The 4th Yamada Symposium Advanced Photons and Science Evolution 14 June 2010 JICA, Osaka Quantum Simulator Using Ultracold Two-Electron Atoms In an Optical Lattice Thank you chairman. First I thank the organizers for kind invitation to this nice seminar, and giving me a chance to talk about our recent work on Ytterbium.  Title of my talk is quantum degenerate gases of Ytterbium atoms. % I am Takahashi from Kyoto University. Kyoto University, JST Y. Takahashi

Quantum Optics Group Members Let me first introduce our group members. These people have been working very hard for the experiments described in this talk. Before going to the discussion of the Yb experiments, let me briefly show you the results for Rb BEC, % which is related to Okano`s poster. %Our lab is located in the North campus, and is quite close from here, so please visit our lab. at any time. %Mr. Okano and Mr. Fukuhara will present posters tomorrow, so please also visit their posters. NTT: K. Inaba M.Yamashita R. Yamazaki, YT, R. Inoue, K. Shibata, J. Doyle, S. Kato Y. Yoshkawa, S. Uetake, S. Sugawa, S. Taie, H. Hara, H. Shimizu, R. Yamamoto, I. Takahashi R. Namiki , H. Yamada, Y. Takasu, R. Murakami, S. Imai, (S. Tanaka. N. Hamaguchi)

Quantum Simulation “Interesting” “HARD” “Controllable” Many-body Quantum System “Interesting” Many-body Classical System “HARD” Many-body Quantum System “Controllable”

Quantum Simulation Hubbard Model: Magnetism, Superconductivity i-th j-th Magnetism, Superconductivity λ/2 Cold Atoms in Optical Lattice

Quantum Simulation of Hubbard Model using “Cold Atoms in Optical Lattice” λ/2 , as : scattering length Controllable Parameters hopping between lattice sites : t lattice potential :V0 On-site interaction :U Feshbach Resonance :as filling factor (e- or h-doping) :n atom density :n No impurity, No lattice defects, Various geometry

Phase Diagram of High-Tc Cuprate Superconductor experiment theory AF SC SC x hole electron hole electron (carrier doping) (carrier doping) [in T. Moriya and K. Ueda, Rep. Prog.Phys.66(2003)1299] There is controversy in the under-dope region

Quantum Simulators using Alkali Atoms Bose-Hubbard Model: Yb Atoms Our Approach two-electron atom 87Rb “Superfluid - Mott-insulator Transition” [M. Greiner, et al., Nature 415,39 (2002)] … Fermi-Hubbard Model: “Formation of Mott-insulator state” [R. Jördens et al., Nature 455, 204 (2008)] 40K [U. Schneider, et al., Science 322,1520(2008)] [K. Günter, et al, PRL96, 180402 (2006)] [S. Ospelkaus, et al, PRL96, 180403 (2006)] Bose-Fermi-Hubbard Model: [Th. Best, et al, PRL102, 030408 (2008)] 87Rb + 40K Bose-Bose-Hubbard Model: [J. Catani, et al, PRA77, 011603(R) (2008)] 87Rb + 41K

Unique Features of Ytterbium Atoms Rich Variety of Isotopes 168Yb (0.13%) 170Yb (3.05%) 171Yb (14.3%) 172Yb (21.9%) 173Yb (16.2%) 174Yb (31.8%) 176Yb (12.7%) This is the result of the calculation of the scattering lengths based on this formula given in this paper. As you can see, the scattering length is very sensitive to the value of the vibrational quantum number at the dissociation energy. We do not know the exact value of this parameter. However, from our previous photoassociation measurement and BEC experiment, We can exclude the very large and very small and negative scattering length for 174Yb. So this is the allowed window. You can see a large variation of scattering length , large positive and large negative, among isotopes according to this calculation. Boson Boson Fermion Boson Fermion Boson Boson

Isotopic Tuning of Interatomic Interaction 25 20 15 10 5 -5 -10 -15 -20 -25 168 170 171 172 173 174 176 13 6.2 4.7 3.4 2.0 0.1 -19 1.9 -0.1 -4.3 -27 11 -0.2 -4.5 -31 23 7.5 -32 22 5.6 7.3 4.2 2.9 -1.3 (nm) Mass number 168 170 171 172 173 174 176 Scattering Length [M. Kitagawa, et al, PRA77, 012719 (2008)] This is the result of the calculation of the scattering lengths based on this formula given in this paper. As you can see, the scattering length is very sensitive to the value of the vibrational quantum number at the dissociation energy. We do not know the exact value of this parameter. However, from our previous photoassociation measurement and BEC experiment, We can exclude the very large and very small and negative scattering length for 174Yb. So this is the allowed window. You can see a large variation of scattering length , large positive and large negative, among isotopes according to this calculation. Collaboration with R. Ciurylo, P. Naidon, P. Julienne

