1 / 45

New analogies between
xQCD and cold atoms
Yusuke Nishida (TITech)
YITP workshop on “thermal quantum
field theories and their applications”
August 28 (2013)

2 / 45

Definition-9(~ 10 K)

Ultracold atoms= nonrelativistic
point-like particles
with short-range interactions

12(~ 10 K)

Extreme QCD= relativistic quarks
with gauge interactions

Plan of this talk3 / 45

1. “Hard probes” in cold atoms- Use of energetic atoms to locally probe
strongly-interacting atomic gases- Y.N., Phys. Rev. A (2012) [arXiv:1110.5926]
2. “Quark-hadron continuity” in cold atoms- Smooth crossover from atoms to trimers
in 3-component Fermi gases- Y.N., Phys. Rev. Lett. (2012) [arXiv:1207.6971]

4 / 45“Hard probes”
in cold atoms

xQCD vs. cold atoms• Elliptic flow

• Small shear viscosity1⌘&s 4⇡• Jet quenching

5 / 456 / 45xQCD vs. cold atoms• Elliptic flow

• Small shear viscosity
100.8
0.6

8

0.4
0.2

60.6

d/s

K. M. O’Hara et al., Science (2002)

0.0
0.7

0.8

0.9

1.0

1.1

420• Jet quenching???

1234E/EF

C. Cao et al., Science (2011)

What is its analogue in cold atoms ?

5Probe atomic gas with atoms
Shoot a probe atom into the target atomic gas
and measure its differential scattering rate

probe atomtarget
atomicgas

θWhat can we learn from the scattering dataon the (strongly-interacting) target atomic gas ?

7 / 45

Probe atomic gas with atoms
Shoot a probe atom into the target atomic gas
and measure its differential scattering rate

k-1

n-1/3Large k >> n1/3 => Few-body scattering problemsd (k)d⌦= ···

8 / 45

Leading contribution
Shoot a probe atom into the target atomic gas
and measure its differential scattering rate

k-1

Large k >> n1/3 => Few-body scattering problems
d (k)
d⌦n
= f (✓) + · · ·k

9 / 45

Sub-leading contribution

10 / 45

Shoot a probe atom into the target atomic gas
and measure its differential scattering rate

k-1

Large k >> n1/3 => Few-body scattering problems
d (k)
d⌦n
C= f (✓) + g(✓)+ ···kk2

11 / 45

What is “C” ?

Probability of finding 2 particles at small separation
2n̂(r)n̂(0)=n• noninteracting gas :• interacting gas : n̂(r)n̂(0)C(4 |r|)22

Rn̂(r)n̂(0)|r|<Rn R3CR

Anomalously enhanced probability isquantified by the “contact density” C

Important characteristic of strongly-int atomic gases
S. Tan, Ann. Phys. (2009); E. Braaten & L. Platter PRL (2008)12 / 45

What is “C” ?

Probability of finding 2 particles at small separation
2n̂(r)n̂(0)=n• noninteracting gas :• interacting gas : n̂(r)n̂(0)C(4 |r|)22Rn̂(r)n̂(0)|r|<Rn R

3CR

Anomalously enhanced probability isquantified by the “contact density” C

Important characteristic of strongly-int atomic gases
S. Tan, Ann. Phys. (2009); E. Braaten & L. Platter PRL (2008)13 / 45

Formulations à la OPE• scattering rate :2 Im ⌃(k)
Zd (k)(k) = d⌦d⌦(k) =• optical theorem :Zikx

dx e hT (x)X=Ai (k)hOi iiG(k) =†(0)iin=h†i, C = h(†2) i, . . .

Lowest few Oi are needed at large k

Systematic large-k expansion !

Differential scattering rate
Many-body physics
d (k)
d⌦n
C
= f (✓) + g(✓)
+ ···
kk2

Few-body physics
Few-body physics plays an important role
to probe many-body physics !

