SPAD detector, is described in Sect. 2.1.

Sub-shot noise metrology is another possible application of unmarried-photon sources in quantum radiometry: information technology exploits them to carry out measurements beneath the standard quantum limit. For this, efficient, nearly perfect sources have to be used. In [11], Chu et al. showed in principle the quantum reward, general ideas are given in [12]. Other, relevant applications for single-photon sources are in the field of quantum imaging [13], both for achieving sub-shot noise imaging [14, fifteen] equally well as for super-resolution [16, 17]. Even quantum illumination [18, nineteen], quantum sensing [20, 21] and quantum reading [22, 23] are expected to take reward of efficient single-photon sources.

"Breakthrough Candela": a realization of the base unit candela using quanta, i.east., countable photons, is intriguing. Therefore, in the mise-en-pratique for the candela [7], the possibility to realize the candela exploiting (unmarried) photons is explicitly stated, thus enabling photometric, radiometric, and their derived quantities to exist expressed in terms of photon-numbers and photon number-based quantities.

Detector calibration with single-photon sources

Unmarried-photon detectors

In contrast to single-photon sources, single-photon detectors are already quite mature and widely commercially bachelor, e.g.: the single-photon avalanche diode (SPAD), the transition edge sensor (TES), and the superconducting nanowire unmarried-photon detector (SNSPD). Medicine, biology, astrophysics, emerging fields similar breakthrough cryptography and quantum calculating too as scientific inquiry in experimental quantum eyes and quantum physics are their main fields of awarding, i.e., wherever low photon fluxes need to be measured. Detailed descriptions of different types of detectors, operation modes and metrological aspects can be found in [1, 2, 4, 24]. In this paper, we focus on the application of unmarried-photon sources for the detection efficiency calibration of SPAD detectors.

There are two factors that demand to exist considered for SPAD detectors: First, they are non photon-number resolving and thus produce at most one 'click' in response to a pulse with one or more photons; second, they have a dead-time when they are non agile afterwards a detection. The use of a Poissonian source (i.east. an attenuated laser) yields both multi-photon pulses and, for CW radiation, a variation in photon arrival times. These factors complicate the scale of SPADS with adulterate laser light. This has been studied in detail for Si-SPAD detectors by López et al. [9] and Georgieva et al. [25].Photons arriving individually with a time interval longer than the expressionless fourth dimension (typically between 10 and 100 ns for SI-SPADs) tin exist fully detected by the Si-SPAD, just the same number of photons arriving within one pulse would only allow i detection event, i.e., in that location is a potent correlation between the dead time and the temporal distribution of photons arriving on the Si-SPAD; the photon number distribution of the photon source used in the calibration experiment is therefore important. Hence, the best source for determining the undisturbed, physically relevant detection efficiency would be a unmarried-photon source that delivers photons with a time interval longer than the expressionless fourth dimension and at which the photon flux tin however be measured with conventional Si diodes, which human action every bit reference, i.e., they are traceable to the standard for optical radiant flux, the cryogenic radiometer.

The nitrogen-vacancy centre in diamond every bit single-photon source

The nitrogen vacancy heart (NV-heart) in diamond is i of the virtually investigated single-photon sources, see e.yard. [26,27,28,29,30]. The reason is that the NV-centre is the most naturally occurring colour middle in diamond and its emission is highly efficient also at room temperature. It was also the beginning commercially bachelor single-photon source [31].

The first comprehensive metrological characterisation of a unmarried-photon source with respect to absolute spectral radiations flux was carried out past Rodiek et al. [32]. In that work, a single-photon source based on an NV middle was metrologically characterised with regard to its near relevant properties. Its photon flux, its spectral radiant flux besides as the purity of the single-photon emission were measured in a traceable manner. The standard measurement dubiety for the photon flux was about 4% [33], see also Fig. one. The total radiant flux was betwixt 55 and 75 fW, corresponding to a total photon flux of 190 000 photons per 2nd and 260 000 photons per second, respectively. The purity of the single photon emission is indicated past the g (2)(0) value, which ranges from 0.10 to 0.23 depending on the excitation power. These values are traceable to the corresponding national standards via an unbroken traceability chain. Fifty-fifty though this source is only suitable for applications to a limited extent due to its broad spectral emission distribution, these first results show the prospects for the general application of single-photon sources, e.thousand., for the calibration of the detection efficiency of single-photon detectors likewise as for the apply as a standard photon source in the low photon flux range.

