We report on the experimental realization of an absolute single-photon source based on a single nitrogen vacancy (NV) center in a nanodiamond at room temperature and on the calculation of its absolute spectral photon flux from experimental data. The single-photon source was calibrated with respect to its photon flux and its spectral photon rate density. The photon flux was measured with a low-noise silicon photodiode traceable to the primary standard for optical flux, taking into account the absolute spectral power distribution using a calibrated spectroradiometer. The optical radiant flux is adjustable from 55 fW, which is almost the lowest detection limit for the silicon photodiode, and 75 fW, which is the saturation power of the NV center. These fluxes correspond to total photon flux rates between 190,000 photons per second and 260,000 photons per second, respectively. The single-photon emission purity is indicated by a value, which is between 0.10 and 0.23, depending on the excitation power. To our knowledge, this is the first single-photon source absolutely calibrated with respect to its absolute optical radiant flux and spectral power distribution, traceable to the corresponding national standards via an unbroken traceability chain. The prospects for its application, e.g., for the detection efficiency calibration of single-photon detectors as well as for use as a standard photon source in the low photon flux regime, are promising.
© 2017 Optical Society of America
Single-photon sources have the potential to be used in a wide field of applications [1,2]. Well known and widely discussed is their use in quantum key distribution, quantum computing, and quantum-enhanced optical measurements . In this paper, we deal with another important application of single-photon sources, i.e., their use in radiometry . In principle, single-photon sources have the potential to become a new type of standard photon source  as there are—in the classical regime—the blackbody radiator and the synchrotron radiation source. The output power of an ideal single-photon source, which emits only one photon per excitation pulse, is simply given by the formula , where is the repetition rate of the excitation laser, is the Planck constant, is the speed of light, and is the wavelength of the emitted radiation. However, the conditions for such a standard source are difficult to realize in practice, because a source with a quantum efficiency of 100%, a perfect purity of the single-photon emission, i.e., , and a collection efficiency of 100% is required. In any case, single-photon sources are ideal sources for the calibration of single-photon detectors, because the influence of photon statistics on the calibration results is omitted [6,7]. In this paper, we present a single-photon source absolutely calibrated by a classical standard detector and a calibrated spectroradiometer and hence traceable to a national standard for optical radiant flux via an unbroken traceability chain. This is considered to be the first step toward the realization of a deterministic absolute single-photon source. Furthermore, the model for the calculation of the absolute spectral photon flux from experimental data is presented in detail.
2. THE EXPERIMENTAL SETUP
The developed single-photon source is based on a nitrogen vacancy (NV) center  -doped nanodiamond (GAF 0.15 from Microdiamond AG) with an approximate median size of 75 nm in each dimension. This nanodiamond was found to exhibit the purest single-photon emission from a sample consisting of nanodiamonds spin coated on a microscope cover glass with a thickness of 0.17 mm.
To achieve high-quality single-photon emission, one has to ensure that only one nanodiamond, which contains only one single NV center, is optically excited. Therefore, a confocal microscope is used for the selective excitation as well as for the collection of the NV-center emission. The confocal microscope setup used in the experiments is shown schematically in Fig. 1. For excitation, a continuous-wave laser operating at a wavelength of 532 nm (Laser Quantum, Ventus 532) is used. A laser line filter (Semrock, Maxline laser line filter, LL01-532-125) is placed into the optical excitation path in order to avoid unwanted emissions at the detection wavelength that leak into the detection path. The lenses L1 and L2 are used to expand the beam. The laser light is reflected by a dichroic beam splitter (Semrock FF560Di01) and focused with an oil immersion microscope objective (Nikon CFI Plan Apochromat Lambda, , NA 1.45; immersion oil: Zeiss Immersol 518F) through the cover glass onto the nanodiamonds. The excitation spot size is approximately 300 to 400 nm in diameter. Note that the spot is bigger than the diffraction limit and has an elliptical shape, both caused by the non-perfect alignment. However, the purpose of this work was the radiometric investigation of the NV-center emission; therefore, this kind of excitation is sufficient. Furthermore, different nanodiamonds can be individually excited by moving the cover glass with a piezo-electric translation stage (PI digital piezo controller E-725.3CDA, PI piezo stage P563.3CD).
