Weak Signal Detection And Its Application In Gravitational Quantum Effects Verification

Verifying the quantum effects of gravity has been an important research topic of physic or signal and information processing. One the one hand, quantization of gravity is still an unsolved research topic, its final settlement would bound to be a landmark achievements in physics. Therefore, it is crucial to find an effective approach to verify the quantum effects of gravity in various kinds quantization assumptions. On the other hand, experimental verifying the quantum effects of gravity can only be showed by some extremely weak electro-optical signal. Thus, realizing the detection of extremely weak electro-optical signal at the quantum level, has become the only way to verify the quantum effects of gravity. With the development of low temperature and micro-scale experimental techniques in recent years, some quantum coherence phenomenas, which were used to be unreadable, have been experimentally observed and controlled. Recently, quantum regulation and control have become a research hotspot.Hawking radiation of black holes, which is an important content of this paper, has always been an important part of phsics. After decades of research, in theory, people no longer doubt its accuracy, theoretically. However, this theory has not yet been given a good experimental verification. There are several major difficulties:(1) We now know that, the nearest black hole from our earth is many light-years away, to actually measure the Hawking radiation is almost impossible; (2) The presence of the cosmic microwave background radiation in space, as a product of the Big Bang, will produce about 2.725K background radiation temperature, while the Hawking radiation temperature of an astronomical black hole will be lower than the temperature of cosmic microwave background radiation, so in order to directly measure the Hawking radiation temperature in space is extremely difficult.Fortunately, by creating a low background temperature, some domestic and foreign research teams have simulated black holes in the laboratory system or object in recent years. Those experimental ways provide a new approach to study the Hawking radiation, and promote the study of Hawking radiation become the focus of theoretical physics. However, those reported experiments seems like some idealized assumption, at least, to a certain extent. In fact, there also exists many difficulties when experimentally carry out those simulation experiments. The most obviously difficulty is that, the Hawking radiation temperature, which is need to be detected, is extremely low, and the requirements of experimental accuracy are very high. Additionally, how to determine the conditions for the formation of a black hole event horizon in is those simulation experiments? This is a crucial barrier which need to be overcome. Although in theory, the condition for the formation of a black hole event horizon can be convincingly proved in those simulation experiments, converting the condition to a visible physical behavior still faces many difficulties. So we want to find an experimental way, which is easier to be controlled, be detected and be trusted in current technical level.The main work of this paper can be divided into two parts:The first part is related to the theoretical study of quantum thermal effect of Hawking radiation and entropy for black holes:Firstly, using the modified tortoise coordinate transformations, we study the Hawking radiations of scalar and Dirac particles in non-stationary Kerr black holes, and Weyl neutrinos in accelerating Kinnersley black holes, respectively. Comparing our result with the one derived from traditional tortoise coordinate transformations, we find that significant deviations exist between the corresponding temperatures under different coordinate transformations. Under some special parameter condition, such deviation can reaches as high as two orders. Since there is no approach to directly measure the Hawking radiation temperature, it is difficult to find a convincing criterion to determine the result derived from which coordinate transformation is more consistent with the actual physics. In other words, we further illustrate the importance and necessity to experimentally verify the Hawking radiation and other corresponding quantum gravitational effects.Secondly, using the non-equilibrium Landauer transport model, we study the Hawking radiation of a Kaluza-Klein black hole. We find that, the corresponding energy-momentum tensor flux derived from such model is self-consistent with the one derived via gauge and gravitational anomaly. Such result laid the theoretical foundation for our following study, in which we analogue Hawking radiation in a composite right/left-handed transmission line.Finally, we discuss the method of calculating black hole entropy via adiabatic invariant, which is proposed by Majhi and Vagenas. Additionally, we adopt the modified adiabatic invariant method to study the properties of black hole entropy and area spectrum for a Kerr-Sen black hole. Our results are consistent with the current widely accepted conclusions, i.e., the entropy spectrum is quantized and equally spaced. However, due to the lacking of a convincing evidence, whether the spacing of the area spectrum is equally spaced or not, is still somewhat controversial.The second part of this paper is mainly related to the experimental verification of quantum gravitational effects, the corresponding contents are:First, starting from an acoustic black hole model, we briefly review the development of the simulation of gravity. Subsequently, we introduce some influential experiments about simulating Hawking radiation of black holes, we also explain the practical difficulties which are suffered by those experiments.Finally, based on the properties of complex right/left-handed transmission lines, we propose an approach to analog Hawking radiation of a black hole in a composite left/ right-handed transmission line. We construct a Painleve-Gullstrand form space time matrix of a black hole in the transmission line, and discuss the possibility of finding an experimentally evidence, which can determine whether an effective event horizon have been constructed in the transmission line. Moreover, we analyze the experimental error and the corresponding ways to improve the experimental accuracy. By analyzing the character of phase transformation in the complex right/left-handed transmission line, we find that the phase transformation equals to zero at the transition frequency. In other words, due to phase velocity transforms from negative to positive abruptly, the corresponding phase velocity approaches infinity. Such characteristic can be used as an reliable criterion for determining the effective event horizon of a black hole. Finally, applying the method of calculating the effective Hamiltonian, we quantize the energy of transmission line, and discuss the effective approach to control the producing direction of disturbed photons. We have established an effective relation between the event horizon of a black hole and the transition frequency of a complex right/left-handed transmission line. By observing the characters of transmission line at the transition frequency, we can find an evidence to determine the effective event horizon of a black hole. Compared with previous similar Hawking radiation simulation experiments, our approach is easier to achieve Hawking radiation simulation, and is better in the ability of anti-interference from noise. Hopefully, our approach has an important reference to experimentally verify and detect Hawking radiation of black holes.The main contents of this article belong to weak signal detection, as well as the leading-edge research topics of experimental study of quantum physics. System in our study belong to mesoscopic systems, the corresponding research in this area has now become an important and remarkable topic in quantum physics research field. By studying this subject, we reveal the physical image of macroscopic quantum phenomenon, which is caused by local vacuum quantum fluctuations. The relevant research results will provide an important reference for weak signal detection, as well as realization of quantum control and quantum measurement on experiment.