experiments with an ultracold three-component fermi gas the pennsylvania state university ken...
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Experiments with an Ultracold
Three-Component Fermi GasThe Pennsylvania State University
Ken O’Hara
Jason Williams
Eric Hazlett
Ronald Stites
John Huckans
• New Physics with Three Component Fermi Gases– Color Superconductivity– Universal Three-Body Quantum Physics: Efimov States
• A Three-State Mixture of 6Li Atoms– Tunable Interactions– Collisional Stability
• Efimov Physics in a Three-State Fermi Gas– Universal Three-Body Physics– Three-Body Recombination– Evidence for Efimov States in a 3-State Fermi Gas
• Prospects for Color Superconductivity
Overview
Color Superconductivity
• Color Superconducting Phase of Quark Matter– Attractive Interactions via Strong Force– Color Superconducting Phase: High Density “Cold” Quark Matter– Color Superconductivity in Neutron Stars – QCD is a SU(3) Gauge Field Theory– 3-State Fermi Gas with Identical Pairwise Interactions:
SU(3) Symmetric Field Theory
• BCS Pairing in a 3-State Fermi Gas– Pairing competition (attractive interactions)– Non-trivial Order Parameter– Anomalous number of Goldstone modes
(He, Jin, & Zhuang, PRA 74, 033604 (2006))
– No condensed matter analog
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
• New Physics with 3 State Fermi Gas: Three-body interactions
– No 3-body interactions in a cold 2-state Fermi gas (if db >> r0 )
– 3-body interactions allowed in a 3-state Fermi gas
• The quantum 3-body problem– Difficult problem of fundamental interest
(e.g. baryons, atoms, nuclei, molecules)
– Efimov (1970): Solutions with Universal Properties when a >> r0
db
db
2/3=F
2/1=F
}
}1
2
3
Three States of 6Li
Hyperfine States Feshbach Resonances
Interactions at High Field2/1−=sm
2/1+=sm
• 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 for a 3-state mixture– (Exclusion principle suppression for 2-state mixture)
2/3=F
2/1=F
}
}1
2
3
Inelastic Collisions
Making Degenerate Fermi Gases
• Rapid, all-optical production of DFGs– 1 DFG every 5 seconds
• Load Magneto-Optical Trap– 109 atoms– T ~ 200 K
• Transfer 5x106 atoms to optical trap
• Create incoherent 2-state mixture– Optical pumping into F=1/2 ground state– Noisy rf pulse equalizes populations
• Forced Evaporative Cooling– Apply 300 G bias field for a12 = -300 a0
– Lower depth of trap by factor of ~100
Crossed Optical Dipole Trap:Two 80 Watt 1064 nm Beams
y = 106 Hzz = 965 Hzx = 3.84 kHz
1.2 mm
Umax = 1 mK/beam
Uf = 38 K/beam
= 732 Hz
DFG and BEC
1.5 mm
1.5
mm
Absorption Image after Expansion
2-State Degenerate Fermi Gas BEC of Li2 MoleculesAbsorption Image after Expansion
1 mm
Making a 3-State MixturePopulating 3 states
– 2 RF signals with field gradient
B (Gauss)
High Field Absorption Imaging– 3 states imaged separately
200 400 600 800 10000
Stability of 3-State Fermi Gas
Fraction Remaining
in 3-State Fermi Gas
after 200 ms
Fraction Remaining
in 2-State Fermi Gases
after 200 ms
Universality in 3-body systems
Vitaly Efimov circa 1970
(1970) Efimov: pairwise interactions in resonant limit
3-Body Problem in QM: Notoriously Difficult
6 coordinates in COM!
Hyper-radius: , + 5 hyper-angles
Hyper-radial wavefunction obeys a 1D Schrodinger eqn.with an effective potential!
Universal Scaling
Vitaly Efimov circa 1970
(1970) Efimov: An infinite number of bound 3-body states
A single 3-body parameter:
Inner wall B.C.determined byshort-range interactions
Infinitely many 3-body bound states (universal scaling):
Universality with Large “a”
Vitaly Efimov circa 1970
(1971) Efimov: extended treatment to large scattering lengths
Trimer binding energies are universal functions of
Diagram from T. Kraemer et al. Nature 440 315 (2006)
Efimov Resonances
Resonant features in 3-body loss rate observed in ultracold Cs T. Kraemer et al. Nature 440 315 (2006)
Resonance Resonance
Universal Predictions
• Efimov’s theory provides universal predictions for low-energy three-body observables
• Three-body recombination rate for identical bosons
E. Braaten, H.-W. Hammer, D. Kang and L. Platter, arXiv:0811.3578
Note: Only two free parameters:
and
Log-periodic scaling
Measuring 3-Body Rate Constants
Loss of atoms due to recombination:
Evolution assuming a thermal
gas at temperature T:
“Anti-evaporation” and
recombination heating:
Trap for 100 nK cloud
Z
y
x
Helmholtz arrangementprovides Bz for Feshbach
tuning and sufficientradial gradient foratom trapping
T = 100 nK
TF = 180 nK
x = z
y = Hz
z = 109 Hz
Ntotal ~ 3.6 x 105
Elliptical beamprovides trappingin z direction
1600
1400
1200
1000
800
600
400
200
0
y-position [micro-meters]
16001400120010008006004002000x-position [micro-meters]
Evaporationbeams
= 42 Hz
kF a = 0.25
Quantum DegenerateGas in SU(3) Regime
Prospects for Color Superfluidity
• Color Superfluidity in a Lattice (increased density of states)– TC = 0.2 TF (in a lattice with d = 2 m, V0 = 3 ER )
– Atom density ~1011 /cc– Atom lifetime ~ 1 s (assuming K3 ~ 10-22 cm6/s)
– Timescale for Cooper pair formation
Summary
• Degenerate 3-State Fermi gas
• Observed “Efimov” resonances – Two resonances with moderate scattering lengths
• Measured three-body recombination rates
• Reasonable agreement with Efimov theory for a ~ r0 – Fits yield 3-body parameters for 6Li at low field
• Measured recombination rate at high field – Color superconductivity may be possible in a low-density gas
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