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Transcript
World of ultracold atoms with strong interaction Daw-Wei Wang National Tsing-Hua University Temperature ? What we mean by “ultracold” ? T 106 K ! Why low temperature ? Ans: To see the quantum effects ! Uncertainty principle: xp p 2 ~ kBT x ~ ~ T , Thermal wavelength 2m p 2mkBT Therefore, if T T Quantum regime when T d ~ n 1/ 3 T d (after Nature, 416, 225 (’02)) Why strong interaction ? P. Anderson: “Many is not more” Because interaction can make “many” to be “different” ! Example: 1D interacting electrons crystalization and no fermionic excitation How to make interaction stronger ? p 2j 1 N H V ( x j ) U ( xi x j ) 2 i j j 1 2m N 1. U ( x) becomes stronger 2. Ek ~ k BT becomes smaller or m becomes smaller 3. V ( x) changes to make lower dimension 4. N becomes larger (for short interactio n); smaller for long range interactio n How to reach ultracold temperature ? 1. Laser cooling ! (1997 Nobel Price) Use red detune laser + Doppler effect How to reach ultracold temperature ? 2. Evaporative cooling ! Reduce potential barrial +thermal equilibrium Typical experimental environment MIT How to do measurement ? Trapping and cooling Perturbing Releasing and measuring BEC (2001 Nobel Price) What is Bose-Einstein condensation ? ( x1 , x2 ) ( x2 , x1 ), + for boson and - for fermion Therefore, for fermion we have ( x, x) 0, i.e. fermions like to be far away, but bosons do like to be close ! When T is small enough, noninteracting bosons like to stay in the lowest energy state, i.e. BEC How about fermions in T=0 ? D(E) Fermi sea E When T-> 0, noninteracting fermions form a compact distribution in energy level. BEC and Superfluidity of bosons (after Science, 293, 843 (’01)) condensate BEC = superfluidity v repulsion Superfluid uncondensate Normal fluid Landau’s two-fluid model Phonons and interference in BEC Phonon=density fluctuation n0U v ph m Interference (after Science 275, 637 (’97)) Matter waves ? Vortices in condensate Vortex = topological disorder E 0 (after Science 292, 476 (’01)) (after PRL 87, 190401 (’01)) 1 2 3 L En,l 0 l 3n 2nl 2n2 lext Vortices melting, quantum Hall regime ? Spinor condensation in optical trap Na F 1, mF 1,0 E F=2 F=1 FIJ B (see for example, cond-mat/0005001) 2 g0 g2 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ H dr i i i j j i i Fij j k Fkl l 2m 2 2 Boson-fermion mixtures Fermions are noninteracting ! phonon fermion phonon-mediated interaction 40 K 87Rb, 6Li7Li, or 6Li23Na D(E) rf-pulse Interacting fermi sea E Sympathetic cooling Feshbach Resonance (i) Typical scattering: B a a0 1 B B0 (ii) Resonant scattering: a B Molecule state Molecule and pair condensate (MIT group, PRL 92, 120403 (’04)) 6 Li (JILA, after Nature 424, 47 (’03)) 40 K 9 / 2,5 / 2 9 / 2,7 / 2 9 / 2,9 / 2 9 / 2,5 / 2 9 / 2,9 / 2 (Innsbruck, after Science 305, 1128 (’04)) First evidence of superfluidity of fermion pairing a B Optical lattice 3D lattice 1D lattice R ( E ) 2 V0 Entanglement control E other lattice E 2 2 Mott-Insulator transition Bose-Hubbard model H t ai a j U ai ai (ai ai 1) ai ai i , j i i n=3 superfluid n=2 n=1 t /U (after Nature 415, 39 (’02)) Fermions in optical lattice Fermi Hubbard model H t ai, s a j , s U ni , ni , i , j i Superfluidity of fermion pairing in lattice is also realized. Transport in 1D waveguide wave guide wire Interference ? Finite temperature + semiconductor technique Dipoles in nature: (1) Heteronuclear molecules (2) Atoms with large magnetic moment (a) Direct molecules p~ 1-5 D (b) But difficult to be cooled Small moment ~ 6 (for Cr) B (Doyle, Meijer, DeMille etc.) But it is now ready to go ! (Stuhler etc.) p ~ 1D, Udd ~ 10K, 1B , Udd ~ 1nK Condensate (superfluid) 6B Tc~700 nK Cold dipolar atoms/molecules (1) Heteronuclear molecules (2) Atoms with large magnetic moment (a) Direct molecules p~ 1-5 D (b) But difficult to be cooled Small moment ~ 6 (for Cr) B (Doyle, Meijer, DeMille etc.) But it is now ready to go ! (Stuhler etc.) p ~ 1D, Udd ~ 10K, 1B , Udd ~ 1nK Condensate (superfluid) 6B Tc~700 nK Interdisciplinary field Traditional AMO Precise measurement Ultracold atoms Quantum Information Nonlinear Physics Condensed matter Soft-matter/ chemistry