Post on 06-Jan-2016
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Stability of a Fermi Gas
with Three Spin StatesThe Pennsylvania State University
Ken O’Hara
Jason Williams
Eric Hazlett
Ronald Stites
Yi Zhang
John Huckans
Three-Component Fermi Gases
• Many-body physics in a 3-State Fermi Gas– Mechanical stability with resonant interactions an open question
– Novel many-body phasesCompetition 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 surfacesNovel Cooper pairing mechanismsAnalogous to mass imbalance of quarks
QCD Phase Diagram
C. Sa de Melo, Physics Today, Oct. 2008
Simulating the QCD Phase Diagram
Rapp, Hofstetter & Zaránd,
PRB 77, 144520 (2008)
• 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)
Universal Three-Body Physics
• The Efimov Effect in a Fermi system– Three independent scattering lengths– More complex than Efimov’s 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
Three-State 6Li Fermi Gas
2/3F
2/1F
}
}1
2
3
Hyperfine States of 6Li
2/1sm
2/1sm
• 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)
2/3F
2/1F
}
}1
2
3
Inelastic Collisions
Making and Probing 3-State Mixtures
Magnetic Field (Gauss)
200 400 600 800 10000
Radio-frequency magnetic fields drive transitions
Spectroscopically resolved absorption imaging
The Resonant QM 3-Body Problem
Vitaly Efimov circa 1970
(1970) Efimov: An infinite number of bound 3-body states for
A single 3-body parameter:
Inner wall B.C.determined byshort-range interactions
Infinitely many 3-body bound states (universal scaling):
)0(TE
)2(TE
)1(TE
· · )(TE
a
. ·
QM 3-Body Problem for Large a(1970 & 1971) Efimov: Identical Bosons in Universal Regime
Note: Only two free parameters:
Log-periodic scaling:
E. Braaten, et al. PRL 103, 073202
7.22)(*
)1(* nn aa
0a0a &Diagram from: E. Braaten & H.-W. Hammer, Ann. Phys. 322, 120 (2007)
Observable for a < 0: Enhanced 3-body recombination rate at
Universal Regions in 6Li
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
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 F=1/2 ground state– Apply two RF fields in presence of field gradient
Making Fermi Gases UltracoldAdiabatically Release Gas into a Larger Volume Trap
Low Field Loss Features
Resonances in the 3-Body Recombination Rate!
Resonance Resonance
T. B. Ottenstein et al., PRL 101, 203202 (2008). J. H. Huckans et al., PRL102, 165302 (2009).
Measuring 3-Body Rate Constants
Loss of atoms due to recombination:
Evolution assuming a thermal
gas at temperature T :
“Anti-evaporation” and
recombination heating:
Recombination Rate in Low-Field Region
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)
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., arXiv:0906.4378 (2009).
Efimov Trimer in Low-Field Region
3-Body Recombination in High Field Region
3-Body Recombination in High Field Region
Determining the Efimov Parameters
using calculations from E. Braaten et al., PRL 103, 073202 (2009).
Determining the Efimov Parameters
using calculations from E. Braaten et al., PRL 103, 073202 (2009).
Determining the Efimov Parameters
using calculations from E. Braaten et al., PRL 103, 073202 (2009).
Efimov Trimers in High-Field Region
also predicts 3-body loss resonances at 125(3) and 499(2) G
3-Body Observables in High Field Region
from E. Braaten, H.-W. Hammer, D. Kang and L. Platter, arXiv (2009).
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
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
Fermi Gas Group at Penn State
Ken O’Hara John Huckans Ron Stites Eric Hazlett Jason Williams Yi Zhang
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