The Pennsylvania State University Ken O’Hara Jason Williams Eric Hazlett Ronald Stites
description
Transcript of The Pennsylvania State University Ken O’Hara Jason Williams Eric Hazlett Ronald Stites
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
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
• 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
Resonant Loss Features
Resonance Resonance
Resonances in the 3-Body Recombination Rate!
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:
Recombination Rate Constants
(Heidelberg)
(to appear in PRL) (Penn State)
Recombination Rate Constants
Fit with 2 free parameters:
*,
* (aeff is known)
Efimov Resonances
3-Body Params. in SU(3) Regime
Unitarity Limit at 2 K
3-Body Params. in SU(3) Regime
Unitarity Limit at 2 K
3-Body Params. in SU(3) Regime
Unitarity Limit at 2 K
3-Body Params. in SU(3) Regime
Unitarity Limit at 100 nK
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
Thanks to
Ken O’Hara John Huckans Ron Stites Eric Hazlett Jason Williams