Universal thermodynamics of a strongly interacting Fermi gas

1
Universal thermodynamics of a strongly
interacting Fermi gas
Hui Hu1,2, Peter D. Drummond2, and Xia-Ji Liu2

1. Physics Department, Renmin University of China
2. ACQAO, Physics Department, University of
   Queensland.

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Why strongly interacting Fermi gases?

• Fermions are the building blocks of matter.
• Strongly-interacting Fermi gases are stable.

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What is unitarity?
scattering l
from Thomas talk
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Unitarity s(k)4p/k2
B0
Magnetic-field Feshbach resonance 6Li and 40K
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Universality Conjecture One length scale L
n-1/3Thermodynamics independent of structure
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Universal thermodynamics in a harmonic trap
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Experimental investigations of thermodynamics
Forced Evaporation
Optical Trap Loading
High-Field Imaging
Problem no reliable thermometry !
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Energy from interacting gas
mask
Potential energy is obtained from axial cloud size
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Isentropic Thermometry
B0
Isentropic sweep to the weak coupling BCS limit
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Entropy from noninteracting gas
mask
true temperature (entropy) for non-interacting
gas
From Thomas- Fermi Fit
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Nozieres and Schmitt-Rink theory
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Mean field thermodynamic potential
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Pair fluctuations
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Gap and particle number equations
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Other BCS-BEC crossover theories?
Theories T am Inter-molecule interactions (BEC)
MF T0 am2aF condensate-condensate
Original NSR TgtTc am0aF None !
Strinati et al. (NSR) T0 am2aF ???
HLD T0 am0.57aF Includes pairing fluctuations
am 0.6aF within 2 accuracy, by Petrov et
al., PRL, 2004
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Comparison to the heat capacity data by Thomas
et al. (6Li)
?

• Cloud size at 840G gives Energy at unitarity
  (Virial theorem)
• Cloud size at 1200G gives Entropy at unitarity
  (isentropic sweep)
• The measurement of entropy is a conceptual
  advance
• owing to John Thomas et al., with accuracy at 1
  level

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Duke, Thomas group L. Luo et al., PRL 98,
080402 (2007).
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Comparison to the heat capacity data by Jin et
al. (40K)
?

• Cloud size at 202G gives potential energy at
  unitarity
• Noninteracting cloud size gives non-interacting
  temperature
• We then re-analyze the JILA data of potential
  energy and
• noninteracting temperature to obtain the energy
  and entropy.

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JILA, Jin group J. T. Stewart et al., PRL 97,
220406 (2006).
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Evidence for Universality
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Perturbation vs Monte Carlo Homogeneous Case Ene
rgy vs T Entropy vs T
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Comparative Studies in a trap
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What about many Fermi species? Color
Superconductors!
Exactly soluble problem in one-dimension - use
LDA to treat a trap
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Deconfining transition - evidence from breathing
mode frequencies
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BCS-BEC crossover with unequal spin populations !
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Like a dance floor with more men than women, the
state contains paired and unpaired entities
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Experiments Polarized Fermi gases
Quantum Phase Transition
Phase Separation
Expt. M. W. Zwierlein et al. Science 311, 492
(2006).
Expt. G. B. Partidge et al. Science 311, 503
(2006).
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Questions

• What is the ground state of a polarized Fermi
  gas?
• Does the FFLO state exist?
• What is the structure of FFLO state?
• What is the intrinsic reason for the phase
  separation state?
• Is there any uniform superfluid state with a
  finite spin population imbalance (i.e., pc 0.10
  in the unitary limit)?
• ?c 0.74 in the unitary limit?

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Polarized Fermi Gas in One Dimension
Method
Exact solution
Mean-field
SPWA
SCBdG
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Phase Diagram of a Uniform System
Spin polarization
dimensionless parameter
Integrable Gaudin Equations (Bethe Ansatz)
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Phase Diagram of a Uniform System
SF BCS-like superfluid state with zero
polarizationSFP Superfluid state with finite
polarization N Fully polarized normal
state
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Structure of SFp Phase
P0.03
P0.16
The SFp is of FFLO Character
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PHASE DIAGRAM IN A ONE-DIMENSIONAL TRAP
??
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Conclusions and references

• We analyze recent experimental measurements on
  the finite temperature properties of a strongly
  interacting atomic Fermi gas and provide
  evidence of universal thermodynamics.
• Extensions exact solutions for 1D color
  superconductors, polarized Fermi gas
• J. T. Stewart et al., Phys. Rev. Lett. 97,
  220406 (2006).
• L. Luo et al., Phys. Rev. Lett. 98, 080402
  (2007).
• G. Partridge et al., Science 311, 503 (2006).
• Hu, Liu Drummond, Europhys. Lett. 74, 574
  (2006).
• Hu, Liu Drummond, Phys. Rev. A 73, 023617
  (2006).
• Hu, Drummond Liu, 3 469, Nature Physics
  (2007).

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