The emission of the NV center occurs predominantly in the spectral region between 550 and 750 nm. It is collected by the microscope objective and passes through the dichroic beam splitter. In order to determine only the emission from the NV center, several transmission filters are placed into the beam path, i.e., a notch filter (Thorlabs NF533, bandwidth 17 nm), two (for enhanced filtering) short-pass filters (Thorlabs, FES0750 and FES0800), and a long-pass filter (Thorlabs, FEL0550). The high contrast, i.e., the high spatial resolution in the confocal microscope setup, is achieved by using a single-mode fiber (core diameter 9 μm) as the aperture diaphragm. Furthermore, the fiber is used to connect the single-photon source with devices needed for further characterization, i.e., to a detector (a silicon single-photon avalanche diode or a silicon photodiode), to a spectroradiometer or to a Hanbury Brown and Twiss interferometer.
The single-photon source is characterized in terms of photon flux, emission spectrum, and photon statistics, i.e., with respect to the purity of the single-photon emission. To get a confocal image by scanning, a silicon single-photon avalanche diode (Si-SPAD) (Perkin Elmer SPCM-AQRH-13-FC-18714) is used for the detection of the emission. The total number of photons is determined by a highly sensitive silicon photodiode (Si-diode), the so-called low optical flux detector (LOFD) designed at the Český Metrologický Institut (CMI) [9,10]. This detector is built for photon fluxes as low as 100,000 photons per second and is composed of an Si photodiode (Hamamatsu S1227 33BQ) in combination with a switched integrator amplifier. For the measurements with the LOFD, two microscope objectives (Edmund Optics , NA 0.25) were placed in front of the LOFD in order to transform the output photon flux of the single-photon source from fiber-based into free-space propagation and to focus the beam on the detector’s active area size (). The spectrum is determined by a spectroradiometer (Horiba Jobin Yvon iHR 320 with ). For the measurement of the second-order correlation function, a Hanbury Brown and Twiss interferometer setup is realized by using a 50:50 fiber optic splitter, two Si-SPAD detectors (Perkin Elmer SPCM-AQRH-13-FC), and a time-correlated single-photon counting (TCSPC) system (PicoQuant Pico Harp 300). The TCSPC works as a correlator that measures the time delay of the detection events between the two detectors. The outcome is the second-order correlation function that displays the number of correlated detection events of the detectors for various time delays. In the case of a real single-photon source, there are no possible correlated detection events for a time delay of , so the function ideally has the value of 0 at . All measurements were taken at room temperature.
3. MODEL FOR THE CALCULATION OF THE ABSOLUTE RADIANT FLUX, THE PHOTON FLUX, AND THE SPECTRAL POWER DISTRIBUTION
For the first time, to our knowledge, the absolute optical radiant flux of a single-photon emitter is determined by means of a standard detector traceable to a national standard for optical power, in this case, to a calibrated high sensitive Si photodetector, i.e., the LOFD [9,10]. In order to characterize a single-photon source thoroughly with respect to its emitted spectral photon flux, we will first set up a model for its calculation from experimental data. For this model, the output signal of the LOFD, its spectral responsivity , and the relative spectral power distribution per wavelength of the NV-center emission need to be known. The output signal voltage of the LOFD, corrected for the dark signal, is related to the photocurrent produced by the absorbed photons according to the equation10]), and is the integration time (here, ). For further details, see Ref. .
The spectral responsivity of the LOFD is obtained from a calibration using the spectral responsivity facility and a transfer standard traceable to the cryogenic radiometer at the CMI for the whole spectral range of the NV center. The detector spectral responsivity is shown in Fig. 2. However, because the NV-center emission is broadband, an effective spectral responsivity needs to be calculated, which takes into account the relative spectral power distribution per wavelength of the single-photon emission is calculated from the spectral power distribution of the NV-center emission with
was determined with a spectroradiometer, which was calibrated against a tungsten lamp in order to determine its relative spectral responsivity. The tungsten lamp itself was calibrated with respect to its spectral irradiance in the “Spectroradiometry” working group at Physikalisch-Technische Bundesanstalt (PTB). In Fig. 3, a schematic overview of the necessary measurements and calculations is given. Then, we obtain
The optical radiant flux is now calculated according to
From the optical radiant flux, the number of photons per second can also be calculated
Additionally, the spectral radiant flux, i.e., the absolute radiant flux per wavelength , and the spectral photon flux, i.e., the absolute photon flux per wavelength of the source, can be determined using
4. MEASUREMENTS OF THE NV CENTERS AND THE ABSOLUTE SINGLE-PHOTON SOURCE
