Photon Statistical Properties Of Light Fields Based On Single-Photon Detection

The research on the physical nature of various classical and nonclassical phenomenons of light fields is one of the important researching issues in quantum optics. In quantum mechanics, a quantum state can be completely described by a density operator. Some information of the elements of the density matrix can be derived with the measurements of quantum states via all kinds of experimental methods, so we can understand the characteristics of the various quantum states from the information. There are many methods for measuring the quantum states. And these methods can reflect the properties of quantum states from different aspects. The degree of coherence of the fields can be derived with correlation measurement. The photon distributions of the fields can be obtained via photon counting technique. The information of the amplitude or the phase of the fields can be acquired by the means of homodyne detection. According to the different experimental systems and ways of detection, there are two ways of measurements, including continuous case and discrete case. The detector converts the intensity of light to the photoelectric current in the continuous case. While in the discrete case the number of photons can be counted by the detector and the detector's outputs are discrete electric pulses.Because this discrete detection may responds to the single photon, it becomes the most sensitive method of photon detection at present, which enables it to be widely used in the modern quantum optical experiments, especially in the applications of manipulating some single particles. In recent years, the preparation and determination of single-photon source has drawn greater attention with the rise of quantum information. The single-photon state has played an important role in the implementation of quantum cryptography and quantum computation. So far single-photon sources have been produced by pumping single molecules, individual quantum dots, and color centers and by the way of cavity-QED for trapping single atoms and ions. The HBT (Hanbury-Brown and Twiss) scheme based on two single-photon detectors is used to judgment and determination of the single-photon source effectively. The interferometry with a single photon is an appealing issue in quantum optics. The nature of the light can be understood profoundly through these experiments, in which the technique of single-photon detection is indispensable. Meanwhile, the single-photon detection as a typical kind of non-Gaussian operation can be applied in the realization of quantum state engineering. Thus it can be seen that the technique of single-photon detection has an attractive prospect in the weak-light detection of quantum optics. Investigation of how to acquire the characteristics of the light fields with single-photon detection fast and effectively is an important topic. Besides, single-photon detection has wide applications in high resolution spectrum measurement, non-destructive material analysis, bioluminescence, high energy physics, astronomy, and so on.The detectors used in the single-photon detection are required to be highly sensitive to single photon and have low thermal noises themselves at the same time. In the latest ten years, the development of single-photon detectors is showing rapid progress. The photon-number resolving detectors as well as the ways of high efficiency detection in the communication wave range are also developing. There are many kinds of single-photon detectors to be used for single-photon counting, such as photomultiplier tubes (PMT), avalanche photodiodes (APD), hybrid photodiodes (HPD), and so on. The combination of microchannel plates (MCP) and charge coupled devices (CCD) can be used for single-photon imaging. At present, the superconducting single-photon detectors are studied in the experiments. Their performances in the quantum efficiency, counting rate, dark counts, etc indicate their attractive prospect. Compared with the semicondunting single-photon detectors, the prime advantage is the ability of photon number resolution. Besides, the single-photon detecting scheme based on frequency up-conversion is utilized to solve the problem of the detectors' low quantum efficiency in the near infrared wave range. A nonlinear crystal used in this scheme converts the infrared photons into visible ones by the way of sum frequency. The single-photon detectors have relative higher quantum efficiency in the visible light. The converting efficiency of this method is high. But it needs higher pumping power. Presently, some ones advise to decrease the pumping power with wave-guide nonlinear crystal.At present, the single photon counting modules made of avalanche photodiodes are widely used in the experiments because of the advantages of their high quantum efficiency in the infrared wave range, low dark counts, steady operating voltage, and so on. In our laboratory, a system for photon number counting and data acquisition and analysis has been established with single photon counting modules (SPCM-AQR-15, PerkinElmer Optoelectronics) and a high-speed data acquisition card. The basic parameters of this system such as dead time, dark counts, and so on have been tested and measured. The photon statistical properties of several quantum states have been analyzed theoretically based on the HBT (Hanbury Brown and Twiss) scheme consisting of two SPCM's when the background noises, the total detection efficiency and the property of SPCM are considered. And the second order degree of coherence of coherent light and thermal light is measured experimentally. The results confirm the theoretical analysis.In this dissertation, the single photon detection system is improved to reflect the characteristics of the light fields more exactly via the theoretical and experimental research. Then the second order degree of coherence of the correlated two-photon pairs generated from optical parametric oscillator (OPO) far below threshold is determined based on the HBT scheme consisting of two SPCM's. Meanwhile, the applications of the single-photon detection in the direct measurement of Wigner function and conditional measurement are discussed.The main works of this dissertation are as follows:1. Photon statistical properties of coherent field and thermal field are experimentally studied by means of direct measuring photon counting via only one SPCM operating in Geiger mode. The second-order degree of coherence affected by photon counting rate and selected time resolution is investigated systematically. By taking into all the experimental factors which can influence the g⁽²⁾, the second-order degree of coherence of an unknown optical field can be determined quickly and simply via single SPCM when choosing proper detected conditions. In our experiment, when the count rate is about 109kc/s and the resolution time varies from 2⁸ ns to 2¹² ns, the measured results can reliably reflect the different second-order degree of coherence of coherent light and thermal light.2. The second-order degree of coherence is experimentally investigated by means of the HBT scheme consisting of two SPCM's. By comparing the results of coherent light with that of the thermal light, we show that the measured is affected by the photon-counting rate and the resolution time from pulsed to continuous wave fields. The proper counting rate and resolution time for characterizing the exact photon statistical properties of input fields are determined. When the count rate is about 50kc/s and the resolution time is 32 ns, the measured second-order degree of coherence of coherent light and thermal light from pulse case to continuous case can be distinguished obviously.3. The second order degree of coherence of the pseudo thermal light and the coherence time are experimentally studied based on HBT scheme consisting of two SPCM's. We investigate the coherence time of the incident beam for different spot sizes on the ground glass and speed of the rotating ground glass. The corresponding coherence time can be obtained from the Gaussian fitting for the measured second order degree of coherence.4. The single-photon detection is utilized to measure the entangled two-photon pairs. The second order degree of coherence of the multimode two-photon pairs in OPO far below threshold is studied when the resolution time of detection system, pumping power and crystal temperature are changed.5. The influences of the photon statistics of different quantum states based on a double HBT scheme consisting of four SPCM's are investigated theoretically. The overall efficiency and background are taken into account. We show that for different quantum states the measured second-order degree of coherence and Mandel parameter Q are affected by the actual experimental conditions. We quantitatively compare the results with those of the single HBT (double SPCM's) scheme and show that the double HBT scheme gives a more realistic picture of the properties of a quantum state, especially for a non-single-photon state.6. The direct measurement of Wigner function is introduced. And Wigner function of the vacuum state is measured via this method.7. The method of quantum state preparation based on the conditional measurement of lossless beam splitter is introduced. And the photon statistical properties of various conditional output states are discussed. We study the effect of conditional measurement, input states and intensity of the input states on the second order degree of coherence and Mandel parameter Q of the conditional output states. This research may be further used in the preparation and transformation of various quantum states under certain conditions.