pure fulde-ferrel-larkin-ovchinnikov state in optical lattices of off-diagonal confinement
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Pure Fulde-Ferrel-Larkin-Ovchinnikov state in optical lattices of off-diagonal confinement. 高先龙. Collaborators: Reza Asgari, 汪泾泾,陈阿海. 2011.8.5 兰州. 金华. 八月. 五月. 框架. Intro: 1D system of FFLO phase Confinement: Diagonal confinement versus Off-diagonal confinement - PowerPoint PPT PresentationTRANSCRIPT
Pure Fulde-Ferrel-Larkin-Ovchinnikov state in optical lattices of off-diagonal confinement
高先龙
2011.8.5 兰州
Collaborators: Reza Asgari, 汪泾泾,陈阿海
金华
八月 五月
框架• Intro: 1D system of FFLO phase
• Confinement: Diagonal confinement versus Off-diagonal confinement
• Results: Pure FFLO state
• Conclusions
1D system of FFLO phase
Introduction
实验物理学家
理论物理工作者
2 2
121 1 1
( )2
fN N N
D i ji i ji
H g x xm x
external potential
Why 1D: Non-Fermi liquid
1D
BCS: Δ(r) const∝FF: Δ(r) exp(iq r)∝ ⋅LO: Δ(r) cos(q r)∝ ⋅
Hunt for the Elusive FFLO State
Attractive Fermi systems, spin polarization and superfluidity are enemies
Conventional: a partially polarized Fermi gas undergoes macroscopic phaseseparation into a polarized normal region and an unpolarized superfluid region
FFLO state: Unconventional superfluid state when , in which fermion pairs with nonzero momentum form a spatially modulated inhomogeneous superfluid phase,
[Fulde & Ferrell (1964); Larkin & Ovchinnikov (1964)]
FFkk
1D Exotic phase:FFLO
Bosonization: Yang Phys. Rev. B 63, 140511 (2001); Zhao & Liu PRA (2008)
Bethe-ansatz: Orso, PRL98 (2007); Hu, Liu, Drummond, PRL98 (2007); Guan, Batchelor, Lee, Bortz, PRB (2007)
DMRG: E. Feiguin and F. Heidrich-Meisner, PRB (2007); M. Tezuka and M. Ueda, PRL (2008); M. Rizzi, et al, PRB (2008)
QMC: M. Casula, D. M. Ceperley, and E. J. Mueller, PRA (2008)
DFT: Gao Xianlong & Reza Asgari, PRA (2008)
Related: mass imbalanced Fermi Hubbard model, B Wang, et al., PRA (2009) SJ Gu, PRB (200?); Cazalilla and Giamarchi, PRL (2005)
Why FFLO in cold atom?
Condensed matter systems: FFLO physics is obscured by impurities, orbital effects, and spin-orbit coupling.
Ultracold atomic systems: the interaction, lattice, and polarization can be chosen at will.
Characterization of the FFLO phase
• Pairing at finite k; nonzero pairing momentum,
q0= kF ≠ 0
• oscillating pairing function, F~cos(kFx).
oscillations in order parameter Δ(r)
• Fulde-Ferrell vs Larkin-Ovchinnikov
• Translational & rotational invariance broken
Suggestions for the experimental observationof the FFLO state
• Image density profiles of : search for oscillations,
absorption imaging; phase-contrast imaging technique
• RF-spectroscopy: Kinunnen et al. PRL 96, 110403 (2006)
• Rapid-sweep-method, time-of-flight: peaks at finite velocities.
