The Pennsylvania State University

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Stability of a Fermi Gas with Three Spin States

• The Pennsylvania State University
• Ken OHara
• Jason Williams
• Eric Hazlett
• Ronald Stites
• Yi Zhang
• John Huckans

2
Three-Component Fermi Gases

• Many-body physics in a 3-State Fermi Gas
• Mechanical stability with resonant interactions
  an open question
• Novel many-body phases
• Competition between different Cooper pairs
• Competition between Cooper pairing and 3-body
  bound states
• Analog to Color Superconductivity and Baryon
  Formation in QCD
• Polarized 3-state Fermi gases Imbalanced Fermi
  surfaces
• Novel Cooper pairing mechanisms
• Analogous to mass imbalance of quarks

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QCD Phase Diagram
C. Sa de Melo, Physics Today, Oct. 2008
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Simulating the QCD Phase Diagram

• Color Superconducting-to-Baryon Phase
  Transition
• 3-state Fermi gas in an optical lattice
• Rapp, Honerkamp, Zaránd Hofstetter,
• PRL 98, 160405 (2007)
• A Color Superconductor in a 1D Harmonic Trap
• Liu, Hu, Drummond, PRA 77, 013622 (2008)

Rapp, Hofstetter Zaránd, PRB 77, 144520 (2008)
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Universal Three-Body Physics

• The Efimov Effect in a Fermi system
• Three independent scattering lengths
• More complex than Efimovs original scenario
• New phenomena (e.g. exchange reactions)
• Importance to many-body phenomena
• Two-body and three-body physics completely
  described
• Three-body recombination rate determines
  stability of the gas

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Three-State 6Li Fermi Gas
Hyperfine States of 6Li
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Inelastic Collisions

• No Spin-Exchange Collisions
• Energetically forbidden
• (in a bias field)
• Minimal Dipolar Relaxation
• Suppressed at high B-field
• Electron spin-flip process irrelevant in
  electron-spin-polarized gas
• Three-Body Recombination
• Allowed in a 3-state mixture
• (Exclusion principle suppression for 2-state
  mixture)

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Making and Probing 3-State Mixtures
Radio-frequency magnetic fields drive transitions
Spectroscopically resolved absorption imaging
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The Resonant QM 3-Body Problem
(1970) Efimov An infinite number of bound 3-body
states for
.



Inner wall B.C. determined by short-range
interactions
Vitaly Efimov circa 1970
Infinitely many 3-body bound states
(universal scaling)
A single 3-body parameter
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QM 3-Body Problem for Large a
(1970 1971) Efimov Identical Bosons in
Universal Regime
Observable for a lt 0 Enhanced 3-body
recombination rate at
E. Braaten, et al. PRL 103, 073202
Note Only two free parameters Log-periodic
scaling
Diagram from E. Braaten H.-W. Hammer, Ann.
Phys. 322, 120 (2007)
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Universal Regions in 6Li
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The Threshold Regime and the Unitarity Limit

• Universal predictions only valid at threshold
• Collision Energy must be small
• Smallest characteristic energy scale
• Comparison to theory requires low temperature
• and low density (for fermions)
• Recombination rate unitarity limited in a thermal
  gas

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Making Fermi Gases Cold

• Evaporative Cooling in an Optical Trap
• Optical Trap Formed from two 1064 nm, 80 Watt
  laser beams
• Create incoherent 3-state mixture
• Optical pumping into F1/2 ground state
• Apply two RF fields in presence of field gradient

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Making Fermi Gases Ultracold
Adiabatically Release Gas into a Larger Volume
Trap
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Low Field Loss Features
T. B. Ottenstein et al., PRL 101, 203202 (2008).
J. H. Huckans et al., PRL102, 165302 (2009).
Resonances in the 3-Body Recombination Rate!
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Measuring 3-Body Rate Constants
Loss of atoms due to recombination
Evolution assuming a thermal gas at temperature
T
Anti-evaporation and recombination heating
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Recombination Rate in Low-Field Region
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Recombination Rate in Low-Field Region
P. Naidon and M. Ueda, PRL 103, 073203 (2008).
E. Braaten et al., PRL 103, 073202 (2009).
S. Floerchinger, R. Schmidt, and C. Wetterich,
Phys. Rev. A 79, 053633 (2009)
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Recombination Rate in Low-Field Region
P. Naidon and M. Ueda, PRL 103, 073203 (2008).
E. Braaten et al., PRL 103, 073202 (2009).
S. Floerchinger, R. Schmidt, and C. Wetterich,
Phys. Rev. A 79, 053633 (2009)
Better agreement if h tunes with magnetic field
A. Wenz et al., arXiv0906.4378 (2009).
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Efimov Trimer in Low-Field Region
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3-Body Recombination in High Field Region
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3-Body Recombination in High Field Region
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Determining the Efimov Parameters
using calculations from E. Braaten et al., PRL
103, 073202 (2009).
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Determining the Efimov Parameters
using calculations from E. Braaten et al., PRL
103, 073202 (2009).
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Determining the Efimov Parameters
using calculations from E. Braaten et al., PRL
103, 073202 (2009).
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Efimov Trimers in High-Field Region
also predicts 3-body loss resonances at 125(3)
and 499(2) G
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3-Body Observables in High Field Region
from E. Braaten, H.-W. Hammer, D. Kang and L.
Platter, arXiv (2009).
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Prospects for Color Superfluidity

• Color Superfluidity in a Lattice (increased
  density of states)
• TC 0.2 TF (in a lattice with d 2 mm, V0 3
  ER )
• Atom density 1011 /cc
• Atom lifetime 200 ms (K3 5 x 10-22 cm6/s)
• Timescale for Cooper pair formation

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Summary

• Observed variation of three-body recombination
  rate by 8 orders of magnitude
• Experimental evidence for ground and excited
  state Efimov trimers in a three-component Fermi
  gas
• Observation of Efimov resonance near three
  overlapping Feshbach resonances
• Determined three-body parameters in the high
  field regime which is well described by
  universality
• The value of k is nearly identical for the
  high-field and low-field regions despite crossing
  non-universal region
• Three-body recombination rate is large but does
  not necessarily prohibit future studies of
  many-body physics

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Fermi Gas Group at Penn State
Ken OHara John Huckans Ron Stites
Eric Hazlett Jason Williams Yi Zhang



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Future Prospects

• Efimov Physics in Ultracold Atoms
• Direct observation of Efimov Trimers
• Efimov Physics (or lack thereof) in lower
  dimensions
• Many-body phenomena with 3-Component Fermi Gases

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