Dynamics Of Two Ultracold Atoms With Interaction In A Three-Dimensional Harmonic Trap

The two-body problem is a hot topic in the field of nonequilibrium physics,which reveals the fundamental laws and properties of systems and provides a foundation for studying complex many-body problems.Ultracold atoms are stable and controllable,making them a great tool for studying two-body systems.In quantum mechanics,the harmonic oscillator is an important model that is not only easy to implement experimentally but also easy to solve theoretically.Under certain conditions,many complex systems can be simplified to harmonic oscillator systems.First,the thesis focuses on the quench dynamics of a two ultracold atoms with interaction in a three-dimensional harmonic trap.The interaction between atoms is represented by the s-wave scattering length,and it can be instantaneously changed via Feshbach resonance.The thesis analyzes the evolution of the average relative distance between atoms and the Contact as a function of time after quenching the system from a scattering length of zero to a finite value.Double-period oscillations in the average relative distance are observed within a certain range of scattering lengths,mainly due to the superposition of the first three eigenstates.The Contact oscillates irregularly with time,and the period of oscillation contains components of multiple eigenenergy differences.This thesis then proceeds to study the Floquet spectrum and evolution of systems with periodic driving of interaction.Even driving frequencies lead to densely packed quasienergy levels,while other positions result in scattered levels.The driving force’s initial position and amplitude significantly affect the convergence of quasienergy levels.The degree of convergence reflects the coupling strength between intrinsic energy levels within a period,and convergence relates to persistent excitation,while dispersion associates with system stability.We propose a mechanism to selectively excite specific intrinsic energy levels by avoided crossings,this is a useful guide for preparing desired initial states in experiments.