Unique Features of Ytterbium Atoms Ultra-narrow Optical Transitions ~15 s (10~40 mHz) ~23 s (15 mHz) 507 nm 578 nm 1S0 3P0 3P2 High-resolution laser spectroscopy as a Local Probe This is the result of the calculation of the scattering lengths based on this formula given in this paper. As you can see, the scattering length is very sensitive to the value of the vibrational quantum number at the dissociation energy. We do not know the exact value of this parameter. However, from our previous photoassociation measurement and BEC experiment, We can exclude the very large and very small and negative scattering length for 174Yb. So this is the allowed window. You can see a large variation of scattering length , large positive and large negative, among isotopes according to this calculation. High-spatial resolution Optical Magnetic Resonance Imaging

Outline of Talk Preparation of Quantum Degenerate Gases BEC, Fermi Degeneracy, Mixture Experiments of Atoms in an Optical Lattice Let me Now switch to the main topic of Yb experiments. First I show you unique properties of Yb atoms. Next I will describe in detail our experiments toward quantum degeneracy both for bosonic and fermionic isotopes. Finally, I summarize my talk and I will mention the unique future possibility, if I have a time. Boson, Fermion, Mixtures Prospects

Outline of Talk Preparation of Quantum Degenerate Gases BEC, Fermi Degeneracy, Mixture Experiments of Atoms in an Optical Lattice Let me Now switch to the main topic of Yb experiments. First I show you unique properties of Yb atoms. Next I will describe in detail our experiments toward quantum degeneracy both for bosonic and fermionic isotopes. Finally, I summarize my talk and I will mention the unique future possibility, if I have a time. Boson, Fermion, Mixtures Prospects

Optical Imaging Cold Atoms CCD Time-of-Flight Image: Iincident(x,y) resonant probe light Iincident(x,y) lens CCD Itransmission(x,y) “The atom distribution after certain time from the sudden release of the atoms corresponds to the momentum distribution” Time-of-Flight Image:

Preparation of Quantum Degenerate Gases Optical Trap (FORT) Cold Hot Bose-Einstein Condensation N~105 T~100nK 174Yb [Y. Takasu et al., PRL 91, 040404 (2003)] gravity This is the result of the calculation of the scattering lengths based on this formula given in this paper. As you can see, the scattering length is very sensitive to the value of the vibrational quantum number at the dissociation energy. We do not know the exact value of this parameter. However, from our previous photoassociation measurement and BEC experiment, We can exclude the very large and very small and negative scattering length for 174Yb. So this is the allowed window. You can see a large variation of scattering length , large positive and large negative, among isotopes according to this calculation.

Quantum Degenerate Yb Gases Boson [Y. Takasu et al., PRL 91, 040404 (2003)] [T. Fukuhara et al., PRA 76, 051604(R)(2007)] 174Yb 160µm TOF: 10ms 120 µm TOF: 8 ms 176Yb 168Yb(0.13%) 30 µm 170Yb This is the result of the calculation of the scattering lengths based on this formula given in this paper. As you can see, the scattering length is very sensitive to the value of the vibrational quantum number at the dissociation energy. We do not know the exact value of this parameter. However, from our previous photoassociation measurement and BEC experiment, We can exclude the very large and very small and negative scattering length for 174Yb. So this is the allowed window. You can see a large variation of scattering length , large positive and large negative, among isotopes according to this calculation. Fermion [T. Fukuhara et al., PRL. 98, 030401 (2007)] [S. Taie et al ., arxiv:1005.3710] 171Yb(I=1/2) T/TF =0.3 (2-component) 173Yb(I=5/2) T/TF =0.14 (6-component)

Ultracold 173Yb: Fermi Gas with 6-spin components [S. Taie et al ., arxiv:1005.3710] SU(6) system novel magnetism [M. A. Cazalilla, et al., N. J. Phys11, 103033(2009); M. Hermele et al.,PRL 103, 135301(2009), A. V. Gorshkov, et al., Nat. Phys. 6, 289(2010)] mF= -3/2 -1/2 -5/2 +3/2 +1/2 +5/2 “Optical Stern-Gerlach Effect” σ+ σ– -5/2, -3/2, -1/2 +5/2, +3/2, +1/2 g TOF 7ms 1S0–3P1 Δ~2π×4GHz, 10mW, 3.4ms, 90µm

