Unitarity Schrödinger Equation and Ground State Properties of the Finite Trapped Superfluid Fermi Gases in a BCS-BEC Crossover |
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| Authors: | ZHANG Wen-Yuan WANG Cheng-Tao MA Yong-Li |
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| Affiliation: | Department of Physics, Fudan University, Shanghai 200433 |
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| Abstract: | On the basis of quantum hydrodynamical equations we derive a unitarity Schrödinger equation of a finite trapped superfluid Fermi gas valid in the whole interaction regime from BCS superfluid to BEC. This equation is just the Ginzburg-Laudau-type equation for the fermionic Cooper pairs in the BCS side, the Gross-Pitaevskii-type equation for the bosonic dimers in the BEC side, and a unitarity equation for a strongly interacting Fermi superfluid in the unitarity limit. By taking a modified Gauss-like trial wave function, we solve the unitarity Schrödinger equation, calculate the energy, chemical potential, sizes and profiles of the ground-state condensate, and discuss the properties of the ground state in the entire BCS-BEC crossover regimes. |
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| Keywords: | 03 75 Ss 67 85 Bc |
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