Journal of Electronic Science and Technology  2019, Vol.17 Issue (3): 204-212   DOI: 10.11989/JEST.1674-862X.90704101 PDF
http://dx.doi.org/10.11989/JEST.1674-862X.90704101
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Article

Cheng-Jie Ding, You-Ying Rong, Yu Chen, Xiu-Liang Chen, E Wu
Direct Measurement of Non-Classical Photon Statistics with a Multi-Pixel Photon Counter
Journal of Electronic Science and Technology, 2019, 17(3): 204-212
http://dx.doi.org/10.11989/JEST.1674-862X.90704101

Article History

revised July. 09, 2019
Direct Measurement of Non-Classical Photon Statistics with a Multi-Pixel Photon Counter
Cheng-Jie Ding, You-Ying Rong, Yu Chen, Xiu-Liang Chen , E Wu
C.-J. Ding, Y.-Y. Rong, Y. Chen, X.-L. Chen, and E Wu are with the State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062 (e-mail: xlchen@phy.ecnu.edu.cn; ewu@phy.ecnu.edu.cn)
This work was supported by the National Natural Science Foundation of China under Grants No. 11722431, No. 11674099, No. 11704127, and No. 11621404, the Program of Introducing Talents of Discipline to Universities under Grant No. B12024, the Shanghai International Cooperation Project under Grant No. 16520710600, the Natural Science Foundation of Shanghai under Grant No. 16ZR1409400, and the Shuguang Program under Grant No. 15SG22 by Shanghai Education Development Foundation and Shanghai Municipal Education Commission
Abstract: Photon number resolving detectors with high accuracy bring broad applications in long-distance laser ranging, ultrafast spectroscopy, and quantum optics. In this paper, we observed the non-classical photon number distribution directly with a multi-pixel photon counter (MPPC) instead of a classic Hanbury-Brown and Twiss (HBT) system. The detector’s photon-number resolving ability was characterized by quantum detector tomography. To show the quantum feature of the detector, we further plotted the Wigner function, which was obtained corresponding to the positive operator value measure (POVM) elements. Finally, we declared the observation of non-classical photon statistics from a single color center in nanodiamond by using this detector.
Key words: Photon counting    photon statistics    quantum detector    quantum optics
1. Introduction

Recently, the photon-number-resolving (PNR) detection catches attention of researchers because it provides a possible way to observe non-classical phenomena directly by discriminating the incident photon numbers. There are different ways to realize PNR detection[1]-[5]. Among them, superconducting transition-edge sensors (TESs) can detect visible and near-infrared light based on the tungsten TES detector. However, it has a limit on practicality due to the stringent requirements on the heat capacity, thermometry, relatively large timing jitter, and dead time (about 100 ns)[6],[7]. The superconducting nanowires PNR detector provides free-running single-photon sensitivity from visible to mid-infrared frequencies, low dark counts, excellent timing resolution, and short dead time, but all this performance is achievable under the operation temperature that is not easy to reach (2 K to 3 K)[8],[9].

Another way of realizing photon number resolving detection is mainly based on the temporal or spatial multiplexing of single-photon detectors[10],[11]. The time-multiplexed detector based on silicon avalanche photodiodes (Si-APDs) splits the incident photon pulse into a time sequence of N weaker pulses, which highly depends on the detection efficiency of APDs and is limited by the effective repetition rate of detection[10],[12]. PNR detectors based on single-photon sensitive cameras like the scientific complementary metal-oxide-semiconductor (sCMOS) camera, intensified charged coupled devices (CCD), and electron-multiplying CCD are spatial multiplexing detectors. Most of them have a limit in illumination levels and need to sacrifice the spatial resolution for higher photon-number resolving capability[13].

Here we focus on the multi-pixel photon counter (MPPC), which is a new kind of spatial multiplexing PNR detector suitable for ultralow photon number distinguishing. It offers high photon detecting efficiency, excellent timing resolution, and immunity to magnetic fields. The high-density matrix of avalanche photodiodes (APDs) provides excellent photon-counting capability[14]. By combining the single-photon frequency upconversion technique with MPPC, the near infrared PNR detector has been achieved as well[15],[16].

In this paper, we characterized a PNR detector based on MPPC by quantum detector tomography. Besides, the Wigner function corresponding to the positive operator value measure (POVM) was given for the quantum performance. The negative value of the Wigner function indicates that this PNR detector is a fundamental quantum detector. To demonstrate the detection capability for the photon statistics of the nonclassical state, we used MPPC to measure the photon-number distribution. We observed the nonclassical quantum state feature of the fluorescence from a single nitrogen vacancy (NV) color center in nanodiamond. In comparison, we measured the photon number distribution of a continuous-wave laser that was attenuated to the same intensity level. The difference in the photon number distribution was observed between the light fields from a single-photon emitter and attenuated laser.

