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![Page 1: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062311/5a4d1b917f8b9ab0599c1516/html5/thumbnails/1.jpg)
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
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Group member (from 2009 Oct.)
Tomohiro Yoshida
Daisuke Maruyama
Shuhei Takamatsu Shunsuke Kawabe
“Non-centrosymmetric Superconductivity”
“Spin triplet Superconductivity”
“FFLO Superfluid”
Sr2RuO4
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Introduction to FFLO state
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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
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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)
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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
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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
![Page 8: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062311/5a4d1b917f8b9ab0599c1516/html5/thumbnails/8.jpg)
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
![Page 9: 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.](https://reader035.fdocuments.net/reader035/viewer/2022062311/5a4d1b917f8b9ab0599c1516/html5/thumbnails/9.jpg)
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-)
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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 ???
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(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)
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BCS theory
Miclea et al. (2006)CeCoIn5
FFLO superconductivity near AFQCP2D Hubbard model + FLEX
Yanase (2008)
Stable FFLO phase
Antiferromagnetic QCP
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FFLO phase in cold Fermi gasesY. Y. PRB (2009)
T. Yoshida and Y. Y. PRA (2011)
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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
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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
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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.
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Toroidal trap
C. Ryu et al. (2007) in NIST
No translation symmetrybut, rotation symmetry !
Our idea FFLO superfluid phase in the troidal trap
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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
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Imbalance:Order parameter
Radial-FFLO
No symmetry breaking
Mean field theory (BdG equation)
Rotation symmetrybreaking !!
Angular-FFLO
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Local Population imbalance
Radial-FFLO
Angular-FFLO
No symmetry breaking
distinguished from phase separation !!
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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)
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Phase diagram in RSTA
Angular-FFLO state is stable near BCS-BEC crossover !!
BCS side near crossover
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Rotating FFLO phasesT. Yoshida and Y. Y. (2011)
Spontaneous rotation symmetry breaking
Intriguing effect of rotation
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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
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T-F phase diagram
Imbalanced gas (A-FFLO state) Balanced gas (BCS state)
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Half quantum vortex state
Half quantum vortex Half period of Little-Parks oscillation
Imbalanced gas (A-FFLO state) Balanced gas (BCS state)
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Blue line: balanced gasRed line : imbalanced gas
The mass current is half quantized in the A-FFLO superfluid state
Half quantized mass current
Rotation
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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
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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