• Noise correlations:
• density of states: RF spectroscopy
Greiner et al. PRL 94, 110401 (2005)Altman et al. Phys. Rev. A 70, 013603 (2004) Luescher et al. PRA (2009)Yang, PRB (2001)
nn ,
kkkkkk nnnnn ,
Inhomogeneous FFLO state in 1D
The 1D attractive Hubbard model: Phase diagram
Bethe ansatz, Phases:
I. Empty lattice
II. (n < 1, p = 1): Fully polarized
III. (n = 1, p = 1): Fully polarized
IV. (n < 1, p < 1): Less than half-filled,
partially polarized: FFLO
V. (n < 1, p = 0): no polarization, fully paired
Essler’s Book, The One-Dimensional Hubbard Model, 2005
Diagonal confinement versus Off-diagonal confinement
Confinement:
DC: 1D-Pairing at finite Q & Spatial decay
DC: Power-law decay of correlations, spatial oscillations
The asymmetric Hubbard model
“BCS”
“FFLO”
( cf. B. Wang et al., PRA79, 2009 )
1 component gas
Spin-independent hopping
The asymmetric Hubbard model
0.0 0.1 0.2 0.3 0.4
10-6
10-5
10-4
10-3
10-2
x/L
x/L
|(x)|
superconducting correlations
‘incommensurate’ densities
unequal hoppings: the model is no longer integrable, hence use DMRG
‘commensurate’ densities
The attractive Gaudin model
Yang Phys. Rev. B 63, 140511 (2001); Orso, Phys. Rev. Lett. 98, 070402 (2007).
The attractive Gaudin model
Yang Phys. Rev. B 63, 140511 (2001); Orso, Phys. Rev. Lett. 98, 070402 (2007) ; XW Guan, PRA
Predictions from field theory and LDA
The attractive Gaudin model: in a trap
Partially-polarized phase associated with FFLO state Yang Phys. Rev. B 63, 140511 (2001);
Bethe-Ansatz + local density approximation:
Two-phase structures: centre partially polarized; edge either fully paired or fully polarized.
Orso, PRL 98, 070402 (2007)Hu, Liu & Drummond, PRL 98, 070403 (2007)Guan, Batchelor, Lee & Bortz, PRB 76, 085120 (2007).
Predictions from BA and LDA
The attractive Gaudin model: in a trap
Mean field theory vs. exact solution
The attractive Gaudin model: in a trap
The attractive Gaudin model: in a trap
FFLO---Experimental Results 6Li
Liao et al., Nature 467, 567 (2010)
FFLO---Experimental Results 6Li
No unambiguous demonstration for FFLO state is obtained in cold atomic systems until now!
Liao et al., Nature 467, 567(2010)
一维系统
Phases induced by external potential
M. Rigol et al., PRL (2003) ; G. Xianlong et al., PRL (2007)
U< 0 U >0
Pure state possible? through different designing
harmonic trapping
Results
Pure FFLO state
Predictions from Bethe-ansatz based DFT: N=36
Predictions from Bethe-ansatz based DFT: N=36
Predictions from Bethe-ansatz based DFT: N=36
Critical FFLO state in a 1D attractive Fermi gas
Pure FFLO state occurs only at the critical polarization!
The effect of disorder on the 1D attractive Fermi gas
Wang Jingjing, Gao Xianlong, JPB (2011)
speckle intensity
the spatial (auto)correlation
FFLO-BCS phase could change to FFLO-N phase while increasing disorder
The effect of disorder on the 1D attractive Fermi gas
Off-diagonal confinement
harmonic trapping
t=0t=0
Phase diagram in DC system
M.P.A. Fisher et al.,PRB 40,546 (1989)
Phase Diagram
The model
Phase diagram
Particle-hole symmetry
Pairing correlations
均匀体系
非均匀体系
N=80
N=70
Spin-spin correlations
detectable in a non-destructive way via spatially resolved quantum polarization spectroscopy.
Spin-spin correlations.
Conclusions
• We show that the off-diagonal confinement supports a region of pure FFLO state, thus provides an ideal system to detect the FFLO state in 1D systems.
• deviates from linear relations
• Magnetic structure factor shows a kink related to finite FFLO momentum
Note for helpful ALPS (Algorithms and Libraries for Physics Simulations) http://alps.comp-phys.org/
Team
感谢: NSFC 的支持
Thanks for your attention