Fig. 1
figure 1

a Traceability chain for the metrological characterization of a single-photon source in terms of its absolute spectral photon flux, adapted from [32]; b Accented spectral photon flux of the single-photon source (bluish curve). The calculation of the presented measurement uncertainty (red strap) is described in [33]. Taken from [33]

Total size prototype

It should exist noted that other impurity centres in diamond, which show a more than suitable spectral power distribution for scale purposes, are currently nether investigation. These are, e.g., the colours centres based on Silicon [34,35,36,37], Germanium [38, 39], Tin [40,41,42,43], Fluorine [44, 45], Helium [46] impurities and Lead vacancy eye [47,48,49,50], see also the overview article from Moreva et al. [51]. In [52], Vaigu et al. successfully used a single-photon source based on a SiV-centre in nanodiamond with an emission bandwidth of Δλ FWHM ≈ 2 nm for the determination of the detection efficiency of a Si-SPAD detector, however, a direct calibration against a reference detector could not be carried out, because of the low photon charge per unit of approx. 60 000 photons per second. Single SnV centres in high-temperature annealed diamond samples show promising properties for calibration purposes, i. e. a high unmarried photon purity g (two)(0) < 0.05 express but by detector night counts and saturation photon rates of upwardly to 150,000 per second [53]. A further increase in photon count rates might be accomplished by combining the SnV centres with nanophotonic structures, e. thousand. optical antennas which were recently demonstrated to enhance the saturation emission rates by a factor of 5–10 [54] yielding up to 500,000 photons per second.

The molecule-based single-photon source for calibration of SPAD detectors

A amend source for the calibration of single-photon detectors is principally a molecule-based single-photon source, which exhibits a narrow-line emission, for two master reasons: spectral corrections are non needed, and the spectral radiant flux is much higher. It should be noted that, for radiometric applications, a linewidth of less than approx. two nm is normally sufficient. Some molecules fulfil these weather, e.grand., terrylene, see e.g. [55], and dibenzoterrylene in anthracene (DBT:Air-conditioning), run across e.g. [56, 57].

With a DBT:Air conditioning source, Lombardi et al. [58] performed for the first fourth dimension a straight calibration of a Si-SPAD detector using a continuously operated single-photon source. This molecule emits narrowband photons when cooled to cryogenic temperatures and show high quantum efficiency, photostability and quantum coherence [56, 59, sixty], fifty-fifty when embedded in small nanocrystals [61]. The source used for the straight calibration of a Si-SPAD detector against a calibrated analogue Silicon reference detector had a photon flux at the location of the detector of upwards to i.32 × tenhalf dozen photons per second, a value for yard (two)(0) (indicating the single-photon purity) < 0.i and a spectral bandwidth of < 0.2 nm. This optical radiant flux tin can yet be reasonably measured with conventional silicon photodiodes, see e.g. [62]. Figure two summarizes in an creative manner the backdrop of the DBT:Air-conditioning unmarried-photon source.

Fig. 2
figure 2

Artistic summary of the properties of the DBT:Ac unmarried-photon source used for the calibration of the Si:SPAD detector. © P. Lombardi

Total size prototype

The calibration process (for details see [58]), is in this example rather simple, i.east., the substitution method is used. The photon flux from the unmarried-photon source was alternatively measured with the SPAD detector and with an analogue reference Si detector, which is traceable to the standard for optical radiant flux, i.eastward., the cryogenic radiometer. Both detectors were equipped with an FC/PC multimode fibre port, then that the output from the fibre coupled single-photon source can be hands measured. The SPAD detection efficiency η SPAD tin can and so be calculated from:

