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Outline of the talk
- Introduction:
The many-body problem in ultracold atoms BCS-BEC crossover and Unitary Fermi gas
- Functional Renormalization Group study:
Ultracold fermions in two and three dimensions Igor Boettcher - - PowerPoint PPT Presentation
Ultracold fermions in two and three dimensions Igor Boettcher - - PowerPoint PPT Presentation
Ultracold fermions in two and three dimensions Igor Boettcher Institute for Theoretical Physics, University of Heidelberg with S. Diehl, J. M. Pawlowski, and C. Wetterich Hirschegg, 27.8. 2012 Outline of the talk Introduction: The
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The many-body problem
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The many-body problem
possibility of a statistical description collective degrees of freedom
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The many-body problem
1st step: Find the right Hamiltonian H 2nd step: Determine the partition function Z
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The many-body problem
1st step: Find the right Hamiltonian H 2nd step: Determine the partition function Z H is known for cold atoms and QCD!
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The many-body problem
1st step: Find the right Hamiltonian H 2nd step: Determine the partition function Z path integral Euclidean quantum field theory H is known for cold atoms and QCD!
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Shopping list
What are the generic features of quantum many-body systems? What are reliable theoretical methods to describe such systems? What observables reveal advancements and short-comings of theory?
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Shopping list
What are the generic features of quantum many-body systems? What are reliable theoretical methods to describe such systems? What observables reveal advancements and short-comings of theory? cold atoms neutron stars nuclear matter heavy ion collisions quark gluon plasma high-Tc superconductors early universe
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Shopping list
Theory Experiments with cold atoms Phase diagram and Equation of state Density distribution Transport coefficients Density images Collective mode frequencies and damping constants Expansion after release from trap Response functions ...
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Shopping list
Theory Experiments with cold atoms Phase diagram and Equation of state Density distribution Transport coefficients Density images Collective mode frequencies and damping constants Expansion after release from trap Response functions ...
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The equation of state
Classical ideal gas: Virial expansion for interacting gas: Van-der-Waals equation of state:
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Pressure P(μ,T)
Bose gas
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Density n=(∂P/∂μ)T
Bose gas
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Bose gas
Isothermal compressibility (∂2P/∂μ2)T
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Isothermal compressibility (∂2P/∂μ2)T
Bose gas
Position of critical line: phase diagram
Superfluid phase transition
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Thermodynamics from density profiles
Figure: S. Nascimbène et al., New Journal of Physics 12 (2010) 103026 T.-L. Ho, Q. Zhou, Nature Physics 6, 131 (2010)
local density approximation
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- N. Navon et al., Science 328, 729 (2010)
imbalanced two-component Fermi gas at T=0:
Thermodynamics from density profiles
- M. J. H. Ku et al.,
Science 335, 563-567 (2012)
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The BCS-BEC Crossover
Two cornerstones of quantum condensation: Cooper pairing
- f weakly attractive
fermions Bose condensation
- f weakly repulsive
bosons BCS BEC
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The BCS-BEC Crossover
Two cornerstones of quantum condensation: BCS BEC
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The BCS-BEC Crossover
Two cornerstones of quantum condensation: BCS BEC Unitary Fermi gas
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The BCS-BEC Crossover
3D BCS-BEC crossover (results from Functional Renormalization Group)
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Microscopic Model
Many-body Hamiltonian
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Microscopic Model
Many-body Hamiltonian Microscopic action
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Macroscopic physics
How to compute the partition function? Integration
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Macroscopic physics
How to compute the partition function? scale dependent partition function
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Macroscopic physics
How to compute the partition function? scale dependent partition function Solve flow equation
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Wetterich equation
effective action
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Wetterich equation
effective action Microphysics Macrophysics fluctuations
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Contact in the BCS-BEC Crossover
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Momentum distribution
Ideal Fermi gas: Fermi-Dirac distribution
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Momentum distribution
Ideal Fermi gas: Fermi-Dirac distribution Interactions
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Momentum distribution
Ideal Fermi gas: Fermi-Dirac distribution Interactions
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Momentum distribution
Tan contact C Several exact relations, e.g.:
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Contact from the FRG
full macroscopic propagator
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Contact from the FRG
full macroscopic propagator
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Contact from the FRG
Factorization of the RG flow for large p:
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Contact from the FRG
Factorization of the RG flow for large p:
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Contact from the FRG
Factorization of the RG flow for large p: Flowing contact
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Contact from the FRG
Universal regime is enhanced for the Unitary Fermi gas
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Contact from the FRG
Universal regime is enhanced for the Unitary Fermi gas
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Contact from the FRG
Temperature dependent contact of the Unitary Fermi gas
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Contact from the FRG
Contact at T=0 in the BCS-BEC crossover
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Contact from the FRG
Momentum distribution of the Unitary Fermi Gas at the critical temperature without contact term with contact term
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Increase of density
Contribution from high energetic particles to the density Substantial effect on at Tc
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Two-dimensional BCS-BEC Crossover
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Two-dimensional BCS-BEC Crossover
Why two dimensions?
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Two-dimensional BCS-BEC Crossover
Why two dimensions?
- Enhanced effects of quantum fluctuations
→ test and improve elaborate methods
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Two-dimensional BCS-BEC Crossover
Why two dimensions?
- Enhanced effects of quantum fluctuations
→ test and improve elaborate methods
- Understand pairing in two dimensions
→ high temperature superconductors
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Two-dimensional BCS-BEC Crossover
Why two dimensions?
- Enhanced effects of quantum fluctuations
→ test and improve elaborate methods
- Understand pairing in two dimensions
→ high temperature superconductors How?
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Two-dimensional BCS-BEC Crossover
Why two dimensions?
- Enhanced effects of quantum fluctuations
→ test and improve elaborate methods
- Understand pairing in two dimensions
→ high temperature superconductors How? Highly anisotropic traps!
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What is different?
Scattering physics in two dimensions Scattering amplitude
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What is different?
Scattering physics in two dimensions Scattering amplitude Crossover parameter
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What is different?
Scattering physics in two dimensions Scattering amplitude Crossover parameter No scale invariance, but strong correlations for
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Equation of state at T=0
for
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Equation of state at T=0
for BKT BCS
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Superfluid phase transition
for
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