As far back as 1939, Allen implemented the experiment of photon counting with a secondary electron multiplier [
Photonics Research, Volume. 3, Issue 1, 24(2015)
Quantum description and measurement for single photon modulation
Single photon modulation has been proposed to overcome the defects of the low signal-to-noise ratio (SNR) and slow process rate of photon counting. In this paper, we present the quantum theory of single photon modulation, and then experimentally investigate the modulation spectroscopy both in the time domain and frequency domain. It is found that the SNR reached 150 in approximately the MHz modulation bandwidth.
1. INTRODUCTION
As far back as 1939, Allen implemented the experiment of photon counting with a secondary electron multiplier [
Photon-counting modulation [
Recently, we presented a single photon modulation method to increase the SNR and speed up the processing rate for low-light-level detection. Compared with the common photon-counting method [
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In this paper, we present the quantum theory of single-photon modulation, and then experimentally investigate the modulation effects from both the time domain and frequency domain. The modulation frequency we achieved experimentally is in the MHz range, and further theoretical simulation shows a similar SNR within the GHz modulation bandwidth.
2. THEORETICAL MODEL
Modulation signal can be represented as a function of time
In a quantum mechanics model, two incident beams are necessary, although one of them is in a vacuum state (as per the quantum optics splitter model). Consider the case in which the signal state and the vacuum state are single modes with annihilation operators
As shown in Fig.
Figure 1.Schematic diagram of the single photon modulation process: (a) single photons appear randomly without modulation; (b) distribution of single photons’ timing sequence changed with the modulation; (c) statistics diagram of
We define
Figure 2.Simulation results of single photon modulation: (a) spectrum has the characteristic of white noise without modulatinon; (b) with the modulation signal, there is a peak at the modulation frequency; inset, enlargement of the rectangular region within the dashed line.
3. EXPERIMENTAL SETUP
The experimental system is described in Fig.
Figure 3.Experimental setup of single photon modulation: red and black lines indicate the optical fiber and electric cable, respectively; Att, optical attenuator; Iso, optical isolator; SPAD, single-photon avalanche diode.
4. RESULTS AND DISCUSSION
First let us analyze the effect of the modulation on single photons in the time domain. As we expected the statistical result of the probability distribution coincides with a sine waveform (Fig.
Figure 4.Statistics diagram of the phase difference between the single-photon signal and the modulation signals in the time domain. Horizontal ordinate is calculated as
Next, we analyze the modulation on single photons in the frequency domain. Some factors affect the spectrum measured by the spectrum analyzer, such as the intensity of the single-photon source, the fluctuation of the photon counts, the modulation frequency, and so on. By analyzing the modulation spectrum, we found that both the peak and background of the modulation spectrum increase with the increase of the mean photon number. It is common sense that as the input power increases, the power spectrum would also increase. The experimental and theoretical results show that the SNR also increased as the mean photon number increased. The experimental results have a statistical property at the single-photon level. With the increase of the mean photon number the statistical results tend to be impeccable; the influence of the dark count and the shot noise decreased naturally. The SNR increases with the increase of the mean photon number, and then tends to be relatively stable. This means that when the mean photon number is large enough the effect caused by shot noise can be negligible, and the SNR would also not increase anymore. The experimental results demonstrate that the interpretation previously mentioned is reasonable (Fig.
Figure 5.(
The definition of SNR is where
Figure
Figure 6.(a) Relationship between the modulation frequency and the signal and background intensity; (b) SNR corresponds to the modulation frequency; red and black points represent experimental and theoretical results, respectively; mean photon number was set to 80 kcps.
The vertical error bar in Fig.
5. CONCLUSION
In summary, we described the single photon modulation process in the manner of quantum optics. The experimental results show that this method has a higher SNR than that of the direct photon-counting measurement. Compared with the slow modulation frequency of photon-counting modulation, single photon modulation makes it possible to obtain quick measurement of a single-photon signal. MHz modulation bandwidth could effectively avoid the infections from flicker noise and reduce the measurement time. These results indicate that single photon modulation has potential applications in weak light detection and information transmission at the single-photon level.
[2] S. S. Raouf, A. R. Sadik, N. K. Wafi, K. M. Aboud. Measurement of noise power spectrum in photon counting PMT’s and the effect of the observed (1/
[3] L. You, X. Shen, X. Yang. Single photon response of superconducting nanowire single photon detector. Chin. Sci. Bull., 55, 441-445(2010).
[16] J. W. Goodman. Statistical Optics(2000).
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Jianyong Hu, Yan Liu, Lingling Liu, Bo Yu, Guofeng Zhang, Liantuan Xiao, and Suotang Jia, "Quantum description and measurement for single photon modulation," Photonics Res. 3, 24 (2015)
Category: Photon Statistics
Received: Oct. 10, 2014
Accepted: Nov. 26, 2014
Published Online: Apr. 15, 2015
The Author Email: Liantuan Xiao (xlt@sxu.edu.cn)