Theoretical Study On Laser Cooling And Trapping Of Ytterbium Atoms For Optical Clock

Study on optical atomic clocks is a hot topic in the field of fundamental physics and frequency metrology as the fractional frequency uncertainty of the microwave atomic clock is approaching the quantum projection noise limit. The need of more accurate atomic clocks for testing the fundamental physical problem such as measuring variation of fundamental constants, testing the relativity theory is very urgent. With the rapid progress in space science and technology, the current atomic clocks also can not fulfill the requirements. As the optical frequency is around several orders of magnitude higher than the microwave frequency, the fractional frequency uncertainty of the optical clock may be much smaller than that of the microwave clock. Therefore, the optical clock is considered as the candidate of the next generation frequency standards. The state-of-art single ion optical clock has achieved the fractional frequency uncertainty on the order of 10-18 and it has been used for testing the variation of fundamental constants and the theory of relativity. The variation of fundamental constants has been restricted in a very small range. However, the single ion optical clock will be limited by quantum projection noise according to the quantum theory. An important way to reduce the quantum projection noise is to increase the number of quantum absorbers. In the ion traps, the number of ions is limited by the coulomb repulsion. The optical lattice clock inherits the merits of the ion clock and the number of quantum absorbers can be greatly increased. The optical lattice clock may surpass the ion clock in the future. Therefore, considerable strides have been taken recently toward this kind of optical clocks. Ytterbium lattice clock is one kind of the lattice clocks. Currently, a key issue of the optical lattice clock is how to make the clock line immune to the environment perturbations. Improving the methods of cooling and trapping of ultracold Ytterbium atoms is the major solution.Cooling and trapping Ytterbium atoms is a complex work. Many problems need to be solved from a control circuit to a laser and the cooling and trapping optical systems. Currently, we need to solve three problems. The first one is designing and constructing highly efficient and compact laser sources for laser cooling and trapping. Increasing the efficiency of the laser and making it smaller can improve the cooling results and simplify the system. The second one is that the final temperature of the second stage Doppler cooling of Ytterbium is much higher than the Doppler cooling limit. The magneto-optical trap on the intercombination transition of strontium can cool the temperature of strontium atoms down to the Doppler cooling limit. However, the final temperature of magneto-optical trap on the intercombination transition of Ytterbium is much higher than the Doppler cooling limit. The third one is cooling the Ytterbium atoms to zero-point energy of motion. Recent frequency evaluation of the Ytterbium atomic clock indicates that density related frequency shift is one of the major sources of the systematic uncertainties. Cooling the temperature of Ytterbium is one way to reduce the density shift. The success of the single ion clock shows that cooling the Ytterbium atoms down the zero-point energy of motion is very important for the high accuracy optical clock.We investigate the three problems in this thesis. In chapter 1, we briefly introduce the development of atomic clocks from micro-wave to optical wave and the basic principle of key technology of optical clocks. We introduce the development of the Ytterbium atomic clock and summarize the current state of it. We briefly describe the relation of the cold Ytterbium between the optical clocks and the principle of slowing and cooling Ytterbium atoms.In chapter 2, we investigate how to efficiently generate the first stage Doppler cooling laser source. Firstly, we calculate the relation of second harmonic power between the focusing of fundamental wave, the walk off effects and the phase matching and obtain an expression of the second harmonic power. Then we use it for optimizing the second harmonic generation of a diode laser at 797.822 nm in a LiNbO3 crystal. Firstly, we calculate the phase matching condition and the relating crystal parameters. Then, we use the expression of the second harmonic power for calculating the optimal condition of the fundamental beam. According to the optimal condition, we design the resonator for enhancing the fundamental wave. According to this scheme, we can obtain more than 180 mW second harmonic power which corresponding to the conversion efficiency of 37%.In chapter 3, we investigate how to efficiently generate the second stage Doppler cooling laser source. Firstly, we study the coupling of the fiber laser output into the waveguide. After the experimental investigation, we find an efficient coupling optical system which is consisted of two fiber collimators and two collimating lenses. The coupling efficiency is about 10% higher than that of the objective lens coupling system. Secondly, we investigate the dependence of the second harmonic generation conversion efficiency on the fundamental light polarization and the waveguide temperature. Thirdly, we study the collimating of the green light. We can obtain a beam quality of M2≤1.1 with an objective lens and a focusing lens. Fourthly, we analyze the asymmetric ripples in the temperature tuning curve measured in this experiment. The result shows that the asymmetric ripple is mainly caused by the optical inhomogeneities. Fifthly, we study the second harmonic generation at high fundamental power. The experimental results show that there is an efficiency drop at the high fundamental powers. Through simulations, we find that the loss can be divided into two stages. In the first stage, the loss is dominated by the absorption. In the second stage, the loss is a combined effect of the absorption and the thermal dephasing.In chapter 4, we study the Doppler cooling mechanism of the 1st stage and the 2nd stage magneto-optical trap. Firstly, we study the mechanical and the thermal dynamical properties of the 1st stage magneto-optical trap and interpret the previous reported experimental results. Secondly, we study the mechanical and the thermal dynamical properties of the 2nd stage magneto-optical trap. The result shows that the 2nd stage magneto-optical trap has to be attributed to two cases according to their mechanical properties. In the first case, the influence of the gravity can be neglected. In the second case, the influence of the gravity can not be neglected. The thermal properties are also different in the two cases. According to the result, we calculate the dependence of the temperature of atoms on the magneto-optical trap parameters.In chapter 5, we study the physical mechanism of the cancellation of the light shift of the clock transition and the control of the cooling and trapping of Ytterbium. Firstly, we derive the formula of light induced polarizability and calculate the "magic wavelength" of Ytterbium lattice clock. Meanwhile, we calculate the optical potential of the one dimension and the three dimensional optical lattices. Secondly, we study how to control the cooling and trapping organically. We integrate the action components with the multifunction data acquisition card and the corresponding software platform. In chapter 6. we study how to cooling the Ytterbium atoms to a lower temperature on the basis of the Doppler cooling in magneto-optical trap and eventually cool the atoms down to the zero-point energy of motion. Firstly, we introduce the interaction of the Ytterbium atoms in the optical lattice and it influence on the optical clock. Secondly, we introduce the principle of the sideband cooling and the physic mechanism of it. Thirdly, we introduce the principle of the Raman transition and study the sideband cooling of the Ytterbium atoms down to the zero-point energy of motion with it. According to the analysis, the temperature of the Ytterbium atoms can be cooled down to 1μK. Combined the sideband cooling and adiabatic cooling, the optical lattice clock can be greatly improved.In chapter 7, we summarize the work in this thesis and propose possible developments in the future.