Rotating FFLO Superfluid in cold atom gases

Niigata University, Youichi Yanase Tomohiro Yoshida

2012 Feb 13, GCOE シンポジウム「階層の連結」 , Kyoto University

Group member (from 2009 Oct.)

Tomohiro Yoshida

Daisuke Maruyama

Shuhei Takamatsu Shunsuke Kawabe

“Non-centrosymmetric Superconductivity”

“Spin triplet Superconductivity”

“FFLO Superfluid”

Sr2RuO4

Introduction to FFLO state

Standard theory of Superfluidity/SC

J. Bardeen L. N. Cooper J. R. Schrieffer

Fermions + Attractive interactionBCS Theory (1957)

Basic Assumption: Total momentum of Cooper pair is zero.

Cooper pairs with q=0

Standard theory of Superfluidity/SC

J. Bardeen L. N. Cooper J. R. Schrieffer

Fermions + Attractive interactionBCS Theory (1957)

Cooper pairs with q=0

FFLO state Condensate of Cooper pairs with q=0Theory: Fulde-Ferrell (1964), Larkin-Ovchinnikov (1964)

D(r)= Dexp(iqx) D(r)= Dcos(qx)

Fulde-Ferrell state Larkin-Ovchinnikov state

Broken translation symmetryBroken inversion symmetry

FFLO Superfluidity/SuperconductivityCondesate of Cooper pairs with finite total momentum

Under current, Non-centro. SC 3He thin film, Superconductor

Multi-component superconductor

D(r)= Dexp(iqx) D(r)= Dcos(qx)

Fulde-Ferrell state Larkin-Ovchinnikov state

Broken translation symmetryBroken inversion symmetry

FFLO Superfluidity/SuperconductivityCondesate of Cooper pairs with finite total momentum

Under current, Non-centro. SC 3He thin film, Superconductor

Multi-component superconductor

D(r)= Dexp(iqx) D(r)= Dcos(qx)

Fulde-Ferrell state Larkin-Ovchinnikov state

Broken translation symmetryBroken inversion symmetry

FFLO Superfluidity/SuperconductivityCondesate of Cooper pairs with finite total momentum

Under current, Non-centro. SC 3He thin film, Superconductor

Multi-component superconductor

Candidates

(1) Superconductors in magnetic field

CeCoIn5, (TMTSF)2X …..

(2) Imbalanced cold Fermi gases

(3) High density quark matter (Color superconductivity)

FFLO Superfluidity/Superconductivity

(4) 3He thin film

Theory: Fulde-Ferrell (1964), Larkin-Ovchinnikov (1964)

(5) Stripe phase in Cuprates

Condesate of Cooper pairs with finite total momentum

MIT, Rice, Paris (2006-)

Why we couldn’t realize FFLO phase in SC for 40 years ?

FFLO phase is suppressed by

(2) Orbital pair-breaking effect Low dimension, Heavy effective mass

We need a high quality single crystal

(3) Fermi liquid correction (F0a < 0)

(1) Disorder

Strongly correlated electron systems

Strongly correlated electron systems ???

(3) l-(BETS)2X

(4) k-(ET)2X

(2) (TMTSF)2X

Matsuda-Shimahara 　 (2007)Radovan et al. (2003)Bianchi et al. (2003)

Uji et al. (2006)

Lortz et al. (2007)

All of these compoundsare close to AFQCP

Fermi liquid correction, retardation effect, parity mixing …

Yanase (2008)(1) CeCoIn5

Clean and Pauli-limited SC

Why we could find the FFLO phase ?

Yonezawa et al. (2008)

BCS theory

Miclea et al. (2006)CeCoIn5

FFLO superconductivity near AFQCP2D Hubbard model + ＦＬＥＸ

Yanase (2008)

Stable FFLO phase

Antiferromagnetic QCP

FFLO phase in cold Fermi gasesY. Y. PRB (2009)

T. Yoshida and Y. Y. PRA (2011)

Superfluid in cold atom gases

E. A. Cornell W. Ketterle C. E. Wieman

BEC in dilute Bose gas

BEC in 87Rb atoms

Reduced temperature

Superfluidity in Fermi gas

Advantages of cold Fermi gases

Cold Fermi gases Superconductors

T

P

T

H

BCS BCS

FFLO

FFLO

(2) No orbital pair-breaking effect Pure FFLO state without vortex

Discussion with Machida and Mizushima

(1) Disorder free

(3) Attractive interaction Fermi liquid correction stabilizes FFLO

Disadvantage ? : Trap potential

Harmonic trap

Experiment ： Shin et al. (2006)

No translation symmetry !!

We cannot distinguish the FFLO state from phase separation

Theory: Mizushima et al.

Toroidal trap

C. Ryu et al. (2007) in NIST

No translation symmetrybut, rotation symmetry !

Our idea FFLO superfluid phase in the troidal trap

Model Lattice model in a trap potential

Method BdG (M.F.A.) , RSTA (Self-consistent 1-loop)

Low density limit Continuum gas

Trap potential

Harmonic potential

Toroidal potential

Imbalance:Order parameter

Radial-FFLO

No symmetry breaking

Mean field theory (BdG equation)

Rotation symmetrybreaking !!

Angular-FFLO

Local Population imbalance

Radial-FFLO

Angular-FFLO

No symmetry breaking

distinguished from phase separation !!

Beyond mean field theory (RSTA)

RSTA= Real Space Self-consistent T-matrix Approximation

= ～= +

Inhomogeneity: Exact

fluctuation: 1-loop

Mesoscopic fluctuation

Thermal fluctuation

History (1) Pseudogap in disordered high-Tc cuprates (2006)(2) Superconductor-Insulator transition in Diamond (2008)

Phase diagram in RSTA

Angular-FFLO state is stable near BCS-BEC crossover !!

BCS side near crossover

Rotating FFLO phasesT. Yoshida and Y. Y. (2011)

Spontaneous rotation symmetry breaking

Intriguing effect of rotation

R

Fermi gas

Rotating FFLO phase in the toroidal trap

One dimensional attractive Hubbard model

quasi-1D model in BCS region BdG equation

Rotation

Phase shift

T-F phase diagram

Imbalanced gas (A-FFLO state) Balanced gas (BCS state)

Half quantum vortex state

Half quantum vortex Half period of Little-Parks oscillation

Imbalanced gas (A-FFLO state) Balanced gas (BCS state)

Blue line: balanced gasRed line ： imbalanced gas

The mass current is half quantized in the A-FFLO superfluid state

Half quantized mass current

Rotation

Summary

We can produce and observe the Angular-FFLO state!!

Toroidal trap + Feshbach resonance

Half quantum vortex stateStudy in future: (A) Trap geometry

(B) Optical lattice

(C) Dipole interaction

Rotation

Summary

We can produce and observe the Angular-FFLO state!!

Toroidal trap + Feshbach resonance

Rotation

Thank you very much for your attentions

Half quantum vortex state