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The Pennsylvania State University Ken O’Hara Jason Williams Eric Hazlett Ronald Stites Yi Zhang

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Stability of a Fermi Gas

with Three Spin States

The Pennsylvania State University

Ken O’Hara

Jason Williams

Eric Hazlett

Ronald Stites

Yi Zhang

John Huckans

- Many-body physics in a 3-State Fermi Gas
- Mechanical stability with resonant interactions an open question
- Novel many-body phases
- Competition 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 surfaces
- Novel Cooper pairing mechanisms
- Analogous to mass imbalance of quarks

C. Sa de Melo, Physics Today, Oct. 2008

- Color Superconducting-to-“Baryon” Phase Transition
- 3-state Fermi gas in an optical lattice
- Rapp, Honerkamp, Zaránd & Hofstetter,
PRL 98, 160405 (2007)

- Rapp, Honerkamp, Zaránd & Hofstetter,
- A Color Superconductor in a 1D Harmonic Trap
- Liu, Hu, & Drummond, PRA 77, 013622 (2008)

- Rapp, Hofstetter & Zaránd,
- PRB 77, 144520 (2008)

- 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

Hyperfine States of 6Li

- 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

- Suppressed at high B-field
- Three-Body Recombination
- Allowed in a 3-state mixture
- (Exclusion principle suppression for 2-state mixture)

Radio-frequency magnetic

fields drive transitions

0

200

400

600

800

1000

Magnetic Field (Gauss)

Spectroscopically resolved

absorption imaging

(1970)Efimov: An infinite number of bound 3-body states for

.

·

·

·

Inner wall B.C.

determined by

short-range interactions

Vitaly Efimov circa 1970

Infinitely many 3-body bound states (universal scaling):

A single 3-body parameter:

&

(1970 & 1971) Efimov: Identical Bosons in Universal Regime

- Observable for a < 0:
- Enhanced 3-body recombination rate at

E. Braaten, et al. PRL 103, 073202

Note:

Only two free parameters:

Log-periodic scaling:

Diagram from:

E. Braaten & H.-W. Hammer,Ann. Phys. 322,120(2007)

- 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)

- Collision Energy must be small
- Recombination rate unitarity limited in a thermal gas

- 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

Adiabatically Release Gas into a Larger Volume Trap

Resonance

Resonance

T. B. Ottensteinet al., PRL 101, 203202 (2008).

J. H. Huckanset al., PRL102, 165302 (2009).

Resonances in the 3-Body Recombination Rate!

Loss of atoms due to recombination:

Evolution assuming a thermal

gas at temperature T :

“Anti-evaporation” and

recombination heating:

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)

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. Wenzet al., arXiv:0906.4378 (2009).

using calculations from E. Braaten et al., PRL 103, 073202 (2009).

using calculations from E. Braaten et al., PRL 103, 073202 (2009).

using calculations from E. Braaten et al., PRL 103, 073202 (2009).

also predicts 3-body loss resonances at 125(3) and 499(2) G

from E. Braaten, H.-W. Hammer, D. Kang and L. Platter, arXiv (2009).

- Color Superfluidity in a Lattice (increased density of states)
- TC= 0.2 TF(in a lattice with d= 2 mm, V0= 3ER )
- Atom density ~1011 /cc
- Atom lifetime ~ 200 ms (K3~ 5 x 10-22cm6/s)
- Timescale for Cooper pair formation

- Observed variation of three-body recombination rate by 8 orders of magnitude
- Experimental evidence for ground and excited state Efimovtrimers 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 HuckansRon Stites Eric Hazlett Jason Williams Yi Zhang

- Efimov Physics in Ultracold Atoms
- Direct observation of EfimovTrimers
- Efimov Physics (or lack thereof) in lower dimensions

- Many-body phenomena with 3-Component Fermi Gases