Study On One-dimensional Spin-orbit Coupling Bose Gases With Harmonic Trapping

In recent years,one of the main advances in cold atom physics is the realization of spin-orbit coupling of neutral atoms,and the idea of photoinduced synthesis specification field is proposed.Previously,the effects of spin-orbit coupling had been studied only in fermion materials such as electron gases,but this development opens up new opportunities to study spin-orbit coupling in boson systems.The cold atom system has good controllability,which can change the frequency of the bound potential well and the wavelength and intensity of the Raman laser.Although most of the theoretical work focuses on the Rashba coupled homogeneous system of spin-orbit coupling,the cold atom systems with spin-orbit coupling under the harmonic oscillator binding potential have also received attention and research.We investigate the Bose gases of Raman induced spin-orbit coupling with an external harmonic trapping.Using the displacement Fock state in quantum optics we seek for an approximate ground state.We find the superposition state of left and right displaced oscillator state with odd parity has lower energy than that of eigentranslational Fock state.Besides,we study the time evolution of both the momentum and the position of the system at single particle level to demonstrate the Zitterbewegung oscillation characteristics.We also use von Neumann entropy and concurrence to measure the entanglement between the internal and external degrees of freedom in the spin-orbit coupling model.The dependence of entanglement on Raman coupling strength and its evolution over time are discussed separately,and the periodic evolution of entanglement over time was qualitatively analyzed.Finally,the fluctuation of atomic position andmomentum,information entropy,and the Wigner function of the ground state are calculated.It was also found that the center of mass motion of the atom exhibits intrinsic squeezing properties with relation to the Raman and spin-orbit coupling strength.The results of this paper can be fully realized in the existing cold atom technology,and these results are also instructive for the cold atom physics field.