2. Photon-Number Distribution Measurement with MPPC

MPPC we used in our experiment has 10 rows and 10 columns of Si-APD pixels (S10362-11-100U, Hamamatsu) within an active area of 1 mm2. Each pixel operated independently in Geiger-mode for detecting the incident photons. The bias voltage of MPPC was set at 68.2 V. MPPC would produce an avalanche pulse whose amplitude was the sum of the response of each APD pixel. The phenomenon that the peak amplitude voltage from MPPC is proportional to the number of detected photons has shown the photon number resolving capability. The APD pixel was passively quenched in the experiment when the photon was detected, causing the dead time of about 30 ns. In order to decrease the effect of dark-count, MPPC was Peltier cooled to −18 °C, and the dark-count rate (DCR) was limited to 1.9×104 s−1.

To look into detector’s performance in quantum detection, we did the quantum detector tomography of MPPC as shown in Fig. 1. The laser used in the set-up was a pulsed super-continuum laser (SC400-4-PP, Fianium). The repetition rate of the laser source was set as 1 MHz and the pulse duration was 10 ps, which conformed to the output avalanche pulse duration of MPPC (200 ns) and its dead time (30 ns). We selected the output spectrum of the laser at 650 nm to meet the central wavelength of the fluorescence of the NV center in nanodiamond. A bandpass filter (BP) at 650 nm with a 40-nm bandwidth was used to filter the laser in the spectrum. Then, the beam went through a set of attenuators, including a variable intensity attenuator (VA) and a fixed intensity attenuator (Attn) with −22-dB attenuation. With VA and Attn, we could first attenuate the laser source to the single-photon level and then vary the intensity of the incident photons continuously from 0 to 50 photons/pulse. A flip-flop mirror (FM) was inserted to send the laser to a power meter when it was flipped up. By measuring the power between the two attenuators, we could monitor the accurate photon flux that went to the detector. The photons were focused on the detecting area of MPPC with a lens (L). The output of MPPC was sent to a digital oscilloscope, triggered by the synchronous signal from the pulse laser. The accumulation curve in Fig. 2 (a) shows that the voltage amplitude has a concentrated distribution on several discrete voltage levels with multiple relations, corresponding to different detected photon numbers. The sampling frequency of oscilloscope was set as 250 MHz and the sampling interval was set at 4 ns, completely meeting the need of accuracy. Then, the raw data were exported to a computer for analysis.

 Fig. 1 Experimental setup of the photon number distribution acquisition. The coherent signal from a pulse laser was filtered with a bandpass at 650 nm, then passed through a two-level attenuation system to get a tunable few-photon-level coherent signal. The attenuated signal was focused on MPPC. The avalanche signal from MPPC was finally sent to an oscilloscope triggered by the synchronous signal from the pulse laser. BP is a bandpass filter at 650 nm with the bandwidth of 40 nm; VA is a variable intensity attenuator; Attn is a fixed intensity attenuator of −22 dB; FM is a flip-flop mirror.

 Fig. 2 Photon number distribution measured by MPPC: (a) Distribution of the peak output signal generated by MPPC. The red solid line shows a fit to the data described in the text and (b) detected photon number distribution. MPPC was illuminated by a 650-nm pulsed laser with an average detected intensity of μ=3.06 photons per pulse.

Due to the high integration of 100 APDs in the area of 1 mm2, MPPC reads extra counts due to dark-count, crosstalk, and afterpulse noise. When a photon hits the APD array, it has the possibility to catch extra electrons or holes generated during discharging and be released after discharging, which will be detected as an afterpulse noise count[17]. This process will cause an increase of multi-photon detection occasion if the afterpulse noise overlaps with the photon-induced pulse. Usually, this process happens within tens to hundreds of nanoseconds after a photon is detected. With a pulsed laser source, the afterpulse noise can be identified since it is not synchronized with the laser source. Therefore, the dark-count and the afterpulse noise were wiped off before further analysis. The crosstalk noise was removed by calculating the crosstalk probability[18]. Accordingly, we got the percentage of the noise in the total counting rate. The afterpulse probability was about 6.7% and the crosstalk probability was about 8.5%. The detection efficiency of MPPC was calculated with the probability of one photon and two photons under a low incident light intensity by

 ${\text{η}} = \frac{{{P_{\rm{1}}} + {\rm{2}}{P_{\rm{2}}} + {\rm{3}}{P_{\rm{3}}}+ \cdots + n{P_n}}}{{\langle m\rangle }},$ (1)

where η is the detection efficiency, Pn corresponds to the probability of detecting n photons, and $\left\langle m \right\rangle$ is the average photon number per pulse.

