Zhejiang Normal University

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Presentation transcript:

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, 266403 (2007) Phys. Rev. Lett. 101, 206402 (2008) Phys. Rev. B 78, 195109 (2008) July 18, 2009 International Conference on Quantum Foundation and Technology 2018年12月2日星期日

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

International Conference on Quantum Foundation and Technology 2. Strong attractive interaction U<-3? 3. Long-time evolution? Friedel Oscillation? References: Phys. Rev. Lett. 98, 266403 (2007) Phys. Rev. Lett. 101, 206402 (2008) Phys. Rev. B 78, 195109 (2008) International Conference on Quantum Foundation and Technology 2018年12月2日星期日