$$ \eta _{{{\rm{SPAD}}}} ={ \frac{{N_{{{\rm{SPAD}}}} }}{{N_{{{\rm{Ref}}}} }} }= {\frac{{N_{{{\rm{SPAD}}}} }}{{\Phi _{{\rm{south}}} E}}} = {\frac{{N_{{{\rm{SPAD}}}} }}{{{{I_{f} } \mathord{\left/ {\vphantom {{I_{f} } {s_{{{\rm{ref}}}} }}} \right. \kern-\nulldelimiterspace} {s_{{{\rm{ref}}}} }}Eastward}}}, $$

where N SPAD is the count charge per unit measured with the SPAD detector, North ref is the photon flux, adamant with the reference detector via the measurement of the photocurrent I f, using the known spectral responsivity s ref and the photon energy E (= 2.53 × ten–nineteen J) for a photon at 785.6 nm). In Fig. three, η SPAD, adamant as described above, for the SPAD detector is depicted for photon rates betwixt 0.144 × 106 and 1.32 × x6 photons/south, corresponding to a power range between 36.5 and 334 fW. It tin be seen from the figure that the photon rate approaches the authorities where the detector dead time affects the detection efficiency measurement η SPAD [9]. In this respect, a considerable improvement for the calibration process would exist an functioning of the single-photon source in pulsed mode while maintaining the high photon flux. The standard dubiety varies in the range of 2–half-dozen%, depending on the photon rate, i.eastward., the lower the photon rate, the college the uncertainty. It was calculated co-ordinate to the Guide to the Expression of Uncertainty in Measurement (Glue) [63]. The highest contribution is the statistical noise of the reference detector, which contributes to more than 90% of the overall uncertainty.

Fig. 3
figure 3

Calibration result for the SPAD detection efficiency (Perkin Elmer, SPCM-AQRH-13-FC) using the molecule-based single-photon source and a low-dissonance reference analog detector. Taken from [58]

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The InGaAs quantum dot based single-photon source for calibration of SPAD detectors

Besides molecules and impurities centres in (nano-)diamond, also semiconductor quantum dots (QD) have been investigated for their use as sources for radiometric applications. QD based single-photon sources are well suited for this purpose, because of the possibility to operate them both continuous moving ridge and triggered, they are robust, durable and photostable. Their emission spectrum has narrow bandwidth, and the wavelength of performance is normally in a range where the calibration of both Si- and InGaAs/InP-SPADs is possible. Furthermore, manufacturing processes, especially with respect to a designed dielectric surround for the QDs, are well advanced and ameliorate constantly. The latter is of highest importance for achieving high extraction efficiencies and thus high photon fluxes. A first significant step towards the use of QD-based single-photon sources in radiometry was demonstrated in [64]. Georgieva et al. characterized an InGaAs QD-based single-photon source metrologically. The single-photon emitter consisted of an InGaAs QD, which was embedded into a monolithic microlens. This structure was positioned on top of a distributed Bragg reflector. With such a structure and using a collecting objective lens with a numerical aperture of 0.vii, an extraction enhancement of upward to 23% is expected, meet [65]. Additionally, an antireflection coating was applied on superlative of the microlens to further reduce collection losses. A detailed clarification of the fabrication process is given in [66]. The maximum photon flux obtained with that source was up to iii.7 × 105 photons per second at a wavelength of (922.4 ± 0.1) nm. The FWHM of the spectral line was adamant to be 42 pm and was limited past the spectrometer's resolution. The single-photon purity evaluated with the second-lodge correlation function at zero delay time, g (2)(τ = 0), was 0.24 ± 0.06. This value was limited mainly by groundwork emission from the sample matrix caused by non-resonant excitation and a long-living disuse component. This source was then practical for the relative calibration of two Si-SPAD detectors against each other. An absolute calibration of the SPAD detectors direct confronting a conventional reference Si-diode was not possible due to the low photon flux. However, the relative standard uncertainty was 0.vii% and the obtained results were consequent with the ones obtained from the standard calibration method using an attenuated laser [9]. Also, an Allan deviation analysis was performed giving an optimal averaging time of 92 s for the photon flux.

