First Program & Quantum Cybernetics
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1 First Program & Quantum Cybernetics 15 December 2011 Kyoto Development of Optical Lattice Quantum Simulator Kyoto University, JST Y. Takahashi
2 First Program : Analogue Quantum Computer/Quantum Simulation Kyoto Group Osaka Group Tokyo Group : ultracold atoms in optical lattice : cold ions in ion-traps : exciton(-polaritons) in semiconductors Quantum Cybernetics : Quantum Control of Cold Atoms Kyoto Group : ultracold atoms in OL NTT(Mukai) Group : cold atoms in atom chips Gakushuin Group Kyoto Group: : BEC in optical trap Quantum Simulation of Hubbard Model This presentation Quantum Feedback Control Poster by Dr. Yamazaki Poster by Dr. Inoue Poster by Mr. Taie
3 Collaborators Optical Lattice: NTT: K. Inaba M.Yamashita Geneva: A. Tokuno, T. Girmarchi Ben Li, Y. Nakamura, R. Yamazaki, S. Sugawa, YT, Y. Takasu, R. Inoue, H. Shimizu, S. Nakajima, S. Uetake, Y. Yoshikawa, H. Hara, (S. Kato, K. Takahashi) H. Konishi, Y. Kikuchi, H. Yamada, R. Yamamoto, S. Taie, R. Namiki, K. Shibata, (Undergraduate: K. Nishimura, T. Nishio, T. Seki, S. Watanabe)
4 Prospects Outline of Talk Quantum Simulation of Hubbard Model Realization of SU(6) Mott Insulator High-Resolution Spectroscopy
5 Quantum Simulation H J Hubbard Model: i, j c i c j U i n i n i i-th t i, j j-th Cold Magnetism, Atoms Superconductivity in Optical Lattice U λ/2
6 Phase Diagram of Repulsive Fermi Hubbard Model 3D 2D AFM d-wave Superconductor hole x (carrier doping) electron [T. Esslinger, Annu. Rev. Condens. Matter Phys : ] [T. Moriya and K. Ueda, Rep. Prog.Phys. 66(2003)1299]
7 Beyond SU(2) Physics: Extension to Larger Spin Degrees of Freedom 2 4 as Hint ( r1 r M SU(N) algebra: S m n 173 Yb: c n c m m [ Hint, ] S n [ S m n, S 0 p q +5/2 +3/2 +1/2-1/2-3/2-5/2 origin of spin degrees of freedom is nuclear spin 2 ) SU(N) system spin permutation operators (generators of SU(N) rotations) Physics of large-spin Fermi gas: ] S E. Szirmai and J. Solyom, PRB71, (2005), K. Buchta, et al., PRB75, (2007) M. A. Cazalilla, et al., N. J. Phys11, (2009), M. Hermele et al.,prl 103, (2009) A. V. Gorshkov, et al., Nat. Phys. 6, 289(2010), etc Valence-Bond Solid, mq p n pn S m q
8 The first quantum gas with SU(N>2) symmetry SU(6) Fermion :Realized 173 Yb:SU(6) +5/2 +3/2 +1/2-1/2-3/2-5/2 [T. Fukuhara et al., PRL. 98, (2007)] T/T F =0.14 (6-component) Optical Stern-Gerlach Spin-Separator [S. Taie et al., PRL105, (2010)] -5/2, -3/2-1/2 +1/2 +3/2 +5/2
9 (h/j) Doublon Production Rate Measurement by lattice modulation modulation N= , 11E R, 18%pp mod. U/J=62.4 Photoassociation doublon production rate Г is a sensitive probe of T lattice [D. Greif et al., PRL106, (2011)] T ini =0.21T F = 24 nk T lattice =5.1J= 16 nk T lattice =27.4J= 83 nk T: low T: high (in a harmonic trap)
10 Spin Degrees of Freedom is Cool Pomeranchuk Cooling [Pomeranchuk, (1950)] Discovery of Superfluid 3 He by Osheroff, Lee, Richardson Pomeranchuk Cooling of an Atomic Gas Initial state: Spin depolarized and also with degeneracy: Adiabatic change Final state: Spin depolarized and also with localization s ~ k B π 2 T/T F liquid 3 He atoms in a trap solid 3 He s ~k B ln(n) atoms in Mott Insulator Next Step: entropy flows from motional degrees of freedom to spin, which results in the low temperature If T/T F =0.14 then s ini ~ k B π 2 T/T F < s fin ~ k B ln(n)
11 Prospects Outline of Talk Quantum Simulation of Hubbard Model Realization of SU(6) Mott Insulator High-resolution spectroscopy
12 New Possibility: High-Resolution Laser Spectroscopy of Strongly Correlated Quantum Many-body System Ultra-narrow Optical Transitions in Yb 3 P 2 ~15 s (10~40 mhz) 507 nm 3 P 0 ~23 s (15 mhz) 1 S nm High-resolution laser spectroscopy as a Local Probe
13 Spectroscopy of Atoms in a Mott Insulating State We can spectroscopically resolve the double and single occupancy n=3 V=15 E R N= n=2 n=1 a eg = -23 nm 2
14 Superfluid-Mott Insulator Transition S. Kato et al V=
15 Phase Diagram of Bose Gas (homogeneous) Normal fluid T lattice Quantum Critical Point Superfluid Mott U/J [S. Trotzky et al., Nature Physics, 6, 998(2010)]
16 Prospects Outline of Talk Quantum Simulation of Hubbard Model Realization of SU(6) Mott Insulator High-resolution spectroscopy
![] Anderson Localization T c vs](/docs-images/85/91514462/images/17-3.jpg "Impurities Heavy Impurity (Yb) in a")
17 Prospects: Simulation of Impurity in Superfluid [F. M.Spiegelhalder,et al, PR L(2009). K. Targonska and K. Sacha, PR A(2010) R. B. Diener and M. Randeria,PRA(2010) E. Vernier, et al, arxiv(2010).] Anderson Localization T c vs Impurities Heavy Impurity (Yb) in a Superfluid (Li) 6 Li 174 Yb M Yb /M li ~ 29 Poster by Dr. Nakajima 6 Li 173 Yb T/T T/T F = 0.07±0.02 F = 0.08±0.02 T = 280 ±20 nk T/T F = 0.52 ±0.12 [H. Hara et al., Phys. Rev. Letters 106, (2011):Editor s Suggestion]
18 Prospects: Super-Lattice 174 Yb BEC decorated square lattice N= [PRA80, (2009)] dp model
19 Prospects Summary Quantum Simulation of Hubbard Model Realization of SU(6) Mott Insulator Demonstration of New Atom Cooling :Pomeranchuk Cooling Starting Point Towards SU(6) Quantum Magnetism High-resolution spectroscopy Possible New Probe of Quantum Critical Behaviors Yb-Li Quantum Mixture : Simulation of Impurity problem Super-Lattice
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