When the incident photon flux is low, we can neglect the contribution of the multiphoton probability with n>3. When the incident average photon number was 1.67 photons per pulse, we obtained a total detection efficiency of 34.5% at the 650-nm wavelength.

MPPC was illuminated by a pulsed laser at the 650-nm wavelength with a varying average detected intensity from 0 to 50 photons per pulse. The avalanche signal from MPPC was a set of pulses, and its maximum voltage gave the information of the photon number detected in each pulse. By recording the maximum voltage of each pulse, we can get the histogram of the peak output signal, as shown in Fig. 2 (a). Here we plot the histogram when the detected average photon number per pulse is 3.06. The discrimination voltage for different photon number states could be obtained by fitting each voltage peak with the Gaussian functions. The Gaussian fitting of the data was demonstrated with the red solid envelope in Fig. 2 (a). The probability for n-photon state is obtained by summarizing all the events within the n-photon peak in Fig. 2 (a) and divided by the repetition rate of the pulse laser, where n is the photon number from 0 to 9 and 0-photon peak is the number of events when there is no photon detected within the pulse window. The detected photon number distribution could be reconstructed as shown in Fig. 2 (b).

3. Quantum Calibration of MPPC with POVM and Wigner Function

When we observe a quantum state with a certain apparatus, the interaction will generate perceptibly[1] a quantum mechanical description corresponding to the information of its POVM[19].

Here, we did quantum calibration of the MPPC detector by determining its corresponding POVM before using it for further measurement. The probability of obtaining an detection outcome can be given by POVM elements and a factor[20],[21]. The detector’s POVM is a set of semi-positive Hermitian operators $\{{\rm{\hat {\text{∏}} }}_n \}$ on the Hilbert space. The probability of obtaining n photon is given by

 ${p_n}({\hat{\text{ρ}}} ) = {\rm{Tr}}[{\hat{\text{ρ}}} {{\rm{\hat {\text{∏}}}}_n}],$ (2)

where ${p_n}({\hat{\text{ρ}}} )$ is the probability of obtaining n clicks, ${\hat{\text{ρ}}}$ is the density operator of the state on the Hilbert space, and Tr is the trace.

By measuring a set of known probe states factors, an unknown apparatus can be characterized by observing the knowledge of its POVM.

In our experiment, we sent a set of various known coherent states generated by varying the intensity of the incident photon flux and recording MPPC’s response to determine the POVM elements as shown in Fig. 3. Coherent states were generated by the attenuated pulsed laser. We measured 100 sets of distribution with an average incident intensity from 0 up to 50 photons per pulse. The integral time of each set was about 40 ms to acquire adequate data for statistics. Since the bias voltage of MPPC is kept at 68.2 V, the data share the same voltage peak value, as shown in Fig. 2. Obtained data are presented with circles in Fig. 3. The number of photon state is noted with arrows. The data re-calculated from the reconstruction of POVM elements of our MPPC are presented with the solid line in Fig. 3. The probabilities for lower photon-number components are higher than the expected due to the influence of afterpulse noise.

 Fig. 3 Detector tomography data measured with attenuated coherent state laser beam as a function of mean photon numbers in each laser pulse. The experimentally measured values are pointed out with circles, meaning different photon numbers, and the re-calculated values are marked as solid lines with the corresponding color, which are the data corrected by POVM as explained in the text. ${\langle m\rangle }$ is the average photon number per pulse from 0 up to 50 photons per pulse, while n is the detected photon number and is marked with arrows to point out the specific photon number of each curve.

The Wigner quasiprobability distribution also called the Wigner function is to describe the wavefunction with a probability distribution in the phase space[22]. To visualize the performance of MPPC, we plot the ‘one click’ and ‘two clicks’ Wigner functions based on reconstructed POVM elements[21],[23], as shown in Figs. 4 (a) to (b). W1(X, 0) represents the value of the Wigner function at the position (X, 0) based on the one-photon distribution, as shown in Fig. 4 (c). The value of the Wigner function near the origin was below zero, indicating a nonclassical distribution. The appearance of the negative value in the Wigner function is regarded as evidence of the full-quantum character of the photon detector. This demonstrates that MPPC is a fundamental quantum detector. Moreover, the negative values can also be observed with the Wigner function for ‘two clicks’, as shown in Fig. 4 (d). Therefore, the nonclassical distribution of the photon source could be observed directly with such PNR detector.

