Coherent Control Of Spin Squeezing In Atomic Bose-Einstein Condensate

In the past two decades, spin squeezing has attracted considerable attention, both theoretically and experimentally. The notion of spin squeezing has arisen mainly from two applications:The study of particle correlation and entanglement, and the improvement of measurement precision in experiments. However, the definition of spin-squeezing parameter is not unique, the most widely studied spin squeezing parameters were proposed by Kitagawa and Ueda, by S?rensen et al and by Wineland et al. In this thesis, we mainly study the coherent control of spin squeezing in Bose-Einstein condensates (BECs) via electromagnetically induced transparency (EIT) and with a strong external field, we also study the coherent control of hybrid spin squeezing between the probe laser and the BECs atoms via EIT. This thesis is divided into three parts:The first part includes chapter 1 and chapter 2. In the first chapter, the background and the main research results of spin squeezing are introduced. In the second chapter, we introduce some basic theories of spin squeezing, including the definitions of spin squeezing, spin squeezing parameters and the relations between spin squeezing and pairwise correlations, quantum entanglement and quantum Fisher information.The second part includes chapters 3 and 4, which is our main works. In chapter 3, we study the coherent control of spin squeezing in BEC via EIT where the probe laser and the coupling laser are treated calssically. We first derive the effective Hamiltonian(generalized one-axis twisting model) with adiabatical elim-ination and secular approximation, and then investigate how to control the mean spin direction, the length of mean spin and spin squeezing parameter definited by Kitagawa and Ueda. In chapter 4, we proposes a scheme to control the hybrid spin squeezing via EIT where the prober-laser field is quantized while the coupling-laser field is treated classically. The system becomes an effective two-mode system in which on member is the probe laser and the other is the condensate in the lowest state with adiabatical elimination. We get the analytical solutions for the mean direction, the length of mean spin and spin squeezing parameter definited by S?rensen. It is shown that these paratmers can controlled by adjusting the probe laser-atom dipole interaction and two-photon detuning.The third part is chapter 5, we investigate another scheme to control the spin squeezing with a external field, where approximate analytical expressions are present with frozen-spin approximation. We find that the mean spin direction is locked in x direction, while the spin squeezing always appears in the z direction with an extended period and that spin squeezing is controlled by adjusting the strength of the external field and adding the total atomic number.A summary of the work and a outlook of this thesis are given in chapter 6.