Title: Connecting two important issues in cold atoms-- Origin of strong interaction and Existence of itinerant Ferromagnetism
1Connecting two important issues in cold
atoms--Origin of strong interaction and
Existence of itinerant Ferromagnetism
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Collaborator Tin-Lun Ho (Ohio State University)
2Strongly interacting Fermi gas (1999-2011)
- Strong attraction highest superfluid TcTF
-
Origin? Any way to achieve stronger?
- Strong repulsion itinerant Ferromagnetism
- Exist or not?
Connecting two issues
The answers are both strongly indicated by
two-body solutions
3Part I Narrow Feshbach Resonance---
alternative way to achieve strong interaction
Tin-Lun Ho and XL Cui, arxiv 1105.4627
4Wide vs. Narrow Feshbach resonance
Many cold atomic isotopes across both wide and
narrow resonance For example, Li-6 s-wave FR
E0, two atoms in open channel
Emergence of bound states
5Wide vs. Narrow Feshbach resonance
s-wave scattering length (with E-dependence)
wide
narrow
weak E-dependence
strong E-dependence
as, r
single as
effective range
6Phase shift
(i) wide
7Phase shift
(ii) narrow
8Two-body spectrum
free levels
2nd molecule in narrow FR
1st molecule in wide FR
9Two-body spectrum
free levels
10Interaction effect studied by High-T Virial
expansion
fugacity
upper branch lower branch
upper bound state excluded lower bound state
included
11Interaction effect studied by High-T Virial
expansion
Comparison between narrow and wide
Wide
Narrow
anti-symmetric Interaction across wide resonance!
12Interaction effect studied by High-T Virial
expansion
Comparison between narrow and wide
Narrow
Wide
13Interaction effect studied by High-T Virial
expansion
Comparison between narrow and wide
Narrow
New features in Narrow FR(i) interaction
effect gained far from resonance(ii) stronger
attraction achieved at resonance than in wide
FR------ a bran-new class of universality!(iii)
strongly asymmetric around resonance
14Conclusions for Part I
- Basic features of narrow resonance
- Strong E-dependence of scattering length
- Energy scale of resonance width ltlt Fermi energy
- Physical consequences
- Interaction effect observed far from resonance
- New generation of universality at resonance
Experiment on Narrow Resonance
easy accessible in experiment many samples,
high-T
preliminary results been achieved in Penn State
(K. OHara group) and Innsbruck (R. Grimm)
15Part II Existence of Itinerant
Ferromagnetism--- where to look for? 1,2,3D?
wide or narrow resonance?
XL Cui and Tin-Lun Ho, to be published
16A long-standing problem Whether itinerant
Ferromagnetism will show up in spin-1/2 fermions
due to strong repulsive interaction?
17Science 325, 1521 (2009)
b. 2009, experiment at MIT
Inconsistence
- based on mean-field calculation in a trap, which
predict large domain structure - not able to observe any domain
18c. 2009-now, theoretical studies
Duine and MacDonald, PRL 95 230403. (2005) 2nd
perturbation Zhai, PRA 80, 051605 (R) (2009) Cui
and Zhai, PRA 81, 041602(2010) variational
approach Pilati et al, PRL 105 030405 (2010 )
QMC Chang et al, PANS 108,51 (2011)
QMC Heiselberg, arxiv 1012.4569 Jastrow wf Barth
and Zwerger, arxiv 1101.5594 fermion-boson
mapping Zhou, Ceperley and Zhang,
arxiv1103.3534 lattice ED He and Huang,
arxiv1106.1345 diagrammatic approach
19c. 2009-now, theoretical studies
Duine and MacDonald, PRL 95 230403. (2005) 2nd
perturbation Zhai, PRA 80, 051605 (R) (2009) Cui
and Zhai, PRA 81, 041602(2010) variational
approach Pilati et al, PRL 105 030405 (2010 )
QMC Chang et al, PANS 108,51 (2011)
QMC Heiselberg, arxiv 1012.4569 Jastrow wf Barth
and Zwerger, arxiv 1101.5594 fermion-boson
mapping Zhou, Ceperley and Zhang,
arxiv1103.3534 lattice ED He and Huang,
arxiv1106.1345 diagrammatic approach
Supportive!
d. INT and DAPAR meeting, Apr-June 2011, MIT
announcement Absence of Itinerant
Ferromagnetism in repulsive Fermi gas
spin susceptibility is measured which never
signals the FM transition!!
20- Now, though the existence of FM in 3D is still
under debate, it seems that nature does NOT
prefer FM !
- Then, is there any place for the cold atom
community to find Itinerant FM?
Yes!
21Repulsive upper-branch in 1D---BA solution
(i) Bose gas Crossover from Tonks-Girardeau to
super-TG regime
Astrakharchik et al, PRL. 95, 190407 (2005)
DMC M. T. Batchelor et al, J. Stat. Mech. 10,
L10001 (2005) BA E. Haller et al., Science 325,
1224 (2009) sTG realized in Innsbruck
(ii) Fermi gas Crossover from Fermionic TG to
sTG regime
Guan and Chen, PRL 105, 175301(2010) BA
Definition of 1D upper-branch from BA
the BAEs also have real solutions for c lt0,
which, however, correspond to some highly excited
states of attractive Fermi systems. The FSTG
state corresponds to the lowest real solutions of
BAEs with c lt0.
22Repulsive upper-branch in 1D---BA solution
Guan and Chen, PRL 105, 175301(2010)
23Repulsive upper-branch in 1D---BA solution
Guan and Chen, PRL 105, 175301(2010)
24Repulsive upper-branch in 1D---BA solution
lower branch
25Repulsive upper-branch in 1D---BA solution
transition to FM
By switching B across quasi-1D resonance to glt0
side, equal and uniform spin mixtures relax to FM
state due to large spin fluctuations, and form
domains.
26Without Bethe Ansatz, any other general approach
to predict FM in 1D?
Yes!
27Understanding FM transition from Tans contact
1D contact
Barth and Zwerger, arxiv 1101.5594
28Understanding FM transition from Tans contact
increased E with -1/g
degenerate energy with FM at ginfty (fermionize)
FM emerges right at ginfty, and is favored at
glt0 (upper branch)
29Any other physically-transparent way to judge the
existence of FM besides 1D?
Yes! from a two-body perspective
- qualitative argument
- reproduce established results in 1D and 3D
- make predictions to many other systems
eg 1D/ 3D narrow resonance, and 2D.
30Existence of Itinerant Ferromagnetism from the
two-body perspective
Narrow abglt0,gbglt0
Narrow abggt0,gbggt0
Wide
1D
Y
Y or N
N
3D
N
N
N
2D
Y or N
31Application in 1D (I)
wide resonance Yes
identical fermions
FM ground state
32Application in 1D (II)
narrow resonance, abglt0 Yes for EFltltB No
otherwise
33Application in 3D
wide resonance No
RHS lowest bound state turn to scattering state,
no s-wave upper-branch any more!
34Application in 2D
Yes for kFa2dgtgt1 (but easily
decay to lower branch) No for
kFa2dltlt1
35Conclusions for Part II
- Existence of Itinerant Ferromagnetism from
existing studies - 3D No (announced recently by MIT experiment)
- 1D Yes (supported by BA solution)
- Understanding the result from other method and
further predictions - Tans adiabatic theorem (using Contact)
- Two-body spectrum
- FM depend on the dimension, resonance width,
background interaction, and size of Fermi cloud
36Thanks for attending!