Bcs-bec Crossover Region Imprisoned Fermi Cohesion Body Ground State And Excitation Spectrum Of Theoretical Studies

The study on ultracold trapped Fermi superfluid in the BCS-BEC crossover has been drawn by many physicists through the Feshbach resonance technique. The basic physical picture of the system appears based on the famous BCS superconducting theory and BEC superfluid theory.Firstly we review the studies on the system in the BCS-BEC crossover. Based on a new phenomenological equation of state and the generalized Gross-Pitaevskii (GP) equation for by the ground state wave function, we solve the nonlinear generalized GP equation by using of variational method and obtain the ground state wave function, the ground state energy and the chemical potential. The excited states satisfy the generalized Bogooliubov-de Gennes (BdG) equations. By choosing the three-dimensional axially-symmetric harmonic oscillator wave functions as a set of base vectors, we expand the wave function of the excited states and convert solving the generalized BdG equations into acquiring the eigen value of a matrix by introducing the Pauli matrix.The ground state equation is solved analytically, while the excited state equations are solved numerically. All the theoretical curves of the equation of state, chemical potential and the ground state wave function display the basical properties of the ground state. Some lower excitations are calculated in the parameter ranges which are hard to get by the analytical method. Compared with the experimental results and others analytical results we find that these numerical results reveal the excited state's properties of the system.