Collective Emission Of Particles From Parametrically Driven Bose-Einstein Condensates

Ultracold atomic gases provide a versatile platform on which one can investigate the exotic behaviors of quantum matters,and explain various fundamental physical problems in manybody systems,such as quantum phase transition,quantum magnetism and nonequilibrium phase.Periodic driving is one of the effective tools in the modulation of particle interactions,which has been widely utilized in exploring nonequilibrium many-body dynamics and their coherent manipulations.In the recent “Bose Fireworks” experiment,by exerting a sinusoidally alternated magnetic field on the trapped Bose condensate and hence tuning the particle interactions,experimentalists observed significant particle jet emission,while in a series of subsequent related experiments they also observed the collective mode,density oscillations,etc.,exhibiting potential applications in quantum simulation and quantum metrology.The key to understanding the above experiments and making accurate predictions is that one constructs effective and intuitive theoretical models,through which one can not only explore the basic conditions of how the excited particles escape from the trap,but also reveal the quantum nature of the matter-wave jet emission.In this thesis,by using one-dimensional lattice models we systematically investigate the behaviors of the collective particle emission from parametrically driven Bose-Einstein condensates.First,we develop a semi-infinite lattice model to simulate the pair emission observed in the “Bose Fireworks” experiment,and find the distinct behavior of the single-particle emission.Within the mean-field theory and the linear response theory,we obtain the explicit expression of the single-particle emission rate under weak drive,and reduce the pair emission rate to onedimensional integrals.By converting the equations of motion into a single variable and then perform numerical calculations,we also explore the full nonlinear behaviors,i.e.,a series of high-order dynamical properties of the single-particle emission,and predict some regimes of realizing the single-particle emission in experiments.For example,the trapping potential should be deep enough to separate the spectrum of different modes,and the drive frequencies are within discrete intervals rather than continuous ones.Second,we study the effect of resonant enhancement based upon infinite lattice model,where in the trap there are two coupled condensates.We explain the density oscillations and the dependence of the emission rate on the modulation strength,and give the physical picture of the threshold,which coincide with the observed characteristics.By exerting periodic drive to the antisymmetric mode,we find that the modulated interactions excite a collective mode rather than directly emit particles,which leads to density oscillations.These collective oscillations in turn drive particle emission and amplify the drive,allowing a weak modulation to produce a macroscopic number of particles.Meanwhile,we find that the amplitude dependence of the emission rate has a typical threshold behavior as seen in the “Bose Fireworks” experiment.I.e.,there exists a minimum drive: if the modulation strength is weaker than the threshold,the total particles in the condensate are almost unchanged for all time,otherwise the trapped particles oscillate in the very beginning,and then distinctly decay.Third,we explore the dynamics of multiple coupled condensates under periodic drives,and find the exotic phenomenon of intermittent emission,as well as further elucidate its internal mechanism.By perturbatively analyzing different modes of the system,which leads to their respective regimes of instabilities,we not only obtain two main frequencies,under which the system can emit a large particle jet,but also find that the emission is intermittent rather than continuous.The time evolution of the trapped particles exhibits a stair-like decay,where a larger drive induces a more significant intermittency.We give an explanation to the intermittency,and illustrate that particle emission of this kind might be the characteristic of multiple-condensate systems with analogous configurations and couplings.