BCSBEC crossover in relativistic system

1
BCS-BEC crossover in relativistic system
Yusuke Nishida (Univ. of Tokyo) with Hiroaki
Abuki (Yukawa Inst.)
????? _at_ KEK22 March, 2005
New fermion superfluidity in 40K Regal et al.,
PRL 92 (2004) 040403
Interaction is arbitrarily tunable using
Feshbach resonance
strong
weak
BEC by molecules
BCS by Cooper pairs
2
Idea of BCS-BEC crossover
Nozieres and Schmitt-Rink, J. Low Temp. Phys. 59
(1985) 195
BCS pairing in k-space
BEC pairing in x-space
kz
bound state
kx
Strongerattractive int.
ky
Condensation ofCooper pairs
Bose-Einstein Condensationof bound bosons
3
BCS-BEC crossover in QCD ?

• Perturbative QCD at high density
• gt BCS instability in color 3, flavor 1 and
  JP0 diquark channel

QGP
?
Color superconductivity
Hadron phase
larger g

• Possible realization of BEC in low or
  intermediate density region of CSC

Abuki, Hatsuda and Itakura, PRD 65 (2002) 074014
4
Our formulation
2-body contact interaction with massive fermion
fermion mass fermion chemical potential
Attractive interaction in color 3, flavor 1 and
JP0 diquark channel
Fermion pair correlation in normal phase ltMean
field Gauss fluctuationgt
Sa de Melo et al., PRL 71 (1993) 3202

• Fixed number density Ntotal
• Ntotal Nfermion Nboson
• Critical temperature Tc by Thouless criterion
• Tc lt pair fluctuation diverges

Nbound Nunstable
5
BCS phase
Weak coupling region
Mean field result
Tc
superfluidphase

• Exponentially increasing Tc
• Mean field result is valid
• m EF
• Fermion density is dominant

6
BEC phase
Intermediate coupling
BEC Tc for MB2m
Tc
MF
superfluidphase

• Slowly increasing Tc
• Well described by BEC
• m lt m
• Bound boson density is dominant

7
Relativistic BEC
Strong coupling
1/T (NF)-1/3
Tc
MF
superfluidphase

• Very large Tc (NF)1/3
• Small interparticle distance
• m 0
• Anti-particles are available

8
Summary
2 crossovers as increasing the coupling
Tdiss
Dissociation ofbound bosons above Tc preformed
boson phase(TcltTltTdiss)
Tc
Cf. pseudogap phase discussed by Kitazawa et
al., PRD 70 (2004) 056003
9
Significance of (R)BEC in QCD

• BEC criterion m lt m

Speculative QCD phase diagram
Hard dense loop gives fermion mass
Cf. diquark bound state above Tc by Shuryak and
Zahed
RBEC
Preformedboson phase
BEC criterion
Probable realization of BEC in
non-perturbativeregion of CSC
BECggt1

• RBEC (large Tc) is realized when large g small
  m

• Future work competition between (R)BEC
  and chiral symmetry breaking

10
Backup Slides
11
BCS-BEC crossover in relativistic system
Yusuke Nishida (Univ. of Tokyo) with Hiroaki
Abuki (Yukawa Inst.)
New fermion superfluidity in 40K Regal et al.,
PRL 92 (2004) 040403
Interaction is arbitrarily tunable using
Feshbach resonance

• Strong coupling
• BEC by molecules
• Weak coupling
• BCS by Cooper pairs

12
Result in non-relativistic system
Sa de Melo et al., PRL 71 (1993) 3202
Dissociationof bound boson
Fermi gas
Bose gas
BCS behavior
BEC behavior
13
Critical temperature vs. coupling
Chemical potential and density on Tc line
superfluidphase
intermediate
strong
weak
BCS
BEC
RBEC
14
Critical temperature vs. coupling
Meanfieldresult
1/T (NF)1/3
Free BEC
Tc
More discussions ? JPS meeting
intermediate
strong
weak
BCS
BEC
Relativistic BEC
15
Entropy vs. coupling
Weak and intermediate coupling region
Strong coupling region
total
boson
fermion
16
Summary
2 crossovers as increasing the coupling
Complementary to pseudogap phase discussed by
Kitazawa et al.
Dissociation of bound boson above Tc preformed
boson phase
17
Significance of BEC in QCD
BEC criterion m lt m
Model independent, if we ignore the interaction
between boson
On the critical temperature of BEC In order
to bind two fermions
Hard dense loop gives fermion mass
Preformed boson phase
BEC criterion
Probable realization of BEC in
non-perturbativeregion of CSC
BECggt1
18
Significance of RBEC in QCD
RBEC with large Tc is realized when g is large
and m is small
Speculative QCD phase diagram
RBEC
Cf. diquark bound state above Tc by Shuryak
and Zahed
Preformedboson phase
BECggt1
Future work competition between (R)BEC and
chiral symmetry breaking