Ground Unconventional Quantum Phase Of Diploe Bose Gas In The Optical Lattices

The study of phase transition characteristics in cold atom systems has become a very active field in modern physics.With the emergence and development of optical lattice technology,cold atom systems in optical lattices provide an excellent experimental platform for studying novel quantum states and quantum phase transitions in complex condensed matter systems.In cold atom systems,the competition between short-range,dipole,three-body interactions,transition energies,and quantum fluctuations can result in a rich variety of phases.The use of optical lattices allows for the study of the effects of three-body interactions and transition energies on the phase transition characteristics of cold atom systems.The properties,stability,and conditions for the existence of phases in this system are currently at the forefront of research in condensed matter physics and cold atom physics.This article introduces key experimental techniques for achieving Bose-Einstein condensation in laser cooling,trapping,magnetic trapping,and evaporative cooling,as well as recent research results and progress on the phase transition of this system.The Bose-Hubbard model and its extension,the extended Bose-Hubbard model including three-body interactions and density-dependent transition energy terms,are described to characterize the cold atom system.Firstly,we solve the generalized Bose-Hubbard model using Landau phase transition theory and mean field methods,obtaining analytical boundaries for the insulator-superfluid/super-solid phase transition in cold atom systems with density-dependent three-body interactions and transition energies.We analyze the effects of three-body interactions and densitydependent transition energy terms on the phase transition.Subsequently,we employed the non-uniform mean-field method to numerically solve the extended Bose-Hubbard model incorporating three-body interactions and density-dependent hopping.A complete phase diagram for the cold atom system with both three-body interactions and density-dependent hopping was obtained.Our calculations reveal that in the extended Bose-Hubbard system with three-body interactions and density-dependent hopping,six different phases can exist: Mott insulator phase,density wave phase,superfluid phase,Checkerboard supersolid phase,one-body staggered supersolid phase and one-body staggered superfluid phase.The repulsive and attractive three-body interactions have different effects on the parameter conditions of these two phases.The repulsive three-body interaction reduces the parameter region of the supersolid phase and one-body staggered supersolid phase,while the attractive three-body interaction enlarges the parameter region of the one-body staggered supersolid phase.Finally,we utilized the nonuniform mean-field method to calculate the phase diagram of the anisotropic extended Hubbard model with nonidentical dipole-dipole interactions and analyzed the effect of three-body interactions on the phase.Our calculations show that in the anisotropic dipolar interaction system,by adjusting the polarization angle,striped density waves and striped supersolid phases can occur.Repulsive three-body interactions suppress the striped supersolid phase,while attractive three-body interactions increase the parameter region of the striped supersolid phase.The study of three-body interactions,dependence on transition energy density,and anisotropic dipole-dipole interactions in cold atom systems is of great significance for understanding and observing complex quantum phases in condensed matter physics and understanding the mechanisms of quantum phase transitions.This provides new ideas and methods for exploring the properties of ultracold atoms,experimental observation of phases,and expanding the application of cold atoms in quantum simulation and quantum computing.