In the subsequent work [67], a new structure of the QD sample was applied. The sample construction is grown by metallic–organic chemical vapor deposition. Suitable QDs were selected by cathodoluminescence spectroscopy, whereas electron-axle lithography (EBL) is used to form micro-mesas at these pre-selected positions. These cylindrical shaped mesas with a radius between 600 and 640 nm have a acme of approx. 800 nm. For further information on the in-situ EBL nanotechnology procedure see [68]. Also, the efficiency of the whole setup was significantly improved by using optimized optical components. The maximum photon flux obtained was (2.55 ± 0.02) × x6 photons per 2d inside a multimode fibre at a wavelength of approximately 929.8 nm. The non-resonant excitation occurred in a pulsed regime at a repetition rate of 80 MHz. The value of the second gild correlation function g (ii)(τ = 0) was betwixt 0.14 and 0.24, depending on the excitation ability. With these parameters, this source is applicative for a Si-SPAD detector calibration directly against a calibrated, conventional reference detector, which is traceable to the national standard for optical radiant flux. Figure 4a depicts the results of the calibration. The apparent detection efficiency is shown every bit a part of the incoming photon flux. The lowest measurement dubiousness obtained is approx. 1.2%. The stability of the QD emission over fourth dimension, the traceable calibration of the spectral sensitivity of the low-noise analogue detector and the change in the coupling loss of the fibre connector are the largest contributions to the overall uncertainty. The detection efficiency is, inside the stated uncertainties, independent from the photon flux. The apparent detection efficiency has a weighted hateful value (i.e., taking the uncertainties into account) of (32.63 ± 0.22) %. For the traditional calibration using an attenuated laser, the measured detection efficiency is, on the contrary, strongly dependent on the incoming photon flux, see Fig. 4b. As expected, with increasing photon flux, a decrease of the apparent, measured detection efficiency is clearly observed. The photon statistics of the laser light together with the dead time of the Si-SPAD detector are responsible for this behaviour.

Fig. 4
figure 4

Si-SPAD detector calibration. a Calibration using the spectrally filtered QD emission for a direct comparing with an analog reference detector. The pinkish area represents the expanded doubt (k = 2) of the weighted mean. b Calibration using a strongly attenuated laser source, where the incoming photon flux has been indirectly determined from a scale of two variable attenuators. The error bars in (a) and (b) indicate the standard measurement dubiety. Inset: comparison of the weighted mean of the DE from (a) with the DE from (b) for the lowest measured photon flux, where the error confined show the corresponding expanded uncertainties (k = two). Taken from [67]

Full size image

Summary and conclusion

In this paper, nosotros reported on the metrological label of different types of single-photon sources and their application for the detection efficiency scale of single-photon detectors, which is a specific aspect within breakthrough radiometry and quantum metrology. Nether investigation for this purpose are currently single-photon sources based on impurity centres in (nano-) diamond, single molecules and semiconductor breakthrough dots, both embedded in dielectric structures for drove efficiency enhancement. Table 1 summarizes the results obtained and so far on the metrological characterization of unmarried-photon sources, which is performed in a traceable way, with respect to photon flux, spectral ability distribution, spectral photon flux and 2d club correlation one thousand (2)(t), as well every bit the lowest uncertainties realized with these sources in detection efficiency calibration of SPAD detectors.

Table ane Summary of obtained results with single-photon sources applied for SPAD detection efficiency scale

Full size table

N ph: full photon flux, Δλ: spectral bandwidth (FWHM), N ph,λ (λ): maximum spectral photon flux (normalized to a radiometric relevant bandwidth of one nm), k (2)(t = 0): value of the second order correlation function at t = 0 (indicator of unmarried-photon purity, T: performance temperature, u(η): doubtfulness realized in SPAD detection efficiency calibrations.