14 / 4515 / 45

Differential scattering rate
d (k)
d⌦n
C
= f (✓) + g(✓, k/⇤ )
+ ···
kk2
Efimov effect

For zero-range interactions
15f (✓)-1.0g(✓, 1.8)

15

10

105

5

-0.5

0.5

1.0

-1.0

-0.5

0.5

-5

-5

-10

-10-15-15forward scattering(θ < 90°) only

backward scattering(θ > 90°) possible

1.0cos ✓16 / 45

Differential scattering rated (k)d⌦n
C= f (✓) + g(✓, k/⇤ )+ ···kk2
Efimov effect

For zero-range interactions
15f (✓)-1.0g(✓, 1.8)

15

101055-0.5

0.5

1.0

-1.0

-0.5

0.5

-5-5-10

-10

-15

-15

1.0cos ✓Backward scattering rate measures contact density
New local probe of strongly-int atomic gases

17 / 45

Differential scattering rated (k)d⌦nC= f (✓) + g(✓, k/⇤ )kk2+ 16 ⇥(cos ✓) (2 cos ✓ k̂ + p̂) ·~jk2+ ···~p~k✓'~jAzimuthal (φ) anisotropy reveals
currents in many-body states18 / 45

Differential scattering rated (k)d⌦nC= f (✓) + g(✓, k/⇤ )kk2+ 16 ⇥(cos ✓) (2 cos ✓ k̂ + p̂) ·~jk2~
p~
k'

✓
~j1
Nmeasured (✓, ') =kZdld (k)d⌦⇥ Nshot+ ···19 / 45

How large is large ?
"E" (k) = 1 + 32⇡

n#ak4

#2k6
7.54 + O(k )2mk4CComparison of E(k)/ F with QMC P. Magierski et al., PRL (2011)
3.5

3.5

3.0

3.0

2.5

2.5

2.0

2.0

1.5

1.5

1.0

1.0

0.5

0.5

0

12

340

12

(af kF ) 1 = 0

T / F = 0.15

(af kF ) 1 = 0.2

C/kF4 = 0.110

Goulko et al, Lattice2010

C/kF4 = 0.156

3k4 kF

T / F = 0.19
Gandolfi et al, PRA (2011)

Reasonable agreement even at k / kF > 1.5 !

220 / 45

Ultracold atom “colliders”
tZ

20n=010n = -1

05S1/2
F=1tZ

Duke (2011)

n = +1NIST (2012)-2-1ky
C Schematic of scattering halo0/kL-1001122
nRamazaanRamxy

1.3  mm

B0MIT (2011)

Otago (2012)1.3  mmb

Time  (1  ms  per  frame)c dkx-1/k L-2

Ultracold atom “colliders”

21 / 45“A laser based accelerator for ultracold atoms”

University of Otago(New Zeeland)
Optics Letters (2012)

Short summary- Energetic atoms => New tool to locallyprobe strongly-interacting atomic gases- Systematic large-k expansions are possible✓ backward scattering => contact density✓ azimuthal anisotropy => current density

probe atomtargetatomicgas

22 / 45

Short summary- Energetic atoms => New tool to locallyprobe strongly-interacting atomic gases- Systematic large-k expansions are possible✓ backward scattering => contact density✓ azimuthal anisotropy => current density

JLab, Science 320, 1476 (2008)- Close connection to nuclear/particle physics

23 / 45

24 / 45

Short summary- Energetic atoms => New tool to locallyprobe strongly-interacting atomic gases- Systematic large-k expansions are possible✓ backward scattering => contact density✓ azimuthal anisotropy => current density

JLab, Science 320, 1476 (2008)- Close connection to nuclear/particle physics“Hard probes” areuseful to reveal
short-range paircorrelations
both in atomic gases
and nuclei (QGP?)25 / 45

“Quark-hadron continuity”
in cold atoms

BCS-BEC crossover

26 / 45• 2-component Fermi gasloosely bound Cooper pairs

tightly bound dimers

Jin Group at JILA

27 / 45

BCS-BEC crossover• 3-component Fermi gasloosely bound Cooper pairs

tightly bound dimers

unpaired atoms?

