Effects Of Crystal-field Parameters On Electromagnetically Induced Transparency In A Rare-earth-doped Crystal

Atomic coherence is an important research topic. In resent years, people have found many new physical phenomenons by researching the interaction between coherence and multi-lever atomic. Such as electromagnetically induced transparency, high disperse without absorption, the coherent seize of particles, the gain of lasing without inversion, and so on. My thesis will research one of those physical phenomenons, the electromagnetically induced transparency (EIT), which has been paid much importance in the researching of non-linearity optical, reversion laser without particles and the area of optical signal. While the EIT in solid, especially the rare-earth-doped crystal is a new project in recent years. In my thesis, I paid much importance to the EIT of rare-earth-doped crystal. I calculated the ETI absorption coefficients and transparent graphs of different crystals in the rare-earth-doped crystals and different transition levels of rare-earth ions in the same crystal and then make analysis.The first part is the basic theory support for my calculation. Firstly, I introduced the conception, researching history and development of EIT. Electromagnetically induced transparency is to change the medium absorption character to a laser by adding an electromagnetic field, so the laser of some frequency can be transparent to the medium. Secondly, I introduced the theory of interaction between light and medium; described the three basic coordinates: Schr?dinger coordinate, Heisenberg coordinate and interaction coordinate; explained the theory tools of analyzing EIT:Ⅰ, density functor, density matrix and method of probability swing and rotation wave approximate;Ⅱ, dressed atomic and theory about it. Lastly, I introduced the theory of crystal field, rare-earth spectrum and Judd-Ofelt.The second part is not only the emphasis of my thesis, but also the innovation. Based on the theory in the first part, in order to achieve a better phenomenon on experiment of EIT in solid , aimed at the shortcomings and lacks in the experiment about the crystal-field strength and phonon which can not be ignored in crystal, we gave out how to select the best rare-earth-doped crystal, the impacts of unfavorable factors will be minimized, as well as how to select ion transition levels to improve the problem that crystal-field strength is too large for rare-earth-doped crystal to achieve EIT.Firstly, there is no Doppler effect because of the heat motions of molecules for EIT in solid like in gas, but impacts of crystal lattice vibration and crystal-field potential which is inherent in the crystal is still not lose sight of. In considering the above two factors, we had these two changes brought about by unfavorable factors add in the calculation of absorption coefficient and simulation of transmission curves of EIT to improve the effect of EIT in rare-earth-doped crystal, shown in fig.1. We found that the effect of crystal-field potential to EIT is big, but because of the shied outside, the effect of photon to EIT is small. So we need the rare-earth-crystals with few impacts of crystal lattice vibration and crystal-field potential to achieve EIT on experiment. Secondly, as an example, we calculated the parameters of Nd3+ in crystal and absorption coefficient and transmission lines of EIT in rare-earth -doped crystal Nd3+: YAlO3. Then we calculated the crystal-field parameters and the absorption coefficients and the transmission curves of EIT of the other five rare-earth-doped crystals, Er3+: YAlO3, Er3+: YAG, Er3+: LaF3, Pr3+: Y2SiO5 and Tm3+: YAlO3 by the same way, besides that we also compared EIT transmission curves of six different rare-earth-doped crystals under the impacts of crystal field, shown in fig.2. we found from fig.2 that the transparent efficiency of EIT in Er3+:YAlO3 is best, Tm3+:YAlO3 is better, the crystal-field strengths of which are smaller. While the transparent efficiency of Er3+:YAG and Nd3+:YAlO3 is not good, which crystal-field strengths are bigger. The crystals with worst transparent efficiency are Pr3+:Y2SiO5 and Er3+:LaF3,which crystal-field strengths are too big. When crystal-field strength is too large, the relaxation rate of rare-earth ion becomes big, the effect of EIT is not good; while the crystal-field strength is too small, the transition oscillator strength of rare-earth ion is not enough, so it is not good for or even can not realize EIT. So when the crystal field strength is limited at a certain range, the smaller the field strength becomes, the better the effect of EIT is.Finally, we studied at the EIT of rare-earth-doped crystal Pr3+: Y2SiO5 which is commonly used for experiment but with big crystal-field strength. Four different sets of coupling and probing levels of Pr3+ ion are selected, under which we calculated and analyzed the four different absorptions and transmission curves of EIT in aΛ-type system. We found that if the crystal-field strength in the rare-earth-doped crystal was too large, the selection of coupling and probing levels of rare-earth ion can overcome the shortage. For aΛ-type system, the smaller the interval between two levels is, the better the transparent of EIT becomes. To sum up, the transparent effect of EIT in solid is more obvious than in gas, but the impacts of crystal-field strength, potential and phonon which can not be ignored in crystals are introduced too. There are some persons before who had discussed the influence of density and temperature to EIT. But no one has considered the factors in crystals. The creative points in my thesis are that, considering the negative factors above which the previous neglected, we made the theoretical calculations and transmission curves simulation of EIT in rare-earth-doped crystals on how to reduce these adverse factors and how to select the most suitable rare-earth-doped crystal to achieve EIT, then analyzed and compared, finally gave out conclusions. This thesis can be considered as theoretical guidance for the further development of experiment.