Ultracold atoms in an optical lattice -an ideal simulator of strongly-correlated quantum many-body system-
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1 GCOE Symposum Development of emergent new felds February Ultracold atoms n an optcal lattce -an deal smulator of strongly-correlated quantum many-body system- Kyoto Unversty Y. Takahash
2 R. Yamamoto P125 Quantum Optcs Group Kyoto Unversty H. Hara P10 Y. Nakamura P66 Dr. Takasu P104 Dr. Namk (GCOE PD) S. Watanabe P121 T. Nsho P71 Y. Sek P82 NTT: K. Inaba M. Yamashta
3 Research Objectves of Our Group n GCOE program Applcaton of atoms to nvestgatng 1) quantum nformaton (scence) and 2) (aspects of) fundamental physcs (ntegratng optcal and atomc experments wth elementary partcle theores)
4 Atom number We have ntated a new research project : Test of Gravty at Nano-meter Scale by usng Bose-Ensten Condensate from the dscusson wth prof. Ando (specal AP of GCOE) Inhomogenety Reproducblty Controllablty atom atom Precse measurement of bndng energes of molecule to detect possble effect of gravty photo-assocaton Current status: ~1kHz khz Revealed Insuffcency of smple mass-ndependent Potental
5 Research Objectves of Our Group n GCOE program Applcaton of atoms to nvestgatng 1) quantum nformaton (scence) and 2) (aspects of) fundamental physcs (ntegratng optcal and atomc experments wth elementary partcle theores) Quantum Smulaton of Hubbard Model
6 Outlne Quantum Smulaton of Strongly-Correlated System dual Mott nsulator of Boson and Fermon SU(6) Mott nsulator hgh-resoluton spectroscopy of SF-Mott nsulator transton Resonant Control of Interacton: ansotropy-nduced Feshbach resonance between 1 S 0 and 3 P 2 states Prospects: Leb lattce Quantum Gas Mcroscope YbL Spn-Orbt Interacton
7 Outlne Quantum Smulaton of Strongly-Correlated System dual Mott nsulator of Boson and Fermon SU(6) Mott nsulator hgh-resoluton spectroscopy of SF-Mott nsulator transton Resonant Control of Interacton: ansotropy-nduced Feshbach resonance between 1 S 0 and 3 P 2 states Prospects: Leb lattce Quantum Gas Mcroscope YbL Spn-Orbt Interacton
8 Interestng H Quantum Smulaton Many-body Quantum System Hubbard Model: t, j c c j U n n -th t, j j-th U Magnetsm, Superconductvty
9 Quantum Smulaton Usng ultracold atoms n an Optcal Lattce a a U H J j ( 1), j 2 clean system, hgh controllablty, varous geometry, etc n n n Optcal lattce = perodc potental for atoms generated by standng wave of laser lght In fact, there are many QS experments usng Alkal-atoms
10 Quantum Smulaton Usng Ytterbum atoms n an Optcal Lattce a a U H J j ( 1), j 2 n n n λ lattce = 532 nm λ lattce = 532 nm λ lattce = 532 nm
11 Unque Features of Ytterbum Atoms Rch Varety of Isotopes 168 Yb (0.13%) 170 Yb (3.05%) 171 Yb (14.3%) 172 Yb (21.9%) 173 Yb (16.2%) 174 Yb (31.8%) 176 Yb (12.7%) Boson Boson Fermon Boson Fermon Boson Boson Attractve Interacton: a BF = nm a BB = +3.4 nm a FF = nm Repulsve Interacton: a BF = +7.3 nm a BB = +5.6 nm a FF = nm
![7, 642 648 (2011)] Boson MI Fermon MI Phase Separaton Composte Partcles Mxed Mott Insulator trgger theoretcal studes boson](/docs-images/82/86654559/images/12-2.jpg "fermom arxv:1205.4026v1 Ehud Altman, Eugene Demler, Achm Rosch Mott crtcalty and pseudogap n Bose-Ferm mxtures arxv:1204.")
