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					           Interacting Ultra Cold Atoms
                           a brief overview

                                  Fei Zhou
                   PITP, University of British Columbia

                   at Quantum Nanoscience conference,
                    Noosa Blue, Australia, Jan 23, 2006


Collaborators: I. Affleck (UBC), E. Demler (Harvard), Z. C. Gu (TsingHua),
         M. Snoek (Utrecht), C. Wu (UCSB), H. Zhai (TsingHua)


                     $:   Office of the Dean of Science, UBC
                                 NSERC, Canada
                           Sloan foundation, New York
                        Quantum information
                           Storages and
                         quantum computers




Few body physics                                      Many-body physics
(Nuclear physics,                                     (condensed matter
 Atomic physics)                                           physics)
                          Ultra Cold atoms



                                               Field theories
       Cosmology and gravity              (emergent gauge fields,
        (Kimble mechanism,                color superconductivity,
        Unruh Radiation etc)               Neutron star physics)
 Topological quantum computer
          (Kitaev, 97)




| g1                    | g2 
Bosons in optical lattices

• S=0 bosons

• S=1 bosons
                        S=0 bosons in lattices
   Mott states ( t << U)



                                              U



   Condensates (t >>U)




In (a) and (b), one boson per site. t is the hopping and can be varied by
tuning laser intensities of optical lattices; U is an intra-site interaction
energy. In a Mott state, all bosons are localized.

M. P. A. Fisher et al., PRB 40, 546 (1989);
On Mott states in a finite trap, see
Jaksch et al., PRL. 81, 3108-3111(1998).
                      Phase diagrams

          n
                            Large t                    n

                          Small t                      2
                                                               1
m
                     m
                                                                    x
    n=4
                                                   E(k,x)
    n=3
              SF or BEC
                                    n=3
    n=2                             n=2
                                    n=1
    n=1
                                                                     x
                      t                   Atomic Mott states in a trap
                          Interacting S=1 bosons

                                               q


                                              f
                      iφ                           iφ
             sin θe                         sin θe
|n(θ , φ)               |1   cos θ|0             | 1 
                    2                             2
                                     
:|  n   (  1 ) |n  ,       n|S |n   0 .
                                     α
                                                         U F (r 1  r 2)   (r 1  r 2) gF ,
             0                  1/ 2                        4aF
                                       
B:( 0 ,φ)   1  ,
                         π
                      R:( ,0 )   0  .                 gF          , g 2  g0 , F  0,2.
                                                                 M
                                   1/ 2 
             0         2
                                        
                                                       Stamper-Kurn et al., 98.
                                                         Ho, 98; Ohmi & Machida, 98; Law,98.
       Condensates of S=1 bosons (sodium type)
                        (d>1)
N(Q)




              Q
         z
         q

                y
  x     f



                      (Zhou, 01)
                 Half vortices in BECs of sodium atoms
In a half vortex, each atom makes a  spin rotation; a half vortex carries one
half circulation of an integer vortex. A half vortex ring is also a hedgehog.

       y                                                               ring
             x
                                                           z
                                               Z


                    y


                             x

                                                       The vortex is orientated
                                                       along the z-direction;
                                                       the spin rotation and
                                                       circulating current
                                                       occur in an x-y plane.
            spin rotation            circulation
     Mott states of Spin-One Bosons



                                Each site is
                                characterized by two unit
                                vectors, blue and red
                                ones. a) nematic BECs
                                (nBEC); b) Nematic mott
                                insulators (NMI); c) Spin
                                singlet mott insulators
                                (SSMI).




         C C                  C C 
                           1
O2                         
                       3      
Nematic-spin singlet transitions (Mott Insulators)




                SSMI                      NMI




                           h10.91

 vs. h (proportional to hopping) is plotted here.
(Snoek and Zhou, 03; Demler, et al., 03; Demler and Zhou, 02)
Fermions

• S=1/2 fermions in Optical Lattices

•   S=3/2 fermions, quintet pairing, exotic vortices studied
     (Wu, Hu and Zhang, 2003-2006).

• Feshbach resonances with population difference
  (Experiments: MIT group, the Rice University’s Group and JILA group;
   Theory effeorts: Son and Stephanov, 2005; Pao et al.,2005; Sheehy and
  Radzihovsky; Gu, Warner and Zhou; …….)


•    Lattice Feshbach resonances
    (Stability of Mott states and invasion of superfluidity,
    factorized superfluids in 1D; Wu, Gu and Zhou, 2005-2006)

And more…...
               S=1/2 Fermions in optical lattices
                        (small band width)




Spin liquids        Neel ordered only at T=0   Neel Ordered
        S=1/2 femions across Feshbach resonances


   E (6Li)



F=3/2

                         B
F=1/2
                                                    Only electron spins shown




  Resonances between state 1 of |1/2,1/2> and state 2 of |1/2,-1/2>.
          Superfluids near Feshbach Resonances


   as




                       B




Binding energy                      x  ( a s k F ) 1
The Chemical potential and Mol. Fraction at resonance




                         Wide resonance
                         (Ho and Diener, 04)


For y <<1, at FbR the many-body states are INDEPENDENT of both
two body parameters such as the bg scattering length, the magnetic
moments and the many-body parameter: the fermi momentum.
      Energy splitting and population imbalance

                    E(k)                        E(k)




                I

                                   k                     k



A conventional quantum statistical system   Cold atoms
Energy Landscape 1: Negative Scattering Length (N fixed)
           (Gu, Warner and Zhou, 05)
Energy Landscape 2: positive scattering length
Energy Landscape 3: Near resonance
     Phase Separation in a Constrained Subspace
                (i.e. population imbalance is conserved)

M                                      M

                                        1
          N
                                             Gapless SF + N



         SF+N                                               Gapless SF


                                 I            Positive scattering length   I
    Negative scattering length

      M-H curve for a global ground state
      Critical population imbalance
       Phase separated states
Zwierlein et al., 2005 ; Also studied by the Rice group.
              Superfluids of polarized fermi gases


               Fully polarized
               F.L.
Splitting
between two
chemical                                               Partially polarized
potentials        SF + Fermi sea                       F.L.
                                          LOFF
                                              (p, -p+Q)




                                                            inverse of scattering length


Resonances take place along the blue dashed line (in the “universal regime”).
( Son et al., 2005; also see Sheehy and Radzihovsky, 2005)
                                   Summary


• many important and exciting new issues in many-body cold atomic
  matter (magnetic superfluids & Mott states, topological phases,
  superfluids with population imbalance etc).

• Cold atomic matter might also be applied to understand various
  fundamental concepts/issues in other fields.

• There are a lot we can learn about/from cold atoms.

				
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posted:8/29/2012
language:English
pages:24