Quantum Degenerate Mixtures of Yb [T. Fukuhara et al., Phys. Rev. A 79, 021601(R) (2008); in preparation ] 173Yb(Fermion) +174Yb(Boson) NB~3×104, BEC 173Yb(Fermion) +170Yb(Boson) NB~8×103, BEC 170Yb(10ms) 173Yb(4ms) 174Yb(Boson)+ 176Yb(Boson) NB~6×104, BEC NB~2×104 171Yb(Fermion) + 173Yb(Fermion) 171Yb(m=+1/2) 173Yb(m=+5/2) T/TF = 0.3 T/TF = 0.33

SU(2)×SU(6) Symmetry 171Yb: N = 8.0×103 T = 95 nK [S. Taie et al ., arxiv:1005.3710] 171Yb: N = 8.0×103 T = 95 nK T/TF = 0.46 (2-component) 173Yb: N = 1.1×104 T = 87 nK T/TF = 0.54 (6-component) [Theory: D. B. M. Dickerscheid et al ., Phys. Rev. A 77, 053605 (2008)] “Spinor Superfluidity”

Outline of Talk Preparation of Quantum Degenerate Gases BEC, Fermi Degeneracy, Mixture Experiments of Atoms in an Optical Lattice Let me Now switch to the main topic of Yb experiments. First I show you unique properties of Yb atoms. Next I will describe in detail our experiments toward quantum degeneracy both for bosonic and fermionic isotopes. Finally, I summarize my talk and I will mention the unique future possibility, if I have a time. Boson, Fermion, Mixtures Prospects

Bose-Fermi Mixture in a 3D optical lattice Repulsive Interaction: aBF = +7.3 nm 174Yb(Boson) +173Yb(Fermion): aBB = +5.6 nm aFF = +10.6 nm Attractive Interaction: aBF = -4.3 nm 170Yb(Boson) +173Yb(Fermion): aBB = +3.4 nm aFF = +10.6 nm λlattice= 532 nm VB ~ VF ωB ~ ωF tB ~ tF ΔzB ~ ΔzF λlattice= 532 nm λlattice= 532 nm

Photoassociation(PA) Study of Atoms in an Optical Lattice [T. Rom, et al., PRL93, 073002(2004)]

Outline of Talk Preparation of Quantum Degenerate Gases BEC, Fermi Degeneracy, Mixture Experiments in an Optical Lattice Let me Now switch to the main topic of Yb experiments. First I show you unique properties of Yb atoms. Next I will describe in detail our experiments toward quantum degeneracy both for bosonic and fermionic isotopes. Finally, I summarize my talk and I will mention the unique future possibility, if I have a time. Boson, Fermion, Mixtures Prospects

Prospects f Optical Feshbach Resonance Using Intercombination Transition Modulation Index λ/2=278 nm 174Yb BEC [K. Enomoto et al.,PRL. 101, 060406 (2008)] [R. Yamazaki et al.,arXiv:1005.3372] Single Site Addressing in an Optical Lattice f [K. Shibata et al., App. Phys. B 97, 753(2009)] 171Yb Nuclear Spin Squeezing [T. Takano et al., PRL. 102, 033601 (2009), T. Takano et al., PRL. 104, 013602 (2010)] YbLi polar molecule [M. Okano et al., App. Phys. B 98, 2(2009)] Simultaneous Optical Trapping

Single Site Addressing: Optical Magnetic Resonance Imaging (MRI) [K. Shibata et al., App. Phys. B 97, 753(2009)] 3P2 Spatial resolution: 250 nm Magnetic field gradient Spectral Resolution Optical absorption line of linewidth 15 mHz ~15 s 1S0-3P2: 507 nm In addition, it is also interesting to perform the optical MRI using this transition. With the modest conditions of 1kHz resolution and 10 G/cm field gradient, Spatial resolution becomes less than 1 micron. The field gradient like this is created by such saddle coils. Esspecially interesting is To apply this technique to atoms in an optical lattice. By 1D field gradient, we can select one particular layer. And by 2D field gradient, we can select one particular line. And by 3D field gradient, we can ultimately select one lattice site. 1S0 f “Optical Spectrum of 1S0-3P2 transition” Nagaoka-ferro Quantum Computation

Cold Atoms in a Thin Glass Cell 1D lattice Transfered Optical Tweezer BEC Formation MOT 14 mm

Summary Preparation of Quantum Degenerate Gases: BEC: 174Yb, 170Yb, 176Yb, 168Yb FDG: 173Yb, 171Yb, Mixture: 174Yb+ 173Yb(BF), 170Yb+ 173Yb(BF), 176Yb+ 174Yb(BB), 171Yb+ 173Yb(FF) Experiments of Atoms in an Optical Lattice: Bose-Fermi Mixtures in a 3D Optical Lattice Prospects: Optical Feshbach Resonance Single Site Addressing Using 3P2 State in an Optical Lattice 171Yb Nuclear Spin Squeezing YbLi polar molecule

Thank you very much for attention 16 August Mount Daimonji at Kyoto