Study On The Dynamics Of Soliton In A Two-component Mixed System

Many academic researchers had studied the macroscopic nonlinear collective phenomena in an ultra-cold atom condensate system by numerical simulations becaue the various parameters in the ultracold atom condensation system can be controlled artificially.In addition,the ultra-cold atom condensate system has also become a platform for studying peculiar phenomena in other fields of physics,such as neutron star simulation and so on.In this paper,we adopts the method of numerical simulation to study the dynamics of solitons in the single-component and two-component Fermi quantum systems under different interaction parameters.1.The dynamics of soliton in the single-component Fermi pair condensate.We study the dynamics of the soliton in the Fermi pair condensate and in the one-dimensional harmonic potential.First,based on the time-dependent macroscopic order parameter equation of ultra-cold Fermi gas,we find that at the BCS superfluid side,with the interaction parameter increases or the number of particles increases,the peak value of the soliton increases and the width of the soliton decreases.At the molecular BEC side,with the interaction parameter increases or the number of particles decreases,the peak value of the soliton continues to increase,and the width of the soliton continues to decrease.Whether it is at the BCS superfluid side or the molecular BEC side,the width of the soliton decreases with the increase of the interaction parameter,and the peak of the soliton increases with the increase of the interaction parameter.However,the soliton peak at the BCS superfluid side is larger than the molecular BEC side,and the width of soliton at the BCS superfluid side is smaller than the molecule BEC side.The nonlinear real-time evolution method is used to analyze the stability of the soliton in the ultra-cold Fermi gas.The analysis find that the soliton can still propagate stably after the disturbance.2.The dynamic properties of soliton in two-component Bose-Fermi mixed gas.The properties and evolution of solitons in a two-component Bose-Fermi mixture gas in a quasi-one-dimensional harmonic potential are studied by using coupled time-dependent nonlinear Schrodinger equations.We adjust the number of particles or the scattering length between atoms to change the strength of the interaction between atoms for studying the spatial distribution of solitons in the two-component Bose-Fermi mixed gas.we find that:(1)The number of Bose atoms remain,and when the number of Fermi atoms is increased,at the molecular BEC side:the peak of the soliton in the Bose component becomes larger and the width becomes smaller,and the peak of the soliton in the Fermi component becomes smaller and the width becomes larger;at the BCS superfluid side:the soliton peaks in the Bose and Fermi components both become larger and their widths become smaller.(2)The number of Fermi atoms remain,and when the number of Bose atoms is increased,at the molecular BEC side:the peak value of the soliton in the Bose component becomes smaller and the width becomes larger,and the peak value of the soliton in the Fermi component becomes larger and the width becomes smaller;at the BCS superfluid side:(a)When the number of bosons is greater than 400,with the Bose atoms increase,the peak of the soliton in the Bose component becomes smaller and the width becomes larger,and the peak of the soliton in the Fermi component becomes larger and the width becomes smaller.(b)When the number of bosons is less than 400,with the number of boson particles increases,the peaks of soliton in Bose and Fermi components both become larger and their widths become smaller.(3)When increasing the absolute value of the scattering length between Fermi atoms,at the molecular BEC side(increasing the positive scattering length between atoms):the soliton peaks in the Bose and Fermi components become smaller and the width becomes larger;at the BCS superfluid side(increasing the negative interatomic scattering length):the soliton peaks in the Bose and Fermi components both become larger and the width becomes smaller.(4)When the negative scattering length between Bose and Fermi atoms is increased,the peak value of solitons in each components becomes larger and the width decreases both at the molecular BEC side and the BCS superfluid side of the Fermi component.The nonlinear real-time evolution method is used to analyze the stability of the static soliton in each components when the Fermi component is at the molecule BEC side and BCS superfluid side.The analysis results show that even if the wave function is multiplied by a strong disturbance factor,the static soliton in each components can propagate stably.