Study Of Atomic Entangled States For Beating The Classical Precision Limit

This thesis is focused on the study of the preparation of atomic entangled states,such as spin squeezed states(SSSs)and twin-Fock states,for beating the classical precision limit.The widely discussed preparation methods are often based on dynamical evolutions,which incure many intrinsic problems.We try to develop solutions or new approaches that can overcome these problems.First,to solve the difficulty of storing the target state generated through dynamical evolution,we propose a scheme that is capable of storing a SSS.The basic idea is to rotate the SSS at the maximal squeezing moment to make it possess a sharp distribution around an eigenstate of the system,which effectively freezes the squeezing at the optimal level.The storage scheme is applied to two proposals capable of realizing effective two-axis counter twisting(TACT)transformed from one-axis twisting(OAT).The nominally stringent experimental requirements of the original protocols are found to be significantly relaxed,leading to greatly improved feasibility.To circumvent the problem of sensitive dependence on the control parameters for the dynamical preparation methods,we try to find metrologically useful steady state or ground state.We investigate the squeezing property of the steady state for a nonHermitian OAT model conditioned on the absence of decay.Enhanced spin squeezing is observed which outperforms the squeezing result from the Hermitian model over a wide range of parameters.We find that for some parameter region,it is possible to provide squeezing that surpasses the squeezing limit of the Hermitian TACT Hamiltonian.The price one has to pay concerns the amount of time it takes to reach the steady state,which is on average much longer than that needed by using dynamical evolution to prepare SSS.We also study the ground state of a spin-1 atomic condensate with antiferromagnetic interaction.By calculating its quantum Fisher information,we find that such a state constitutes a useful resource for quantum metrology.We discuss how such a ground state can be prepared and the choice of observables that are capable of exhibiting the theoretical precision limit.Additionally,the influence of a non-zero temperature is taken into account by calculating the quantum Fisher information of the equilibrium state at finite temperatures.Finally,we develop an approach capable of generating twin-Fock state by adiabatically driving a condensate undergoing spin mixing through two consecutive quantum phase transitions.Compared with the traditional approach utilizing spin mixing dynamics,our approach overcomes the strong fluctuations on the total atom numbers of the twin-Fock state and gives an improved conversion efficiency.Several problems that could be encountered in the implementation are analyzed in detail.The remarkable number squeezing and nearly perfect effective spin length observed implicate the superior properties of the prepared state,which lies in the very vicinity of the ideal twin-Fock state.The entanglement depth inferred from the experimental data represents the best world record in comparable systems.