 Fig. 4 Wigner quasiprobability distribution of single-photon state and two-photon state measured by MPPC: (a) Wigner function in 3D coordinate system obtained by exploiting the reconstructed POVM elements corresponding to the probability of one-photon detected, and (c) its cross section at Y=0; (b) Wigner function in 3D coordinate system obtained by exploiting the reconstructed POVM elements corresponding to the probability of two photons detected, and (d) its cross section at Y=0. The dashed line marked out the boundary of classical and non-classical optical analog.
4. Nonclassical Photon Statistics Observation with MPPC

To demonstrate the reliability of the PNR detector based on MPPC, we measured the photon number distribution of the fluorescence emitted by a single NV color center in nanodiamond. The center wavelength of the spectrum of the fluorescence from the NV color center was about 650 nm. The NV color center in nanodiamond was excited with a continuous-wave Nd:YAG laser at the 532-nm wavelength and collected with single-photon detector through a scanning confocal microscope system[24],[25].

The unitary of the emitter was first verified by a Hanbury Brown-Twiss (HBT) arrangement, which was composed of a beam splitter with two Si-APDs on each output port. The detected fluorescence intensity from the single NV center in nanodiamond was about 100 kcounts/s including 10 kcounts/s background photon counts for each APD. The two APDs (PicoHarp 300, PicoQuant GmbH) were connected to the start and stop inputs of the time-correlated single-photon counter, respectively, for the second-order correlation function g(2) measurement to get the photon pair time interval distribution. For an ideal single-photon source, the antibunching effect can be detected by looking into the value of g(2)(τ) at τ=0, which provides the evidence of the unitary of the emitter. As shown in Fig. 5, g(2)(0)≈0.2, which proves that this NV color center in nanodiamond is a single-photon source. While for the coherent state, there will be no antibunching effect. The g(2)(τ) measurement verified that this NV center in nanodiamond gives an obvious non-classical phenomenon and single-photon number distribution.

 Fig. 5 Second-order correlation function of a single NV color center in nanodiamond. This NV color center in nanodiamond gives a second-order correlation g(2)(0)≈0.2 at τ=0. Inset: The fluorescence map of the single NV color center with a confocal scanning microscope system under the excitation of a continuous-wave laser at the 532-nm wavelength. The fluorescence detected was about 100 kcounts/s with a background of about 10 kcounts/s.

For the photon number resolving detection, the HBT arrangement was replaced by MPPC. The fluorescence intensity of the NV center detected by MPPC was about 180 kcounts/s, including 36 kcounts/s background noise photon counts. In order to get the reliable statistic result, we extended the integral time to 200 ms. As a comparison, a coherence laser beam attenuated to almost the same counting rate at the single-photon state detection as the NV center was also measured by MPPC with the same integral time.

The histogram of the photon number distribution is plotted in Fig. 6. The photon number distribution was with background correction. The red bar demonstrates the photon number distribution of fluorescence from the single NV center with background correction, whereas the blue stripe bar gives that of the attenuated laser. As shown in Fig. 6, the one-photon probability of fluorescence from single NV center is higher compared with the attenuated laser, whereas the multiphoton probabilities for the single NV center are lower, indicating the deviation on the non-classical photon number distribution of the single emitter from the classical coherent light source. The experiment reveals that the photon-number distribution of the Fork state could be directly observed with MPPC.

 Fig. 6 Normalized detected photon number distribution of the fluorescence from a single NV center (red solid bars) and attenuated continuous-wave laser at 532 nm (blue stripe bars).

However, with continuous-wave excitation, the fluorescent photons were emitted randomly, causing the superposition of photon-induced signal avalanche pulses and the noise pulses, and the afterpulse and the crosstalk could not be well distinguished from each other in the time scale. The influence of these error signals gave a rise to extra multiphoton probability. The quantum phenomenon could be observed more clearly if a triggered single-photon source could be used to provide a synchronized detection gate, so as to suppress the afterpulse[26],[27].

5. Conclusions

We characterized a PNR detector based on MPPC by quantum detector tomography. The negative value in the Wigner function proved that this PNR detector is a fundamental quantum detector and capable for the detection of the non-classical photon states. To witness the quantum effect of non-classical state, we used MPPC to measure the photon number distribution of the fluorescence from a single NV color center in nanodiamond. The deviation in the photon number distribution compared with the coherent state photons from the attenuated laser demonstrated the non-classical effect of photon antibunching with the single NV color center.

Acknowledgment

The authors would like to express their appreciation to Lei Li and San-Jun Zhang, who are with East China Normal University, for the use of their equipment.

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