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Collective modes of a trapped strongly interacting Fermi gas near the unitary limit regime 陆振帮 华中师范大学粒子物理研究所 (IOPP, CCNU) 武汉科技学院理学院 (WUSE) 合肥 2009
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OUTLINE 1. Background 2. Equation of state 3. Collective modes 4. Summary
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Background Unitary limit Universality BCS-BEC crossover Feshbach resonance
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Background Collective behavior Hydrodynamics Breathing modes Exp. data Strongly interacting many-body problem Ground state energy Equation of state (EOS)
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Equation of state Hamiltonian Zero temperature ground state energy
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Equation of state
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Collective modes Hydrodynamic equations Equation of continuity Euler equation
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Collective modes Polytropic EOS Dilute gas of Fermi atoms in both hydrodynamic and superfluid limits Fermi gas and BEC in unitary limit Dilute interaction dominated BEC
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Collective modes
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Linearization Considering the breathing modes
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Collective modes In an axial symmetric trap where is the anisotropy parameter.
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Collective modes ± signs correspond to the radial and axial modes respectively. purely geometric, irrelevant to EOS.
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In a cigar-shaped trap as being equipped in the experiments whose data are now available The radial modes: The axial modes: Collective modes
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The radial breathing modes compared with experimental data. Collective modes
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The axial breathing modes compared with experimental data. Collective modes
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Summary With the proposed equation of state, we have analyzed the hydrodynamic modes. For Fermi gas in a cigar-shaped harmonic trap potential, the radial and axial breathing mode frequencies are derived. The results are in agreement with the experimental measurements.
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Thank you!
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