Study Of Spin Dynamics In Spinor Bose-Einstein Condensates

This thesis focuses on the study of spin exchange dynamics in a spinor BoseEinstein condensate(BEC),from the following three aspects:physical phenomenon(associated with universal dynamics),engineering and tuning of the spin-exchange strength,and optimal control of the dynamics.We find that the driven critical dynamics exhibit qualitatively distinct behaviours in a finite system,as a result of the competition between two different scales in system near the quantum critical point:NKZ decided by external driving rate and the finite system size N.When NKZ dominates the dynamics(NKZ<N),the system displays universality and its excitations scale as ?-1(? is the driving time duration)given by the Kibble-Zurek mechanism in the thermodynamic limit,and when N dominates(N<NKZ)the dynamics,effects from external driving behave perturbatively and the excitation probability scales as ?-2 as in a trivial gapped system.We also present a dynamical scaling hypothesis which is experimentally falsifiable and lead to a more complete characterization of dynamical universality in a finite system(in contrast to the Kibble-Zurek scaling).Besides we also discuss associated quantum phase transitions in the excitation spectrum(analogous to transitions in the ground state).Excited state quantum phase transition implicates transitions of dynamical properties along the excited spectrum,which could be revealed by the evolution dynamics after a sudden quench.To circumvent the nominally small and difficult to tune spin-exchange interaction strength,we propose a scheme to engineer spin-exchange processes mediated by a single cavity mode.The effective interaction strength can be tuned by changing the intensity or the detuning of the pump laser.At typical experimental parameters,the effective exchange strength is estimated to be much larger than the interaction strength from binary collisions of ground state neutral atoms.Assuming the cavity remains unexcited and far detuned from the atoms,the effective spin-exchange dynamics is found to be insensitive to cavity loss and atomic spontaneous decay.Finally,optimal dynamical control during the preparation of quantum states is investigated.In contrast to a widely studied adiabatic scheme,we apply the method of reinforcement learning to the optimization of quadratic Zeeman shift during the preparation of atomic twin-Fock state,and obtain improvement over adiabatic sweeps.Policies given by the reinforcement learning can be intuitively interpreted,and the optimized policy is robust against the noises in the control fields and could be applied directly to systems with more atoms(showing the policy is generalizable).