Thermal Entanglement Properties in two Kinds of Two-qubit Spin Squeezing Model

Using the concurrence (C) criterion, we investigate the thermal entanglement properties in two-qubit spin squeezing model for two kinds of squeezing interaction: one-axis twisting model (OATM) and two-axis countertwisting model (TACM) with a transverse field. To the OATM, in the limit case of T -> 0, the ground state entanglement is initially increased from zero to the maximum value, then decreased in a period of time and suddenly disappeared finally with further enhancing the external magnetic field Omega. One interesting thing is that instead of decaying slowly to zero the entanglement is sudden disappeared with further enhancing Omega or mu (the spin squeezing interaction in X direction), and decreasing the parameter mu or Omega can obviously broaden the scope of entanglement exists. For the finite temperature case, a novelty point is the sudden birth phenomenon occured in the behaviors of entanglement, it is initially to be zero (persists for some time), with further improving Omega and mu the entanglement will be suddenly appeared, and the time interval (persists to be zero) before sudden birth is obviously prolonged with decreasing two parameters. The temperature range of entanglement exists can be extended evidently with increasing mu or Omega, and one can obtain entanglement at higher temperature through changing them. When to the TACM, the ground state entanglement is initially decreased from the maximum value and then suddenly disappeared with increasing Omega. While increasing gamma the ground state entanglement is increased initially from zero to the maximum value and then sudden disappeared with further improving gamma (the spin squeezing interaction in XY plane), proper tuing gamma or Omega can prolong the lives of entanglement evidently. For the finite temperature case, the sudden birth phenomenon also occured in the the evoluted concurrence, the variation of parameters Omega and gamma can reduce the time interval before sudden birth. The influence of the temperature T on thermal entanglement property is also investigated. The temperature range of entanglement existence can be extended evidently with increasing gamma, one can obtain entanglement at higher temperature through changing parameters gamma and Omega.