Controlling Spin Exchange And Spin Dynamics In Spinor Condensates

This thesis describes our studies on problems related to controlling spin-exchange interaction and dynamical preparation of quantum spin state in spinor atomic conden-sates.First,to solve the problem that spin-exchange interaction is nominally weak and easily suppressed by magnetic field in a spinor condensate,we propose a scheme for inducing resonant spin exchange between heteronuclear atoms via external periodic driving,i.e.,by directly compensating for the single particle energy mismatch through driving field.Our proposal is applied and affirmed numerically in a⁸⁷Rb-²³Na spinor mixture.We present a second scheme that employs the coupling between atom and an emp-ty optical cavity mode to induce effective spin-exchange interaction among atoms.By preparing the cavity to be initially in a vacuum state and relying on proper laser fre-quencies and their coupling strength with atoms,coherent spin-mixing in spin-1 atoms is achieved and whose strength can be tuned.We further investigate the associated spin dynamics and the effects of cavity dissipation in this coupled system.Finally,to develop better protocols in dynamical preparation of quantum spin s-tates,we use reinforcement learning?RL?to directly learn the?sub-?optimal control policy.We first explore the use of reinforcement learning in the problem of twin-Fock state preparation and specify proper definitions of state space,action space and re-ward function.At least for small system size?e.g.,with smaller number of atoms?,we find that RL can learn control protocols of magnetic field that performs better than the greedy policy or adiabatic protocol.These protocols can be generalized to systems with different particle numbers and are robust to noise.For the preparation of spin-squeezed state,RL is found to be capable of learning a new pulse sequence based on one-axis twisting?OAT?model that approach or even achieve Heisenberg limit squeez-ing?or the two-axis-counter twisting squeezing?over the OAT time scale.Compared with other pulse schemes,the RL policy requires only a few pairs of±?/2 pulses and is insensitive to noises of control field.Thus it can be readily implemented under current experimental conditions.