Studying Laser Cooling In Quantized Micro-cavity Using Algebraic Dynamical Method

Using the algebraic dynamical method, this paper investigates the laser cool-ing of a single atom in a quantized micro-cavity. The laser cooling of a two-level and three-level atom is discussed respectively.Firstly, a simple introduction about the development of the technology of laser cooling and the theory of the algebraic dynamical method is presented.In Section 2, the interaction between a moving two-level atom and a quan-tized cavity field is studied by the algebraic dynamical method and analytical solutions of the optical force and the cooling temperature are given. To explore the effects of the parameters on the radiation force and the temperature, we plot several figures to explain this. These results show that with the increasing of the coupling strength the radiation force increases but the temperature decreases, while the force decreases as the detuning increases. In addition, the coordinate of the atom and the trapping time have great influence on the force and the temperature.In Section 3, to begin with, the Hamiltonian of the interaction between a moving three-level atom and a quantized cavity field is given. Secondly, we find the algebraic generators of the system by means of the algebraic dynamical method, and thus the Hamiltonian can be written as a linear combination of the algebraic generators. Then, the density operator is calculated accordingly. Finally, based on the reduced density operator of the atom, the cooling force and the final temperature of the three-level atom are obtained. One can find the results of the three-level atom are different from that of the two-level atom, the three-level atom can explore more rich phenomena and there are more parameters that are varied to control the cavity cooling. Also, experimental results show the three-level atom can be cooled at a lower temperature.A summary is given in the last Section. Besides, we discuss some future research directions of the work.