Multi-Component Degenerate Quantum Gas Dynamics

Quantum simulation has attracted widespread attention as an emerging research field in recent decades.With the development of laser cooling and evaporative cooling technology,people have successively realized the condensation of bosons and fermions on the ultracold atomic platform.Ultracold atoms have many quantum-control schemes,such as the coupling of atomic spin and center-of mass momentum through artificial gauge fields,the interactions between atoms can be controlled by magnetic Feshbach resonance,and the atoms can be loaded into optical lattices,etc.people have done a lot of interesting and meaningful work on the ideal quantum simulation platform of ultra-cold atoms,for instance Bardeen-Cooper-Schieffer(BCS)-Bose-Einstein-Condensation(BEC)crossover,quantum droplets in binary BEC,and the quantum simulation of in-teresting phenomena such as Josephson oscillation,quantum Hall effect and topological physics.With the enrichment of quantum control,we can simulate the macroscopic prop-erties of quantum systems under different interaction parameters.For a BEC formed by microscopic bosons that comply with the Bose statistics,when the interaction is weak,we can use the Gross-Pitaevskii(GP)equation to describe its ground state and its dynamic behavior under the Hartree-Fock mean field approximation.While the Fer-mi superfluid can be described by the BCS pairing theory.With the advancement of experimental technology,the research can be broadened to the interaction system of multi-component ultracold atoms,to study the macroscopic quantum characters of multi-component coupling systems.Such as the quantum phase transition caused by the two-component boson coupling interaction,the vortex lattice of the Bose Fermi mixed system,etc.Further,we can consider a more accurate model to describe the higher-order effects of Bose and Fermi interactions,to obtain the quasi-particle excita-tion spectrum and the changes of the ground state affected by quantum fluctuations in a multi-component coupled system.This thesis focuses on the study of some interesting physical processes generated by the coupling of multi-component ultracold atoms and systematically reveals their physical connotations.The specific research contents are as follows:1.Dynamics of two-component boson in a double potential wellWe have studied the tunneling dynamics of a two-component BEC in a deep double well potential.We consider a model where the two components of BEC are affected by different potential fields:one in a double-well potential and one in a simple harmonic potential.The coupling of different BEC components makes the system exhibit many novel oscillatory behaviors.We use the two-mode approximation to reduce the coupled GP equations to the oscillation equation of the atoms in the double well,and find that the Josephson oscillation of BEC in the double well depends on the dynamics of the BEC in harmonic potential.We numerically study the coupling dynamics of two components of BEC,and found that the BEC in the double well exhibits a strong nonlinear behavior due to the coupling with the BEC in the harmonic potential.Further,we analyzed the phase transition of the BEC from the oscillating phase to the self-trapping phase in the double well due to the difference in the particle-number ratio and coupling strength.2.Chiral Majorana edge states in the vortex core of a p+ip Fermi superfluidBased on the huge potential of Majorana zero modes in quantum computing,we s-tudy the Majorana zero mode properties of 2D p+ip Fermi superfluids in the vortex core.For s-wave repulsive interaction between bosons and fermions,with the increasing of bosons atom in the the vortex core,the repulsive interaction will deplet fermion density in the vortex core.A dynamically driven local interface appears,and this soft boundary can carry Majorana edge modes.We systematically study the structure changes of the Fermi superfluid vortex caused by the increase of the boson density and the formation of edge modes.Among them,we found that the edge mode sensitively depends on the flow direction of the Fermi superfluids vortex.Under appropriate parameters we can obtain a relatively pure Majorana zero mode,which can be applied to topological quan-tum computing.Our study presents an illuminating example on how topological defects can be dynamically controlled in the context of cold atomic gases.3.Quantum droplet in a mixture of Bose-Fermi superfluidsRecently,people have experimentally realized a novel quantum state-quantum droplet in the two-components BEC system.Based on this progress,we investigate whether the same quantum state exists in the Bose Fermi mixed system.We investigate the formation of quantum droplets in a Bose-Fermi mixture.We focus on hybrid sys-tems with a repulsive Bose-Bose interaction and an attractive Bose-Fermi interaction.We further assume that the interaction between fermions can be adjusted by a magnetic Feshbach resonance.We find that quantum droplets can exist in a large range of param-eters under the combined action of fermion-pairing energy and higher-order effects of Bose-Fermi interactions.We carefully study the phase diagram as the Fermi atoms are modulated from the BCS to the BEC regime.We systematically discuss the parameter space where quantum droplets can exist stably,and revealed the important role of Fermi superfluids in the formation of quantum droplet in Bose-Fermi mixtures.