Theoretical Study On Interaction Effects In Ultracold Bosonic Gases

As a controllable ideal experimental platform,Bose-Einstein Condensation(BEC)plays an indispensable role in precision measurement,quantum simulation and so on.With tech-nologies like Feshbach resonance and magneto-optical trapping,people are able to manipulate the interactions among atoms,which greatly enriches the study content of ultracold atoms.In this thesis,we mainly investigate the interaction of the Bose system.Concretely,we study the interaction between impurities and quantum droplets,respectively.In this thesis,the first work is study of the interaction between two impurities present in a homogeneous Bose gas.For the sake of the accuracy of results,during the derivation,we use the perturbation method to carry out the calculation.The calculation results are retained up to second order.Due to the divergent term in the calculation,we employ the renormalization to deal with this divergency.We then obtain the Gross-Pitaevskii(GP)equation of the system,and obtain the ground state by using MATLAB.After that,we visualize and analyze the results of the interaction between impurities from three aspects: ground state energy,interaction force and system density.It turns out that the effective interaction between two impurities,attractive or repulsive,is related to the interaction between each impurity and surrounding bosons.In the second work,we study quantum droplets,which are new quantum exotic states.Quantum droplets are induced by the competition between the attractive mean-field term of the ground state energy of the Bose gas and the Lee-Huang-Yang(LHY)correction term derived from quantum fluctuations,which causes a stable state instead of collapse.We consider the three-dimensional two-component Bose gas with spin-orbit coupling,and then obtain the excitation spectrum within the Bogoliubov theory.We also calculate the equilibrium density and ex-tract the GP equations.Results of the LHY correction energy caused by quantum fluctuations show that the spin-orbit coupling may enhance the repulsive interaction caused by this energy.Therefore,with a suitable parameter in certain range,that is,when the attractive mean-field term of the ground state energy is in balance with the LHY correction term derived from quan-tum fluctuations,a stable quantum droplet state may exist.Our study paves the way for further exploring the exotic states like quantum droplet.