1. Zhejiang Normal University
Collective excitations of one-dimensional Fermi gases:
a study from density-functional theory
高先龙(Gao Xianlong)
Department of Physics, Zhejiang Normal University
Collaborators: Wei Li, Marco Polini, Giovanni Vignale
Phys. Rev. Lett. 98, (2007)
Phys. Rev. Lett. 101, (2008)
Phys. Rev. B 78, (2008)
July 18, 2009
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

2. Zhejiang Normal University
Outline
@ Introductory Part
Optical lattices and cold atoms
Our starting point?
@ Time-dependent density-functional theory
and its application in 1D
@ What we can and what we cannot
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

3. Zhejiang Normal University
Outline
@ Introductory Part
Optical lattices and cold atoms
Our starting point?
@ Density-functional theory and local density
approximation and its application in 1D
@ What we can and what we cannot
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

4. International Conference on Quantum Foundation and Technology
Realization of 1D quantum gas in optical lattice
For a 2D optical lattice, the atoms are confined to an array of tightly
confining 1D potential tubes.
In each tube, radial motion confined to zero point oscillations
effective 1D quantum gas
H. Moritz et al., PRL (2003), Nature 429, 277 (2004), Science, 305, 1125 (2004)
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

5. Realization of Anderson Localization in OL
Billy et al., Nature 453, 891(2008)
Roati et al., Nature 453, 895 (2008)
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

6. International Conference on Quantum Foundation and Technology
Spin-charge separation in atomic systems
Charge: Spin:
atomic mass density two internal (hyperfine)
atomic states (e.g. 6Li)
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

7. Zhejiang Normal University
Collective dynamics in 1D Fermi gases
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

8. International Conference on Quantum Foundation and Technology
Pull one hair and
you move the whole
body.
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

9. Zhejiang Normal University
Outline
@ Introductory Part
Optical lattices and cold atoms
Our starting point?
@ Time-dependent density-functional theory
and its application in 1D
@ What we can and what we cannot
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

10. International Conference on Quantum Foundation and Technology
Our model: time-dependent Hamiltonian
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

11. International Conference on Quantum Foundation and Technology
Time-dependent DFT theory
Runge-Gross theorem: the density of the interacting system
can be reproduced by the non-interacting potential
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

12. International Conference on Quantum Foundation and Technology
Applications: Collective excitations in 1D Hubbard model with OBC
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

13. A. Preparation of the initial state
Bethe-ansatz-based local-spin-density approximation
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

14. B. Time-evolution with TDDFT
Bethe-ansatz-based adiabatic local-spin-density approximation
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

15. International Conference on Quantum Foundation and Technology
Unpolarized
U=2
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2018年12月2日星期日

16. International Conference on Quantum Foundation and Technology
polarized
U=2
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

17. International Conference on Quantum Foundation and Technology
unpolarized
U=6
polarized
U=6
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

18. International Conference on Quantum Foundation and Technology
Repulsive interacting U=2, but switch off interaction
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

19. International Conference on Quantum Foundation and Technology
Repulsive interacting U=2
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2018年12月2日星期日

20. International Conference on Quantum Foundation and Technology
Attractive Interacting U=-1
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2018年12月2日星期日

21. International Conference on Quantum Foundation and Technology
Spin and charge dynamics in 1D
ultracold Fermi gases
Tunable interaction strength
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

22. International Conference on Quantum Foundation and Technology
Spin-density-functional theory
What is Vdyn?
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

23. International Conference on Quantum Foundation and Technology
Go beyond ALSDA?
Spin-drag related force
: spin-drag relaxation time
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

24. International Conference on Quantum Foundation and Technology
Spin-charge separation in the Gaudin-Yang model with OBC
Zero-temperature Spin-Charge Separation
t=2.5
t=1.25
t=0
t=5
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

25. International Conference on Quantum Foundation and Technology
Gaudin-Yang model: simulation of spin-charge separation
Gao, et al., PRL(2008)
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

26. International Conference on Quantum Foundation and Technology
Gaudin-Yang model: simulation of spin-charge separation
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

27. International Conference on Quantum Foundation and Technology
Why good agreement happens?
Magic of ALDA
Short-range nature of the interaction
Exact thermodynamic compressibility
and spin susceptibility
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

28. International Conference on Quantum Foundation and Technology
2018年12月2日星期日

29. Zhejiang Normal University
Outline
@ Introductory Part
Optical lattices and cold atoms
Our starting point?
@ Time-dependent density-functional theory
and its application in 1D
@ What we can and what we cannot
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

30. International Conference on Quantum Foundation and Technology
Conclusions: What we can do
1. Static properties of 1D systems
2. Collective excitations: spin charge dynamics/
spin-drag effect
3. The influence of disorder on 1D model:
Speckle; impurities; quasi-disorder, spin-chain
4. Some novel quantum phases: Luther-Emery phase;
LOFF pairing mechanism
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

31. International Conference on Quantum Foundation and Technology
What we cannot do:
Charge/Spin gap: non-convergence of KS-eqs
Solutions: Ensemble DFT/thermodynamic DFT?
International Conference on Quantum Foundation and Technology
2018年12月2日星期日

32. International Conference on Quantum Foundation and Technology
2. Strong attractive interaction U<-3?
3. Long-time evolution? Friedel Oscillation?
References:
Phys. Rev. Lett. 98, (2007)
Phys. Rev. Lett. 101, (2008)
Phys. Rev. B 78, (2008)
International Conference on Quantum Foundation and Technology
2018年12月2日星期日