In this work, a comprehensive experimental investigation of the photon statistics in random fiber laser (RFL) is conducted using the classical temporal second-order correlation function, and its unique evolutionary behavior is unveiled for the first time.
The statistical behavior of spectral intensity fluctuations in a Raman gain random fiber laser is investigated for the first time, to the best of our knowledge. Through a fiber Fabry–Perot tunable filter, the intensity of the filtered single wavelength from random laser (RL) spectra is measured at different pump powers. The probability density function (PDF) of spectral intensity values is analyzed. Well below the lasing threshold, the intensity of a single wavelength is stable in the time domain, and the PDF exhibits a typical Gaussian behavior. However, around the threshold, strong fluctuations in intensity emerge. In this case, the statistical distribution is characterized by a power-law-tailed function consistent with a Lévy α-stable distribution. We identify the statistical evolution as the injected pump power increases, from a Gaussian to a Lévy and then back to a Gaussian distribution, which is similar to the case of RLs with a strong disorder due to the presence of photon scatterers and gain related to electronic transitions in the active medium, indicating the universal existence of such statistical properties in random lasing systems.
By investigating the intensity correlation function, we study the temporal mode properties of spontaneous Raman photons generated in single mode fibers pumped by short pulses. We find that the intensity correlation function of the Raman photons is related to the dispersion induced temporal mismatch among the Raman photons generated in different subparts of the fiber. When no temporal mismatch exists, the intensity correlation function only depends on the ratio between the pulse width of the pump and the coherence time of the Raman photons. With the ratio decreasing, the intensity correlation function increase. Our study is helpful for easily creating high-quality true thermal light which will be a useful resource for second-order coherence based remote sensing.
Photon statistics is a branch of physics that involves observing the behavior of single or a small number of photons and then aggregating the results through statistical averaging. This process is essential to obtain meaningful and reliable data, especially in quantum optics research. Photon statistics provides valuable information about correlations in the electromagnetic field and characteristics of the type of light being measured. For example, second-order correlation function obtained via Hanbury Brown and Twiss experiment is the fundamental way to differentiate between coherent, chaotic and quantum light. Moreover, extensive investigations into the quantum properties of light resulted in significant progress that allows for precise control of quantum optical systems and sets the stage for genuine quantum engineering. This progress extends to applications in confirming the generation of entangled photons and exploring their properties for various purposes. The non-classical correlation between the entangled photons has resulted in various quantum optical techniques that enable the practical implementation of conceptual experiments that probe the core principles of quantum theory. This enhanced control over quantum phenomena offers exciting opportunities to explore novel information-processing approaches, with the potential to revolutionize technologies rooted in quantum information science. Driven by the significance and pivotal role of photon statistics, our research pursuits were directed toward two specific domains: the characterization of nanolasers and the characterization of time-bin entangled photons. In the first segment, we delve into the realm of metallic coaxial nanolasers, renowned for their intriguing threshold-less lasing behavior. Through comprehensive photon statistics analysis, we seek to unravel the coherence properties inherent in these nanolasers. Our focus also lies on understanding the elusive threshold-less operation, which has remained a subject of debate and intrigue. To evaluate this unique lasing characteristic, we conduct rigorous second-order coherence measurements alongside time-resolved second-order correlation analyses. The second segment of this study ventures into the generation and characterization of high-dimensional time-bin entangled states, a critical resource for quantum technological applications. We simulate a synthetic photonic lattice by employing a coupled fiber-loop system to perform various quantum walk schemes to generate and process high-dimensional time-bin entangled states. Our investigation focuses on the quantum interference phenomena through detailed photon statistics analysis, with an emphasis on their applications across diverse quantum technologies. Through these two interconnected research endeavors, this thesis demonstrates the profound significance of photon statistics as a versatile tool, bridging classical and quantum realms, and paving the way for advancements in diverse applications, ranging from nanolasers to quantum technologies.
The probability distribution p(n) for the detection of n photons emitted by a single-mode dye laser in a short time at various excitations is measured, together with the distribution of time intervals between pairs of detected photons. The first measurement yields the probability density p(I) and the moments of the light intensity I, and the second one the two-time intensity-correlation function. Measurements are also performed at three different wavelengths. p(I) is found to have a two-component structure, and the relative intensity fluctuations $\frac{〈{(\ensuremath{\Delta}I)}^{2}〉}{{〈I〉}^{2}}$ grow, apparently without limit, as the excitation tends to zero, so that no thermal state is reached. A possible explanation in terms of pumping fluctuations is discussed. The correlation function has the form of a sum of three exponential functions, and the amplitudes and decay constants of the three components are derived. The effective decay-time constant exhibits a thirteenth-power-law dependence on frequency of the laser light.
The second-order correlation function of photons is the primary means to quantitatively describe the second-order coherence of a light field. In contrast to the stationary second-order correlation function, the temporal second-order correlation function can be used to study the second-order coherence of a transient light field. Based on the Monte Carlo algorithm, we carried out theoretical simulation on the temporal second-order correlation function from the perspective of photon statistics. By introducing experimental factors into the simulation, such as intensity jitter of the light field and time resolution of the instruments, the effects of imperfect experimental conditions on the measurement of second-order correlation function have also been elucidated. Our results provide theoretical guidance and analysis methods for experimental measurements on the second-order coherence of light fields.
True random numbers are essential for cryptography and secure communications. Algorithmically generated pseudo-random numbers lack true physical randomness, while conventional lasers as physical entropy sources introduce time-delay signatures (TDS) and require complex post processing. To address this challenge, this study presents a high speed, real-time true random bit generator utilizing a modeless Raman fiber laser (RFL). A modeless RFL was constructed using an ultra-low reflectivity (-27 dB) fiber Bragg grating (FBG) and a high-reflectivity FBG serving as cavity mirrors. The laser delivers stable modeless Raman lasing within the pump power range of 5 W to 10 W. Compared with multilongitudinal-mode operation, the modeless laser exhibits significantly lower temporal coherence. By truncating the four least significant bits of the 8-bit digitized temporal intensity signal from the modeless RFL, random bit sequences were generated at a rate of 320 Gbps. The resulting random bit stream shows a uniform distribution of bits 0 and 1, its autocorrelation function contains no TDS, and it successfully passes the NIST statistical test. In contrast, the same generation method fails to produce qualified random bits when applied to the Raman fiber laser operating in the multilongitudinal-mode regime. The demonstrated modeless RFL system combines real-time operation, high speed, and stability, offering a robust physical entropy source for cryptographic and secure communication applications.