华南师范大学：Simulation of Condensed Matter Physics with ultrocold atoms（PPT讲稿）

a Simulation of Condensed Matter Physics an with ultracold atoms 朱诗亮( Shi- Liang Zhu) 广州华南师范大学物理与电信工程学院 shilzhuayahoo.com.cn 全国冷原子物理和量子信息青年学者学术讨论会 山西太原 2007,7,2-6

1 Simulation of Condensed Matter Physics with ultrocold atoms 朱诗亮 (Shi-Liang Zhu) 广州 华南师范大学物理与电信工程学院 shilzhu@yahoo.com.cn 全国冷原子物理和量子信息青年学者学术讨论会 山西 太原 2007,7,2-6

Outlines 1 Background Quantum simulation; Ultracold atoms 2 Spin- Hall effects 3 Relativistic dirac fermions

2 Outlines 1 Background Quantum simulation; Ultracold atoms 2 Spin-Hall effects 3 Relativistic Dirac fermions

I Spin-hall effects for cold atoms in a light-induced gauge field S L Zhu, H. Fu, C.J. Wu, S C. Zhang, and L M. Duan. PRL97,240401(2006) M E(FOCUS center and MCTP, University of Michigan 吴从军(CJWu)(KITP,UC, Santa barbara) 张首晟(S.C. Zhang)( Stanford University) 段路明(L. M. Duan)( FOCUS center and MCTP, University of Michigan) 2 Simulation and detection of dirac fermions with cold atoms in an optical lattice S L Zhu, B. Wang, and L M. Duan, PRL98, 260402(2007 王伯根(南京大学)段路明(niv.Mch)

3 1 Spin-Hall effects for cold atoms in a light-induced gauge field S. L. Zhu, H. Fu, C. J. Wu, S. C. Zhang, and L. M. Duan, PRL 97,240401 (2006). 傅浩 (FOCUS center and MCTP, University of Michigan 吴从军(C.J.Wu) (KITP, UC, Santa Barbara) 张首晟(S. C. Zhang) (Stanford University) 段路明(L. M. Duan) (FOCUS center and MCTP, University of Michigan) 2 Simulation and detection of Dirac fermions with cold atoms in an optical lattice S. L. Zhu, B. Wang, and L. M. Duan, PRL98, 260402 (2007) 王伯根 (南京大学) 段路明(Univ. Mich.)

Simulate a quantum system with a classical computer is very hard Simulate a quantum system by a quantum computer accurately control every basic operation 2 Simulate a quantum system by a quantum simulator Quantum simulator with ultrocold atoms

4 Simulate a quantum system with a classical computer is very hard 1 Simulate a quantum system by a quantum computer accurately control every basic operation 2 Simulate a quantum system by a quantum simulator Quantum simulator with ultrocold atoms

Quantum computation: a universal set of quantum gates Two noncomputable One nontrivial two-qubit gate single-qubit gates U Ux()=exp(ir, o, /2) If lwm)is a product state U2(y)=ex(-iy2a:/2) out) is an entangled state then u is nontrivial a general U can be decomposed into single-qubit rotations and a nontrivial two-qubit gate

5 Quantum computation: a universal set of quantum gates • Two noncommutable single-qubit gates • • • One nontrivial two-qubit gate If is a product state is an entangled state then U is nontrivial •A general U can be decomposed into single-qubit rotations and a nontrivial two-qubit gate U ( ) exp( / 2) X x x x U  = −i  ( ) exp( / 2) Z z z z U  = −i  U C T  in  out

1 The parameters of a system are well-controllable 2 measurable System Simulator

6 1 The parameters of a system are well-controllable 2 measurable System Simulator

Atoms at optical lattices Bose-Hubbard Hamiltonian H ∑ bb+∑6n+2 ∑(-1) D Jaksch et al(1998) 60 nm array of 1D tubes M. Greiner et al., Nature(2002) You can control almost all aspects of the periodic structure and the interactions between the atoms

7 Atoms at optical lattices You can control almost all aspects of the periodic structure and the interactions between the atoms M. Greiner et al. , Nature (2002) D.Jaksch et al (1998)      + = − + + − i j i i i j i i ni ni U H J b b n ˆ (ˆ 1) 2 Bose  ˆ -Hubbard Hamiltonian

Cold atomic systems Quantum information Ultra cold atoms Many-body system Few-body system (condensed matter physics Field theories

8 Cold atomic systems Ultra cold astoms Quantum information Many-body system (condensed matter physics) Few-body system Field theories

Real space or momentum distributions of the atoms Time of flight measurement time of flight 2 ms 6 ms 14 ms 18 ms Individual condensates in the lattice expand and interfere with each other, revealing the momentum distribution of the atoms in the lattice

9 Real space or momentum distributions of the atoms

33 103 Spin hall effects I Gauge fields in atomic systems 2 Spin Hall effects and Atomic spin Hall effects 3 Detection 4 Conclusions

10 Spin Hall Effects 1 Gauge fields in atomic systems 2 Spin Hall effects and Atomic spin Hall effects 3 Detection 4 Conclusions