BCS-BEC crossover

28 / 45• 3-component Fermi gasloosely bound Cooper pairs

tightly bound dimers

unpaired atoms

unpaired timers“Atom-trimer continuity” = New crossover physics !

3-component Fermi gas• 3 spin states ( i = 1, 2, 3 ) of 6Li atoms

near a Feshbach resonance :f (k) =1
1
ik + a• a12 = a23 = a31

K. M. O’Hara, New J. Phys. (2011)29 / 45

30 / 45

3-component Fermi gas• 3 spin states ( i = 1, 2, 3 ) of 6Li atoms

near a Feshbach resonance :f (k) =

1
1
ik + a• a12 = a23 = a31 => SU(3) × U(1) invariance
L=

†i

2

ri@t +2m!

i+g2

†i

†jji

• Problem ! 3 fermions form an infinitely deepbound state (Thomas collapse)

No many-body ground state :-(31 / 45

3-component Fermi gas• 3 spin states ( i = 1, 2, 3 ) of 6Li atoms

near a “narrow” Feshbach resonance :f (k) =

1f (k) =1
ik + are↵ =1
1
ik + a + Rk2

2R is the effective range• R regularizes short-distance behaviors( => no Thomas collapse)

Universal many-body ground state(depends only on a, R, kF)

32 / 45Phase diagram0•↑ narrow resonance← weakattraction

RkF

0-•

?

strong →attraction↓ broad resonance

1/akF

•

33 / 45Phase diagram0•↑ narrow resonance

BCS
superfluid+← weakFermi
attraction
surface

RkF?

BEC
superfluid+ →strongnoFermiattraction
surface

Trimer Fermi gas
0-•

1/akF

•

34 / 45Phase diagram
0•

Large RkF expansion
BCS
superfluid+
Fermi
surface

RkF?

BEC
superfluid+
no Fermi
surface

Trimer Fermi gas
0-•

1/akF

•

35 / 45Phase diagram
0•

BCS
superfluid+
Fermi
surface

RkF

1=
akF

?

4(1/4)24⇡
RkF

!1/4

BEC
superfluid+
no Fermi
surface

Trimer Fermi gas
0-•

1/akF

•

36 / 45Phase diagram
2 ENmR*

•

N-0.2

0.2

atom -0.02

BCS
superfluid-0.04+
Fermi -0.06
surface

RkF-0.08

00-•

Dilutelimit
kF→0?

0.4

trimer

BECsuperfluid+
noN=3
Fermi
surface

N=2

Trimer Fermi gas

1/akF

R*
0.6 a

Dilutelimit
kF→0•37 / 45Phase diagram
2 ENmR*•N-0.20.2

atom -0.02

BCS
superfluid-0.04+
Fermi -0.06
surfaceRkF

0-0.08?

0.4

trimer

-•

1
=
akF

0.0917
RkF

1/akF

BEC
superfluid
dimer+
noN=3
Fermi
surface

N=2

Trimer Fermi gas
0R*
0.6 a

Dilutelimit
kF→0•38 / 45Phase diagram
2 ENmR*•N-0.20.2

atom -0.02

BCS
superfluid-0.04+
Fermi -0.06
surfaceRkF

0-0.08?

R*
0.6 a0.4

BEC
superfluid
dimer+
noN=3
Fermi
surfacetrimer

N=2

Trimer Fermi gas
0-•

1/akF

dimer SF+ trimer FS•

39 / 45Phase diagram
0•

BCS
superfluid+
Fermi
surface

RkF

?

