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