Controlling Dynamics Of Ultracold Atoms By Super-Gaussian Light Fields

Ultracold atoms have played an important role in precision measurement and quantum simulation due to their high purity and excellent controllability.One commonly used quantum simulation method is to manipulate the dynamics of ultracold atoms through optical fields,such as using optical lattice potentials to study physical problems.In recent years,the emergence of flat-top beams has provided a new preparation method for super-Gaussian barriers and potential wells,allowing us to use super-Gaussian light to simulate square barriers and study some classical models in quantum physics,such as particles tunneling through square barriers and the FermiUlam model in Fermi accelerators.In this paper,we use super-Gaussian barriers to investigate the dynamic evolution of ultracold atoms in the above two models and obtain the following conclusions:(1)By numerically computing the momentum evolution of a quantum particle with a Gaussian wave packet tunneling through a square potential barrier,we have discovered a novel phenomenon: even though the initial energy of the particle is lower than the height of the barrier,there is still a significant probability for the particle to gain energy higher than the barrier when entering the barrier region.This phenomenon can be understood as a result of the non-locality of the momentum state,in which momentum can be transferred among different states.Alternatively,it can be considered from the perspective of the Heisenberg motion equation of the momentum operator,in which the uncertainty principle allows the particle to accelerate after entering the barrier region.This phenomenon provides a new perspective for us to deeply understand particles tunneling through square barriers.Moreover,the duration for the particle to have energy higher than potential barrier could be explored for defining quantum tunneling time.(2)We proposed a Fermi-Ulam model with a square potential barrier of finite height,and investigated the effects of the barrier height,amplitude,and oscillation frequency on the dynamics of ultracold atoms.We found that although a small part of wave packets with energy larger than the barrier are reflected by the barrier walls,the limit of particle acceleration still decreases as the barrier height is lowered.The maximum value of particle velocity also dependes on the amplitude and frequency of the oscillation of the barrier,where larger amplitudes and frequencies lead to higher maximum instantaneous velocity of the barrier after experiencing an elastic collision with the moving barrier,according to the law of momentum conservation.However,due to the presence of tunneling effect,a higher speed of the barrier movement will greatly increase the transmission rate,resulting in a reduction in the number of particles that are accelerated.Therefore,when using the Fermi-Ulam model to accelerate particles,it is necessary to consider the effects of barrier height,amplitude,and frequency on the quality of acceleration.