copenhagen, june 15, 2006 unitary polarized fermi gases erich j. mueller cornell university sourish...

Copenhagen, June 15, 2006

Unitary Polarized Fermi Gases

Erich J. Mueller

Cornell University

Sourish Basu

Theja DeSilva

NSF, Sloan, CCMR

Outline:

•Interesting Questions

•What goes wrong with mean field theory and LDA

•Speculations about the phase diagram

•Collective modes [no time, but ask me about them]

CopenhagenJune 15, 2006 Erich Mueller -- Polarized Fermions 2 of 18

Questions

1. Nature of normal fluid at zero T at unitarity?

2. Existence of exotic phases?a) Modulated Order parameters [FFLO]

b) Deformed Fermi surfaces

c) Polarized s-wave superfluids [Sarma, Breeched gap]

3. Properties?a) Equation of state

b) How to probe?


Questions

1. Nature of normal fluid at zero T at unitarity?





b) How to probe?

Simplest assumptions (ex. Fermi-liquid) -- calculate properties

Controlled approximations: Limit n=0


Questions

1. Nature of normal fluid at unitarity?





b) How to probe?

Homogeneous:•Mean Field Phase Diagram•Fluctuations and Stability•Scaling Arguments

Trap:•Surface tension•Collective modes

How to explain experiments


Summary

• Hulet’s “wings” can be explained by surface tension in the normal-superfluid interface

• Hulet’s low polarization data is a mystery

• Preliminary theoretical studies indicate:Partially polarized normal phase at unitarityMay be partially polarized superfluid phase at unitarity

Probably breaks translation/rotation symmetry [eg. FFLO]


Homogeneous Phases

Mean Field Theory:

a>0 a>0 [near resonance] a<0

Red: 1st order transition Normal-FFLO: Continuous SF-FFLO: Discontinuous(Schematic)


Application to TrapLDA

P. Pieri, and G.C. Strinati, PRL 96, 150404 (2006) ; W. Yi, and L. -M. Duan, cond-mat/0604558; M. Haque and H.T.C. Stoof, cond-mat/0601321; Zheng-Cheng Gu, Geoff Warner and Fei Zhou, cond-mat/0603091 ; C.-H. Pao, S.-K. Yip, J. Phys.: Condens. Matter 18 (2006) 5567;Theja N. De Silva, Erich J. Mueller, Phys. Rev. A 73, 051602(R) (2006)

BECBCS


Beyond Mean Field Theory + LDA• Discrepancies with experiments:

PData: Rice/MIT


LDA in harmonic trap:

Integrate:

Axial density should be monotonic [in LDA]

Beyond Mean Field Theory + LDA• Wings -- A violation of LDA


• Simple Explanation:

Beyond Mean Field Theory + LDA

Large Aspect Ratio Trap:LDA:

Surface Tension:

z

Unitarity constrains form:


• Calculating :Beyond Mean Field Theory + LDA

x

E

Gradient expand quadratic term Take rest to be local, but go to all order in

MFT minimizes

Equivalent to approximate solution of BdG eqns.

Ansatz:

Find by minimizing E()


• Surface tension resultBeyond Mean Field Theory + LDA

=0.9 10-3 at unitarity

P= 0.14

P= 0.53

P= 0.72

Theja De-Silva and EJM, Cond-mat/0603068Data: Hulet


Beyond Mean Field Theory + LDA• Discrepancies with experiments:

PData: MIT

Experimentalist interpretation:Evidence of partially polarized normal phase

Crude theorist argument:Possibly existence of partially polarized superfluid phase

[Vortex experiments seem to not be consistent with this]

a>0 [near resonance]


Normal State at T=0

Start fully polarized:

Energy to add single spin down =

Ignore Pauli blocking [Leggett ~1999]

Include Pauli Blocking

=(0,0)= + + + …

(Generalization of Hartree to include beyond-Born scattering)

[Part of a systematic self-consistent theory -- but appears to be important bit]-- NSR+approximate self-consistency


Normal State at T=0

20 1.04

Thouless criterion:Normal state is unstable to pairing with q=0.6k [k=0.44k (n/n=0.09)]

1.18

Fully Polarized Normal [Exact]

1.885

Unpolarized Superfluid[Monte-Carlo]

?????


Experimental Clues

Chevy [cond-mat/0605751]Bulgac and Forbes [cond-mat/0606043]

LDA:

Upper bound from self-energy


Normal State at T=0

20

1.8851.04

Thouless criterion:Normal state is unstable to pairing with q=0.6k [k=0.44k

(n/n=0.09)]

1.18

Transition to unpolarized superfluid must be right of this line


Alternative Pictures

Gubbels, Romans and Stoof, cond-mat/0606330

Finds MIT data is consistent with Finite T + polarized superfluidExplains temp dep of Rice critical polarization


Differences

MIT• Resolves 3 shells• No distortion of aspect

ratio• No “critical polarization”

for phase separation– Compares lowest T data

• Superfluid-normal transition at P=0.7

Rice• Resolves 2 shells

– May be 3 shells• Interacting normal gas looks a

lot like superfluid

– May be in different regime [above tricritical point]

• Sees distortion of aspect ratio– Surface energies important:

Large aspect ratio + small particle number

• Observes “critical polarization”– Increases with increasing T


Summary

• Surface Tension:– Another illustration of strong interactions in such

dilute gases

• Phase Diagram– Argument that there may be a polarized superfluid --

normal state is only stable for quite low polarizations.– Normal state instability is at finite q [FFLO?]

copenhagen, june 15, 2006 unitary polarized fermi gases erich j. mueller cornell university sourish...

Documents

field theory ldawings

polarized normal phase

polarized superfluid

finite t

existence of exotic

forbes condmat0606043lda

breeched gapproperties

equation of statehow