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