12 By loadng the BF mxtures nto 3D optcal lattce, we successfully create Strongly Interactng Dual Mott Insulators [S. Sugawa, K. Inaba, et al., Nature Physcs. 7, (2011)] Boson MI Fermon MI Phase Separaton Composte Partcles Mxed Mott Insulator trgger theoretcal studes boson fermom arxv: v1 Ehud Altman, Eugene Demler, Achm Rosch Mott crtcalty and pseudogap n Bose-Ferm mxtures arxv: Ippe Danshta and L. Mathey Counterflow superflud of polaron pars n Bose-Ferm mxtures n optcal lattces
13 Unque Features of Ytterbum Atoms Rch Varety of Isotopes 168 Yb (0.13%) 170 Yb (3.05%) 171 Yb (14.3%) 172 Yb (21.9%) 173 Yb (16.2%) 174 Yb (31.8%) 176 Yb (12.7%) Boson Boson Fermon Boson Fermon Boson Boson 173 Yb (I=5/2) +5/2 +3/2 +1/2-1/2-3/2-5/2 orgn of spn degrees of freedom s nuclear spn 2 4 as Hnt ( r1 r M 2 ) SU(6) system Expermental realzaton s very dffcult n sold state system
![98, 030401 (2007)] +5/2 +3/2 +1/2-1/2-3/2-5/2 T/T F](/docs-images/82/86654559/images/14-2.jpg "=0.14 (6-component) SU(6) Hubbard model Optcal")
14 The frst quantum gas wth SU(N>2) symmetry SU(6) Fermon 173 Yb:SU(6) [T. Fukuhara et al., PRL. 98, (2007)] +5/2 +3/2 +1/2-1/2-3/2-5/2 T/T F =0.14 (6-component) SU(6) Hubbard model Optcal Stern-Gerlach Spn-Separator for nuclear spn [S. Tae et al., PRL105, (2010)] -5/2, -3/2-1/2 +1/2 +3/2 +5/2 +5/2
![, PRL106, 145302 (2011)] T](/docs-images/82/86654559/images/15-5.jpg "lattce =5.1t= 16 nk N=1.")
15 (h/t) Lattce Modulaton Technque modulaton Photoassocaton doublon producton rate Г s a senstve probe of T lattce [D. Gref et al., PRL106, (2011)] T lattce =5.1t= 16 nk N= , 11E R, 18%pp mod. U/t=62.4 T lattce =27.4t= 83 nk T: low (n a harmonc trap) T: hgh We could successfully create SU(6) Mott Insulator
16 Lower temperature s acheved wth larger spn system [S. Tae et al, Nature Physcs 8, 825(2012) ] SU(6) versus SU(2) SU(2) SU(6) Enhanced Pomeranchuk Coolng of an Atomc Gas solated spn carres large entropy of log(n) Theory (T > t): [M. A. Cazallla, et al, N. J. Phys.11, (2009)] [K. R. A. Hazzard, et al, arxv: (2010]
17 Unque Features of Ytterbum Atoms Long-lved metastable state /Ultra-narrow Optcal Transtons 3 P 2 ~15 s (10~40 mhz) 507 nm 3 P 0 ~23 s (15 mhz) 1 S nm Hgh-resoluton laser spectroscopy
18 ms Spectroscopy of Atoms n a Mott Insulatng State We can spectroscopcally resolve and ndependently control the sngle, double, and trple occupancy ms ~2(U eg -U gg ) ~U eg -U gg ms
19 Spectroscopy of Superflud-Mott Insulator Transton Theory (NTT) and Experment (Kyoto) E R 2 kl 2m 2
20 Spectroscopy of Superflud-Mott Insulator Transton Theory (NTT) and Experment (Kyoto) E R 2 kl 2m 2 Hgh-resoluton laser spectroscopy s a powerful tool for the study of SF-Mott nsulator transton
21 Outlne Quantum Smulaton of Strongly-Correlated System dual Mott nsulator of Boson and Fermon SU(6) Mott nsulator hgh-resoluton spectroscopy of SF-Mott nsulator transton Resonant Control of Interacton: ansotropy-nduced Feshbach resonance between 1 S 0 and 3 P 2 states Prospects: Leb lattce Quantum Gas Mcroscope YbL Spn-Orbt Interacton
