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by: Sadie Gusikowski


Sadie Gusikowski
GPA 3.87


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Class Notes
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This 37 page Class Notes was uploaded by Sadie Gusikowski on Thursday October 22, 2015. The Class Notes belongs to INT 1 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 19 views. For similar materials see /class/226876/int-1-university-of-california-santa-barbara in Interdisciplinary Sciences at University of California Santa Barbara.

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Date Created: 10/22/15
Exotic quantum es of polar molecules lticomponent systems DaWWei Wang National TsingHua University Taiwan 7 Outline 1 Introduction to dipolar atommolecules and dipolar condensate II New states of dipoles in bilayer system Dimer SF and Schrodinger s cat state 111 New states of dipoles in multilayer system dipolar chain liquid IV New states of dipoles in double wire system Spin ferromagnetism V Summary Why dipoles are interesting Dipoles in nature Most available Candidates 1 Heteronuclear molecules 2 Atoms With magnetic moment a Direct molecules p 15 D b But dif cult to be cooled Doyle Meijer DeMille etc T Artificial dipoles quot a yr HRbC ST E gm LESS 1 Feshbach resonance an 3 Mb 5 r 5 3 KRb JILA ETH etc m 1m WWW 0 err 777 But not 1n ground state E W T A u 39 l weak dlpole moment g i short life time E m 6000 I I I j Jr D HO 0 2000 4000 J Sage et al PRL 94 203001 05 Internuclear distance R A v H 7 39 Condensate suner uid pure CrBEC 105 atoms optical density 400 200 400 4100 A Griesmaier et al PRL 94 160401 2005 TC7 11K Theoretical work on dipolar BEC You Santos Lewenstein Zoller Bohn 0 Dell Cooper etc 1 Pseudopotential and condensate pro le far 2 2 V2730 2 47th as 5rD21 3030s 6 m r LAquot 1 2 Phonons and instability in 3D 3 Roton minimum in 1D amp 2D Single pa icle i1 Instability toward collapse if it 10 shortrange repulsion is weak 9 1 5 10 4 Vortex of dipolar BEC 0 5 5 Others Phonon In Beyond BoseEistein condensation 1 Wigner crystal39in 2D liomogeneous space Zoller Demler etc l3 D2 Vr 3 gt the smaller rs n the stronger 1nteract10n r Vr 2mD2 N l h2 2mr2 hzr Wigner crystal occurs when 2 Superso J state in 24 opticaffattice Troyer Prokofev Das Sarma etc l 10 120 I ET t1 I LE 3 I 1 5 I i 39 r 3 q i U SF 39I PS 55 PS V 6 In Optical lattice 392 f 4 quot quot 1 SF 1 r H 1quot g H rZa aj g 61 21 VZIMIJ Eff PS W i W a I r I 600 025 050 075 P PRL 94 207202 2005 DY EZRA I l I 3 Spin texture Jae to spinor itaf interaction Ueda Ho etal a Hint JS1SZ D272 S1S2 12S2r12 f y I u 9 C t 318 ms h f 0 1115 f a r fillfWWMlIn If quot quot d f 57711 1115 W IIMi MI e I 33 ms 2ka U f f 53 ms Withnut dipnlnr illm zurtinn 1f r 39 4 Dipo zs near Mott state 1D gistem Altman Santos et al s cmmlnlmns 0 range 5393 3 7 3 W DW 2 HI I 2 4 6 m H EU 0 4135 04 D45 005 01 015 02 4 Laser induced39dipol39es in opticafl39attice Zoller Demler et al L1m101 EV L0 m0 Sg lgt x 5 I ix x 513 quot T I I lt 11 39125 Il 4114 I Il E 01 Il1E Reference 1 DW Phys Rev Lett 98 060403 2007 Dipole interaction in bilayer T T Id W21 T T Within Born approx intralayer interaction is always much larger than the interlayer 4 2 2 4 However this is invalid in 2D system Fquenex Born Apprx intralayer Zeroenergy resonance Pseudopotential approach similar to 3D atom gas Jig J0quot 1391quot v 1 a 39 39 39 mu Orah 1 gtu Correct In the low energy limit it Huang and Yang PR 105 767 1957 IquotI Jquot1rquotquot139 a 39 tut Phase shift for intraO and inter1 ayer scattering 4 TI 2 Unbound t Dimers U0 E g C 2 dipoles