Study On The Dynamic Characteristics Of Cold Atom Gas In Harmonic Trap

In recent years,with the development of experimental technology,cold atoms trapped in external potential have become an important research system by properly controlling the interaction between atoms and external potential.Based on this research system,we have proposed a novel atomic interferometer scheme,which improved the measurement accuracy of gravitational acceleration greatly compared with the previous measurement results.While,in this atomic interferometer scheme,the experimental realization of the measurement accuracy is greatly depends on the density distribution of the atomic gas.Therefore,this paper focuses on the discussion of the atomic interferometer program and the density distribution of Fermi gas at different temperature is also discussed in detail.Firstly,based on one novel multi-modes Kaptiza-Dirac(K-D)atomic interferometer[1],a Multi-mode atomic interferometer under the multiple K-D optical pulses was addressed[2].By the K-D optical pulse act on the cold atom which were trapped in the harmonic trap(the effect of the mirror operations),so that the cold atoms were divided into the multiple beams with the same as the initial atomic beam.Under the effect of the harmonic trap,these atomic beams would be automatically collected during a full cycle.Then,we took the second and even the n times of K-D optical pulses act on the cold atoms,to achieving a complete dynamic process.Eventually,at the time half of the cycle after the n times of K-D optical pulse,different phases of atomic beam between neighboring modes could be estimated by measuring the number of particles.We can calculate the measurement accuracy of the gravitational acceleration in this interferometer to9g/ g10 / n-(35)(28)with according to the Fisher information and Cramér-Rao bound.It can be seen that by increasing the number of K-D pulses,it can effectively increase its measurement accuracy.Then,on the basis of this interferometer scheme,we discuss theinfluence of the measurement accuracy with the harmonic trap under the external disturbance,and find that the measurement accuracy of the interferometer decreases with the increase of the disturbance intensity.Then,by switching on and off the gravitational field in different cycles,we find that it has a certain effect on the measurement.Finally,by considering the displacement deviation between the center position of the harmonic trap and optical field,we calculate it to find that it have the same order of magnitude with the measurement of gravitational acceleration.Therefore,the principle of the multi-mode atomic interferometer can also be applied to the production of a new type of displacement sensor.In the third chapter,starting from the quantum many body theory,we deduce the density distribution function of Fermi gas under the ideal Fermi system.Then,based on the Fermi-Dirac distribution law and the exact solution of wave function in the one-dimensional harmonic trap,we derive the expression of the density distribution of the Fermi gas in the one-dimensional harmonic trap.In addition,we discuss the related properties of Fermi level,Fermi temperature and chemical potential in the Fermi system by combining the theory of free electrons in metals and related literature.Finally,on this basis,we plot the density distribution of Fermi gas in one-dimensional harmonic trap and compare it with the density distribution satisfying the Boltzmann distribution law at high temperature...