22 Quantum Smulaton Usng Ytterbum atoms n an Optcal Lattce a a U H J j ( 1), j 2 n n n λ lattce = 532 nm one mportant ngredent s mssng Independent Control of U λ lattce = 532 nm λ lattce = 532 nm
23 Potental How to Control U for alkal-atoms Magnetc Feshbach Resonance ( 2 S 1/2 + 2 S 1/2 ) Couplng between Open Channel and Closed Channel results n Resonant Control of Interacton(a s ) a s ( B) a bg (1 B B B 0 ) Molecular State F 2 +F 2 Two Atoms -C 6 /R 3 F 1 +F 1 [C. Regal and D. Jn, PRL90, (2003)]
24 How to Control U for Yb atoms Optcal No Feshbach Resonance for Yb atoms ( 1 S S 0 ) "Optcal Feshbach Resonance Usng the Intercombnaton Transton K. Enomoto, et al., PRL,101, (2008), Submcron Spatal Modulaton of an Interatomc Interacton n a BEC R. Yamazak, et al., PRL,105, (2010) Manpulatng Hgher Partal-Wave Interatomc Interacton wth an Optcal Feshbach Resonance R. Yamazak et al., arxv: There s a sgnfcant loss due to Photoassocaton
25 Unque Features of Ytterbum Atoms Long-lved metastable state 3 P 2 ~15 s (10~40 mhz) 507 nm 3 P 0 ~23 s (15 mhz) 1 S nm Another Useful Orbtal States wth Dfferent Characters
26 Magnetc Feshbach Resonance between 1 S 0 and 3 P 2 1 S 0 3 P 2 (m= + 2) : 174 Yb 1 S 0 3 P 2 (m= - 2) : 170 Yb [S. Kato et al., arxv: ] We can study varous nterestng physcs wth resonant nteracton
27 Outlne Quantum Smulaton of Strongly-Correlated System dual Mott nsulator of Boson and Fermon SU(6) Mott nsulator hgh-resoluton spectroscopy of SF-Mott nsulator transton Resonant Control of Interacton: ansotropy-nduced Feshbach resonance between 1 S 0 and 3 P 2 states Prospects: Leb lattce Quantum Gas Mcroscope YbL Spn-Orbt Interacton
28 Non-Standard Lattce-Leb Lattce- E. H. Leb, PRL 62, 1201 (1989) =0 0 E (, k) E 0 C E (, k) A B a E 2 4t 2 {cos 2 ( k x a / 2) cos 2 ( k y a / 2)} proposal for optcal lattce mplementaton R. Shen et al., PRB81, R,2010 λ 1 = 532 nm λ 2 =1064 nm
29 Developng Yb Quantum Gas Mcroscope Boson, Fermon, Bose-Ferm Mxture
30 Smulaton of Impurty System wth Yb-L atomc mxture the hoppng rate t Yb << t L localzed mpurty Anderson Hubbard Model J c c U n n H m, j, m, Yb,, j m,, W Hgh-resoluton Spectroscopy: Anderson Othogonalty Catastorophe n W L delocalzed carrer Random Potental W (wth Yb) 0 (wthout Yb)
31 0 E 10 E 15 E 20 E Smulaton of Impurty System wth Yb-L atomc mxture the hoppng rate t Yb << t L localzed mpurty Anderson Hubbard Model J c c U n n H m, j, m, Yb,, j m,, Superflud-Mott nsulator Transton of Yb W n W L delocalzed carrer Random Potental W (wth Yb) 0 (wthout Yb)
32 Summary Quantum Smulaton of Strongly-Correlated System dual Mott nsulator of Boson and Fermon SU(6) Mott nsulator hgh-resoluton spectroscopy of SF-Mott nsulator transton Resonant Control of Interacton: ansotropy-nduced Feshbach resonance between 1 S 0 and 3 P 2 states Prospects: Leb lattce: mplementaton of 2D super-lattce Quantum Gas Mcroscope: fluorescence magng wth dual molasses YbL: optcal lattce setup for mpurty problem spn-orbt Interacton
33 Thank you very much for attenton 16 August Mount Damonj at Kyoto
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