h d EK vg n a cc 0 3939 v as 4 n 3407 2 Ragga 7 T l 0 4 0 397 l l 4 I I I I O O 5 l l 5 0 F 56 a mfcafeii i 27 f5 Schrodinger Cat State Superposition of two macroscopic coherent states Unbound O 2 dipoles g1 gt go gt O 2 A E O G 2 C r 3940 0L5 1 1 5 U0 Schrodinger Cat State H t 1330 63 7 23 713 i i b 2N A A A C m2N m 252Nj 3 1agb0 53 Tf b WW m gt 08 06 S U 04 o o 150 200 U ULTL 3939xquot39151U7j Cum AA 1 F 1 gag0 Z a Agl EN 2tsin6005 Ag00526 2tt Agt9 7r2Ag t46 7r22 QampA about Cat State Q Phase separation T T T T T M T A No because it causes too much surface energy Besides interlayer pseudopotential also becomes weaker in large k Q How to observe lvlmgtamei bm0gt A Since quantum measurement will break the Wavefunction into one of the two macroscopic state no intereference pattern even in single shot TOF Phase diagram for bilayer Adiabatic moving Dipolar Dimer Dimer condensate condensate Wigner Crystal o71 45 U0 Adiabatic moving Dipolar Cat Dipolar Dipolar BEC state BEC WC O71 15 18 K estimated by HP B8chler etc Reference DWW M D Lukin and E Demler Phys Rev Lett 97 180413 2006 i2 j1 Trlal wavefunctlon lt gt 2 39 1 R1 wan9115 exp 11 Binding energy of a single chain r 2 gtxlt Z U081 U03 2R 0 N 1 e 5R Xp wIH M22 M81 O U 0 L0 E3EIM 1 05 1 15 2 25 W Li NuH tU U 0 Nonmonotonic distribution of chains in nite temperature High temperature 3 3 2D version of Saha s equation 211 QJILI Q A hm j GHEtquotMr39rkBT L kg K Mediate temperature L Aquot nonmonotonic ditribution 1 2 0 7L 0 6 o 8 M 1 LOW temperature Condensation of the Iongestchains NMNtotxm 3 t Ei mrgtt tgr gnaw Hrqrumd twirwijiitr Condensate Tc of chain liquid 0 2 5 O O 2 L2 E O 1 Condensation of long chains 0 39 Condensation of O 5 1 5 2 2 5 n oun Ipo es X 1 Excitations of dipolar chains Expansion in large dipole moment limit 2 1H 1139 a 0 1 1 57 S 23sjsjsj H 2 A I 6 J M d Ell JP Ell JP 12 iltj T c Excitation spectrum 2f kgkd 1 2 d39 3111 2 j i 25 32 Ad l Possible phase diagram for multilayer systems m ejw IBECE W gmef Iys za hg ame 39 Super Chain BEC Solid QMC method is developed for exploring these phases U0 ongoing project with ChiMing Chang and PoChung Chen Wire radius R y E R ltlt d ltlt L Wire length L i 6 y seperation between two Wires d X 1 Why this system is interesting We may have D 1ntraw1re interaction V H 31 3 cos2 6 D2 d2x1 x221 3c0526 d2 x1 xz232 d2 x1 x22 where x1 x2 is the seperaction of the molecular in x direction interwire interaction Vi H L i v7 777 1 V M I Arr y UU UtiUit time we Avie xiii I Ut1tranla onmx direction y a U g 1 gauge symmetry P hase d lag ram E 22 two Wires symmetry 6 X 555 55 U1 g Strong coupling limit 6 55 0 lt gt n LUIU m I L l H 2 t2 aka1 blb 1 hC 221 L L l T i U nini n H1 l am 123 First order phase transition to Ferromagnetic Phase Fixed L8N4t1U1O 4 7587705 II 1II i 4 7587725 I I I I I 1 105444 1 105452 1 105460 I 7 7 7 y heee diag am L8N 4t1 N4t 1 U10 12 Increasing dipole moment I m 39 Ferromagnetlc Phase 39 39 Ferromagnetic phase Loaf V x 12 06 39 V 1 02 100 Symmetric phase W ww M v H H m n v V lwe Feew ae ei jwjel ei x f f wemn m j mama Also called interlayer coherence or exciton condensate B gt W w 1 1 v 2 2 d 40 dIB NO QHE l O 7 6 O 7 0 QHE 20 3 r I o I I w w v 000 002 004 006 008 010 ASAs 92 81B J Eisenstein et al Summary Ultracold dipolar atomsmolecules are fantastic systems for studying interesting manybody phenomena Multicomponent dipolar systems may mimic some strongly correlated systems in solid states Theoretically proposed quantum states are expected to be realized and observed experimentally within a few years


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