Equally tin can be seen, all-time results thus far were obtained with the InGaAs/GaAs semiconductor quantum dot source with respect to all parameters. Next steps are the design and fabrication of optimized structures to farther enhance the outcoupling efficiency and thus the single photon flux. Also, it is important to reduce the g (two)(t = 0) value in society to avoid problems with multiphoton events in case of loftier photon rates. Still a drawback is the necessity to apply cryogenic temperatures. Also, for the single molecule DBT:Ac based source, very promising results were obtained. Farther improvement is planned into the management of pulsed operation, to avert variation in photon inflow times or a Poissonian-like behaviour, as observed in the presented calibration results. It should too be noted that, thus far, dielectric structuring was not carried out for the molecule samples, so there is significant room for improvement. As for the semiconductor breakthrough dots, cryogenic temperatures are required for functioning. With impurity centre-doped unmarried-photon sources detection efficiency calibration could non exist carried out, because of the low spectral photon flux in case of the nitrogen vacancy based single-photon source, resulting from the broadband emission. Whether other sources based on the silicon, germanium, can and atomic number 82 vacancy centres will exhibit sufficient spectral photon flux, while maintaining single-photon purity, is currently under investigation. As far as structuring in diamond is concerned, a lot of progress was realized using east.g., focused ion beam (FIB) and other techniques. The largest advantageous characteristic of diamond based single-photon sources is the possibility to exist operated at room temperature.

Nonetheless, it should be pointed out already, that the traceability gap betwixt classical and quantum radiometry is closing with the help of the single-photon sources presenting in this paper. Further development will not just pb to even better results, i.e., lower uncertainties, but also to stable and robust operation. Also, inside the EMPIR articulation inquiry project SEQUME (Single- and entangled photon sources for breakthrough metrology) [69, 70], further metrological applications using single-photon sources will be investigated.

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Acknowledgements

This work was funded by the project 17FUN06 SIQUST. This project has received funding from the EMPIR programme co-financed by the Participating States and from the European Union'southward Horizon 2020 research and innovation programme. This project (EMPIR 20FUN05 SEQUME) has received funding from the EMPIR plan co-financed by the Participating States and from the European Union'due south Horizon 2020 research and innovation program. We gratefully acknowledge the support of the Braunschweig International Graduate Schoolhouse of Metrology B-IGSM and the DFG Research Training Group 1952 Metrology for Complex Nanosystems. This work was also supported by the Deutsche Forschungsgemeinschaft (DFG, German Inquiry Foundation) under Germany's Excellence Strategy—EXC- 2123 QuantumFrontiers—390837967.

Funding

Open Admission funding enabled and organized by Projekt DEAL.

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Affiliations

  1. Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Deutschland

    Stefan Kück, Marco López, Helmuth Hofer, Hristina Georgieva, Justus Christinck & Beatrice Rodiek

  2. Laboratory for Emerging Nanometrology, Braunschweig, Germany

    Stefan Kück & Justus Christinck

  3. Český Metrologický Institut (CMI), Okruzni 31, 63800, Brno, Czechia

    Geiland Porrovecchio & Marek Šmid

  4. Department of Physics, Graduate School in Avant-garde Optical Technologies (SAOT), Friedrich Alexander University (FAU) Erlangen-Nürnberg, 91052, Erlangen, Deutschland

    Stephan Götzinger

  5. Max Planck Plant for the Science of Light, 91058, Erlangen, Germany

    Stephan Götzinger

  6. Fachrichtung Physik, Universität des Saarlandes, Campus E2.vi, 66123, Saarbrücken, Germany

    Christoph Becher & Philipp Fuchs

  7. Istituto Nazionale di Ottica (CNR-INO), Florence, Italy

    Pietro Lombardi & Costanza Toninelli

  8. Università degli Studi di Firenze, Florence, Italy

    Marco Trapuzzano

  9. LENS, Università degli Studi di Firenze, Florence, Italy

    Maja Colautti

  10. Istituto dei Sistemi Complessi (CNR-ISC), Florence, Italia

    Giancarlo Margheri

  11. Istituto Nazionale di Ricerca Metrologica (INRiM), Torino, Italy

    Ivo Pietro Degiovanni & Paolo Traina

  12. Institut für Festkörperphysik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany

    Sven Rodt & Stephan Reitzenstein

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Correspondence to Stefan Kück.

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Kück, S., López, M., Hofer, H. et al. Single photon sources for quantum radiometry: a brief review nearly the current state-of-the-art. Appl. Phys. B 128, 28 (2022). https://doi.org/10.1007/s00340-021-07734-2

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