BEC
superfluid+no Fermi
surface

Trimer Fermi gas
0-•

1/akF

dimer SF+ trimer FS•

40 / 45Phase diagram
0•
SF + FSASF

Unpaired fermions
are atom-like
SF+FST(meff ~ m)
Unpaired fermions
are trimer-like(meff ~ 3m)

RkF

Trimer FG0-••“Atom-trimer continuity”1/ak= NewF crossover physics !

41 / 45

Quark-hadron continuity
VOLUME 82, NUMBER 20

PHYSICAL REVIEW LETTERS

17 MAY 1999

Continuity of Quark and Hadron Matter
Thomas Schäfer and Frank Wilczek
School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540(Received 30 November 1998)
We review, clarify, and extend the notion of color-flavor locking. We present evidence that for threedegenerate flavors the qualitative features of the color-flavor locked state, reliably predicted for highdensity, match the expected features of hadronic matter at low density. This provides, in particular,a controlled, weak-coupling realization of confinement and chiral symmetry breaking in this (slight)
idealization of QCD. [S0031-9007(99)09191-7]
PACS numbers: 12.38.Aw

In a recent study [1] of QCD with three degenerate flavors at high density, a new form of ordering was predicted,
wherein the color and flavor degrees of freedom become
rigidly correlated in the ground state: color-flavor locking.
This prediction is based on a weak-coupling analysis using a four-fermion interaction with quantum numbers abstracted from one gluon exchange. One expects that sucha weak-coupling analysis is appropriate at high density, forthe following reason [2,3]. Tentatively assuming that thequarks start out in a state close to their free quark state,i.e., with large Fermi surfaces, one finds that the relevantinteractions, which are scattering the states near the Fermi
surface, for the most part involve large momentum transfers. Thus, by asymptotic freedom, the effective coupling
governing them is small, and the starting assumption isconfirmed.
Of course, as one learns from the theory of superconductivity [4], even weak couplings near the Fermi surface canvor quantum numbers, including integral electric charge.
Thus, the gluons match the octet of vector mesons, thequark octet matches the baryon octet, and an octet of collective modes associated with chiral symmetry breaking
matches the pseudoscalar octet. However, there are alsoa few apparent discrepancies: there is an extra massless
singlet scalar, associated with the spontaneous breaking of
baryon number (superfluidity); there are eight rather thannine vector mesons (no singlet); and there are nine rather
than eight baryons (extra singlet). We will argue that these“discrepancies” are superficial—or rather that they are features, not bugs.
Let us first briefly recall the fundamental concepts ofcolor-flavor locking. The case of three massless flavors
is the richest due to its chiral symmetry (and adding acommon mass does not change anything essential) so weshall concentrate on it. The primary condensate takes theform [1]New link between atomic and nuclear systems !

42 / 45

Mean-field + trimer model⌦ MF+T = ⌦ mean field + ⌦ trimer
knows correct asymptotic behaviors
R# k F

0.8

SF ! FSASF0.6

SF ! FS T
0.4

R*kF =0.38

0.2

Trimer FG
1"2"10123 ak F

43 / 45

Critical temperature

See also, S. Floerchinger et al., PRA (2009)

A pair of quantum critical points(complete depletion of SF) appear for R*kF < 0.38
Tc !T F

0.20

0.15

R*kF > 0.38
R*kF < 0.38

Normal

0.10

0.05

SFSF
0.0

0.2

0.4

0.6

10.8 ak F

Summary of this talk

44 / 45

1. “Hard probes” in cold atoms- Use of energetic atoms to locally probe
strongly-interacting atomic gases- Y.N., Phys. Rev. A (2012) [arXiv:1110.5926]
2. “Quark-hadron continuity” in cold atoms- Smooth crossover from atoms to trimers
in 3-component Fermi gases- Y.N., Phys. Rev. Lett. (2012) [arXiv:1207.6971]

45 / 45

Summary of this talk
Extreme QCD

Ultracold atoms

New ideas wanted !