Dynamical Quantum Phase Transition For Spinor Bose-einstein Condensate

Quantum phase transition refers to the sudden change of properties of matter after changing the parameters of the system.It is of great value to study the properties of matter,such as the parent phase of antiferromagnetism in high-temperature supercon-ductivity which turns into a superconducting phase after doping.This paper studies the dynamical quantum phase transition in spinor Bose-Einstein condensates and detects it by using spin-squeezing.This paper introduces the relevant theoretical knowledge and experimental prepa-ration methods of Bose-Einstein condensates,as well as some universal laws of spinor condensates as non-equilibrium systems.The derivation of the Gross-Pitaevskii equa-tion and the time-dependent Gross-Pitaevskii equation are studied,as well as the mean field theory and some effective and reasonable approximation methods of spinor con-densates.Quantum phase transition,dynamical quantum phase transition,and the quan-tum quench dynamics process that have received much attention in recent years are introduced.Then the dynamical stability of non-equilibrium systems is discussed,and the stability conditions are analyzed.This paper concludes by discussing the detection methods of dynamical quantum phase transitions in quantum systems during quenching processes.The spin-squeezing state,the particle fractional population,and the optimal squeezing time of the spin F=1spinor Bose-Einstein condensate are used to characterize the phase transition between the ground state and excited states.The results show that the quenching dynamics of the spin-squeezing state exhibit a non-analytical change and demonstrate that the squeezing state can not only detect the ground state phase diagram but also the quantum phase transition of the excited state.This paper further analyzes the system’s dynamical stability and proposes its relationship with dynamical quantum phase transitions.The research results of this paper are applicable to spinor condensates with sodium atoms（c₂>0）and rubidium atoms（c₂<0）.