Stability of a Fermi Gas
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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. Three-Component Fermi Gases. Many-body physics in a 3-State Fermi Gas

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

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The pennsylvania state university ken o hara jason williams eric hazlett ronald stites yi zhang

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


Three component fermi gases

Three-Component Fermi Gases

  • 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


Qcd phase diagram

QCD Phase Diagram

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


Simulating the qcd phase diagram

Simulating the QCD Phase Diagram

  • 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)

  • Rapp, Hofstetter & Zaránd,

  • PRB 77, 144520 (2008)


Universal three body physics

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 6 li fermi gas

Three-State 6Li Fermi Gas

Hyperfine States of 6Li


Inelastic collisions

Inelastic Collisions

  • 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)


Making and probing 3 state mixtures

Making and Probing 3-State Mixtures

Radio-frequency magnetic

fields drive transitions

0

200

400

600

800

1000

Magnetic Field (Gauss)

Spectroscopically resolved

absorption imaging


The resonant qm 3 body problem

The Resonant QM 3-Body Problem

(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:


Qm 3 body problem for large a

QM 3-Body Problem for Large a

&

(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 regions in 6 li

Universal Regions in 6Li


The threshold regime and the unitarity limit

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

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 ultracold

Making Fermi Gases Ultracold

Adiabatically Release Gas into a Larger Volume Trap


Low field loss features

Low Field Loss Features

Resonance

Resonance

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

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

Resonances in the 3-Body Recombination Rate!


Measuring 3 body rate constants

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


Recombination rate in low field region1

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 region2

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


Efimov trimer in low field region

EfimovTrimer in Low-Field Region


3 body recombination in high field region

3-Body Recombination in High Field Region


3 body recombination in high field region1

3-Body Recombination in High Field Region


Determining the efimov parameters

Determining the Efimov Parameters

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


Determining the efimov parameters1

Determining the Efimov Parameters

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


Determining the efimov parameters2

Determining the Efimov Parameters

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


Efimov trimers in high field region

EfimovTrimers in High-Field Region

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


3 body observables in high field region

3-Body Observables in High Field Region

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


Prospects for color superfluidity

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= 3ER )

    • Atom density ~1011 /cc

    • Atom lifetime ~ 200 ms (K3~ 5 x 10-22cm6/s)

    • Timescale for Cooper pair formation


Summary

Summary

  • 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


The pennsylvania state university ken o hara jason williams eric hazlett ronald stites yi zhang

Fermi Gas Group at Penn State

Ken O’Hara John HuckansRon Stites Eric Hazlett Jason Williams Yi Zhang


Future prospects

Future Prospects

  • 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


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