| The highly controllable nature of ultracold atoms makes them an ideal platform for the simulation of dynamical processes in systems.The regulation of interactions between ultracold atoms is a hot research topic in the study of the dynamical evolution of systems,and periodic and quasiperiodic driving is an effective method of regulation in dynamical studies,where the regulation of interatomic interactions using periodic or quasiperiodic driving can lead to many novel phases.This paper therefore investigates the dynamics of cold atomic systems under these two types of driving methods,using both periodic and quasi-periodic driving of cold interatomic interactions.In the first part of this paper,the dynamics of a two-cooled atomic system with periodically driven interactions in a three-dimensional resonator potential well is investigated.The effects of drive frequency,square wave duty cycle and drive amplitude on the average relative distance between atoms,the probability of atoms occupying the eigenstate and the dynamics of the Tan’s contact are investigated using a square wave modulation of the s-wave scattering length.We find that when the drive frequency satisfies the energy level difference relation,the system is excited to a specific eigenstate and a two-energy oscillation occurs,while the frequency component of the Tan’s Contact oscillation with time coincides with the frequency of the average relative distance between atoms oscillating with time.When the driving frequency is approximately equal to the average of the energy level differences corresponding to each of the two scattering lengths,the system undergoes strong coupling.Changing the duty cycle of the square wave modulation in a two-energy level oscillation system shifts the position of the driving frequency corresponding to the strong coupling.We use the extended Rabi formula to obtain the conditions for the system to undergo resonance satisfaction.As the driving amplitude increases,the system increases from exciting one state to exciting more states,and the excited states will be higher than the eigenstates corresponding to satisfying the energy polarity relation.The second part of this paper investigates the dynamical evolution of a system with quasi-periodically driven two-atom interactions.Two approaches to quasi-periodic driving interactions are used.The first one is to superimpose two square waves with different driving frequencies and to study the dynamical evolution of the system corresponding to changing the driving amplitude and duty cycle of one of the square waves.We find that by increasing the driving amplitude of the square wave,the atoms occupy higher eigenstates and that adjusting the duty cycle of the square wave changes the location where the strong coupling of the system occurs.The second is a Fibonacci quasi-periodic sequence driven interaction,where the scattering length varies according to the Fibonacci quasi-periodic sequence and the system is in a steady state.1 and m are used as parameters affecting the proportion of the scattering length occupied in the generalised Fibonacci sequence,and when the scattering length varies according to the first type of generalised Fibonacci quasi-periodic sequence,as the value of 1 increases,the system will experience dienergetic oscillations.Finally,studying the case of the scattering length driven by the second type of generalized Fibonacci quasi-periodic sequence,we find that the system will gradually weaken and stabilize from resonance as m increases.In this paper,we focus on two-body systems with periodically driven and quasiperiodically driven interactions,and obtain the basic laws for the dynamical evolution of these two types of systems,which provide some basis for the study of complex many-body problems. |
