The Rotor Model And Its Application In Dynamics Of Cold Atoms

Since the invention of the laser and the successful applications of lasers in atomic physics, the control of atomic motion has experienced a big development in the mid80’s. In the experiments with a proper frequency adjustment near to atomic transition frequency, the atomic gas can be cooled down to a very low temperature to realize a new phase:Bose-Einstein condensation. In the lateral cooling or trapping experiments on atomic ensembles, the beam of the controlled atoms can reach an unprecedented intensity and a single atomic motion as well as the collective motion of atoms can be precisely controlled. Nowadays, in the atomic wave guides or on the atomic chip, people can freely confine cold atoms into a very small region and coherently control the internal and external freedom of the atoms by using certain high-intensity local fields.Under the background of dynamic control on quantum systems, this thesis is devoted to study the classical and quantum dynamics of partials controlled by electromagnetic fields with the nonlinear dynamic method under simple rotor models. For different particles in different trap potentials, the classical behaviors and quantum dynamics are extensively analyzed by using different mappings. First, the standard mapping rotor (which is related to many physical processes such as molecular rotation, spin dynamics, et. al) is investigated in detail and readily applied it on cold atoms manipulated by a phase-modulated standing wave. The linear classical diffusion of the cold atom in the modulated standing light filed is studied with the mapping dynamics of the standard rotor model. Bashed on quantum theory, the quantum dynamics of the cold atom is comparatively considered. Because of the quantum coherent effect, coherent interferences between different angular waves, the quantum dynamics exhibit a manifest localization behavior which suppresses the linear diffusion of the atom in a long-time evolution. Then the mapping model of harmonic rotor (which is closely related to the dynamic of a charged particle in an electromagnetic field) is studied. The mapping dynamics reveals different regular patterns in phase space and find phase transitions between regular patterns and chaotic distributions by the damping processes. The results indicate that the damping can either enhance the chaotic randomness of the system or depress the randomness of the system depending on the specific parametric regions. Finally, the single rotor model is generalized to a collective model of global-coupled rotors, which is also applied to the cold atomic gas in a cavity light. In this section, the cold atoms in a ring cavity are studied first under a general pumping condition. Based on semi-classical equations of motion, the dynamical spectra of the atoms under different mechanical environment are investigated. The physical mechanism of the light gain and the nonlinear Raman resonance conditions are given by a simple quantum analysis. Then, under a large detuning, the system can simplify to a collective standard rotors which is globally coupled to a cavity light field. This simple collective rotor models can dramatically reduce the freedom of dynamical study on the collective behavior for the atomic gas often consist of a large number of atoms above105.The conclusions of this paper are as follows:(1) The dynamical simulation and the classical statistical method both demonstrate that the diffusion coefficient of a standard mapping is a constant under large kick intensity, which reveals a linear diffusion behavior of the rotor stimulated by a lager-amplitude pulsing force.(2) The cold atoms in opto-magnetic trap are investigated both under the standard rotor model and under the quantum wave method. The classical dynamics shows a linear diffusion with a large phase modulation and the corresponding quantum dynamic demonstrates a localization characteristic of the atomic motion in long-time evolution.(3) With the picture of a charged particle trapping in a harmonic trap, a harmonic rotor model is derived under the pulsed electromagnetic field. In a certain parametric region, random net structures appear in the phase space and a phase transition from regular pattern to random distribution can be realized in this system. By including the damping process, the chaotic features of the system will be enhanced or depressed by the damping process with different parameters.(4) For dynamic behaviors on the the collective rotors, a global-coupled model is available on the cold atoms in a ring cavity. The study on the full model without adiabatic conditions indicates that the collective spectrum of the atoms is dramatically influenced by the external motion of the atoms. The simulation of collective dynamics of free atomic gas gives the usual Mollow spectrum. Compare the Mollow spectral structure with the confined spectrum of the trapped atoms, a high gain dynamical scattering spectrum with a comb-like profile is found. The spectrum lines directly reflect the trapping constraint of the dynamics with a simple Raman resonant relation. Second, in a big detuning of the pump field the system is equivalent to a large number of collective resonant rotors which are globally coupled with a cavity field. The model used to study the collective behaviors is given in the end.