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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 a 24 / k
Universality
BCS-BEC crossover
Feshbach resonance
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Background
Collective behaviorHydrodynamics
Breathing modes
Exp. data 6 Li
Strongly interacting many-body problem
Ground state energy 0.42 0.46 Equation of state (EOS)
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Equation of state
Hamiltonian
Zero temperature ground state energy
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Equation of state
1fk ax
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Collective modes
Hydrodynamic equations
Equation of continuity
Euler equation
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Collective modes
Polytropic EOS
1P Cn
2
3
1
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
ln( ) 1
ln
d Px
d n
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Collective modes
Linearization eqn n n v n
Considering the breathing modes i ti i iia re ev
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Collective modes
Equantions for ( 1,2,3)ia i
2 2 2( 2 )i i i jj
a a
In an axial symmetric trap
rad 1,2 0
ax 3 0
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:
rad rad2( 1)
ax ax
3 2
1
1
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!