| During several decades after the proposal of the Bose-Einstein statistics,theoretical and experimental skills in atoms,molecules and optics have been developed rapidly.These skills help experimentalists to cool the atomic gases from several hundreds Kelvin to tens or hundrends nano Kelvin and to trap the atoms in a magnetic or an optical well,and finally lead to the condensation of atomic gases in experiments.As spin-1Bose-Einstein condensate has several interesting ground states under the single mode approximation and two theories,including mean field theory and quantum theory,are applied to describe the spinor condensate.The predictions from these two theories about the ground states are consistent except for the ground state of an antiferromagnetic spin-1 condensate.This is due to the fact that the atom number fluctuation of the ground state of an antiferromagnetic spin-1 condensate is very large.The ground state spontaneously breaks some symmetries under the mean field theory.However,a beautiful non-rigid pendulum model in ρ0-θ phase space under the mean field theory was proposed and was demonstrated in experiment.After taking the magnetic dipolar interaction into consideration,the non-rigid pendulum model in the angular momentum space was also proposed under the mean field theory.Many-body entangled singlet state is a long-sought state in experiment.We propose a fast method utilizing multilevel oscillations to generate high-fidelity massively entangled states,including singlet state and twin-Fock state,in an antiferromagnetic spin-1 Bose-Einstein condensate.Combining the multilevel oscillations with additional adiabatic drives,we greatly shorten the necessary evolution time and relax the requirement on the control accuracy of quadratic Zeeman splitting,from micro-Gauss to milli-Gauss,for a23 Na spinor BEC.The achieved high fidelities over 96% show that two kinds of massively entangled states,the many-body singlet state and the twin-Fock state,are almost perfectly generated.The generalized spin squeezing parameter drops to a value far below the standard quantum limit even with the presence of atom number fluctuations and stray magnetic fields,illustrating the robustness of our protocol under real experimental conditions.The generated many-body entangled states can be employed to achieve the Heisenberg-limit quantum precision measurement and to attack nonclassical problems in quantum information science.After considering the magnetic dipolar interaction,we propose three methods transferring the magnetic dipolar interaction into the two-axis twisting operator.Then,we investigate the effects of stray magnetic fields on the spin squeezing process.The numerical and analytical methods show the detrimental effects of noisy environments which destroy the spin squeezing.By applying concatenated dynamical decoupling pulse sequences with a moderate bias magnetic field to suppress the effect of the noisy environments,we faithfully reconstruct the spin squeezing process under realistic experimental conditions.Our noise-resistant method is ready to be employed to generate the spin squeezed state in a dipolar spin-1 Bose-Einstein condensate and paves a feasible way to the Heisenberg-limit quantum metrology. |