Figure 4 shows the scanned image of the investigated sample with the NV-doped nanodiamonds. Several fluorescent emitters, identifiable as bright spots, are observed. The nanodiamond indicated in Fig. 4 by a red circle was chosen for the characterization since it provided excellent single-photon emission properties. The spectrum of the NV-center emission with its characteristic zero phonon line (at 642 nm) is shown in Fig. 5, already given in absolute photon fluxes per wavelength and in absolute radiant fluxes per wavelength . The steep decline on the long-wavelength side at 750 nm is caused by the short-pass filter used in the detection path. Using Eqs. (3) and (6), the effective spectral responsivity and the average photon energy can be calculated using
The normalized second-order correlation functions are shown in Fig. 6 for excitation powers of 292, 690, and 1050 μW. As is typical for NV-center emission, the shelving level effect shows up in the form of a bunching peak at short delay times. The functions were fitted using the three-level model ,
In Fig. 7, the total radiant flux and the total photon flux, calculated from Eqs. (4) and (5), respectively, at the position of the LOFD are depicted as functions of the excitation power. As can be seen, the single-photon source is adjustable in terms of emitted photon flux, i.e., an increasing excitation power leads initially to an increase in the emitted photon flux. At about 275 μW of excitation power, approx. 190,000 photons per second, corresponding to approx. 55 fW, are emitted from the NV center. However, the photon flux saturates at approx. 260,000 photons per seconds, corresponding to 75 fW, for an excitation power of approximately 1.25 mW. In Fig. 7, the calculated total photon flux, the NV-center photon flux, and the background photon flux are shown. The NV-center total photon flux is calculated by fitting the saturation model to the photon flux experimental data and taking into account a linear dependence of the background photon flux from the excitation power,
Furthermore, it should be noted that providing a complete suppression of the background emission, this source is a stable absolute source, because in the saturation region, fluctuations of the excitation power should not have any effect on the number of emitted photons.
Additionally, we determined the absolute radiant flux per wavelength and the absolute photon flux per wavelength of the source according to Eqs. (7) and (8), respectively. The result is shown in Fig. 5 for the spectral range of the NV-center emission from 600 to 750 nm.
An absolute single-photon source based on the emission of a nitrogen vacancy center in a nanodiamond was realized via an unbroken traceability chain to a national standard. The total radiant flux, the total photon rate, as well as the wavelength-dependent measurements of the absolute radiant flux per wavelength and the absolute photon flux per wavelength were determined. The background corrected output of this source saturates at the photon flux rate of approx. 240,000 photons per second. It is expected that further improvement of the dielectric structure, e.g., an optimized (metal-)dielectric antenna structure, surrounding the NV-center-doped nanodiamond, would lead to an increase of the photon flux rate. Furthermore, the background may be eliminated or at least significantly lowered by using higher purity materials for the microscope cover glass and possibly additional dielectric layers for the immersion oil and also for the microscope objective itself. A completely eliminated background emission would lead to a pure single-photon emission up to the saturation level. For applications like the direct calibration of single-photon detectors, these two improvements would lead to a significant decrease in the measurement uncertainty in the direct calibration of single-photon detectors. The single-photon character of this source was proven by the second-order correlation function with at low excitation powers, indicating an almost-pure single-photon emission. Even at higher excitation powers, the source still acts as a non-classical light source. The perspectives of this absolute source are its use in the detection efficiency calibration of single-photon detectors; investigations into this direction are under way. Additionally, wavelength-dependent calibrations in the broad spectral range of the NV emission are possible by filtering out certain wavelengths. Furthermore, the single-photon source can be used as standard photon source for the low optical flux region. We consider these results as first steps toward the realization of a deterministic absolute single-photon source. Moreover, we also plan to calibrate single-photon detectors in a wavelength-resolved way by using an absolute single-photon source based on Si-vacancy centers [12,13]. An absolute characterized SiV emitter, despite its low quantum efficiency of , would be also interesting for many calibration applications because of the narrow bandwidth of the spectral emission at room temperature .
European Commission (EC).
This work was funded by the project “Single-Photon Sources for Quantum Technology” (SIQUTE) of the European Metrology Research Program (EMRP). The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union. We gratefully acknowledge support by the working group “Spectroradiometry” of the Physikalisch-Technische Bundesanstalt, the Braunschweig International Graduate School of Metrology B-IGSM, and the DFG Research Training Group GrK1952/1 “Metrology for Complex Nanosystems.” We also thank Saulius Nevas, Peter Sperfeld, and Sven Pape from the PTB Spectroradiometry working group for providing the calibrated tungsten lamp.
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