Interacting Ultra Cold Atoms
a brief overview
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
Sloan foundation, New York
Few body physics Many-body physics
(Nuclear physics, (condensed matter
Atomic physics) physics)
Ultra Cold atoms
Cosmology and gravity (emergent gauge fields,
(Kimble mechanism, color superconductivity,
Unruh Radiation etc) Neutron star physics)
Topological quantum computer
| g1 | g2
Bosons in optical lattices
• S=0 bosons
• S=1 bosons
S=0 bosons in lattices
Mott states ( t << 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).
Large t n
Small t 2
SF or BEC
t Atomic Mott states in a trap
Interacting S=1 bosons
sin θe sin θe
|n(θ , φ) |1 cos θ|0 | 1
:| n ( 1 ) |n , n|S |n 0 .
U F (r 1 r 2) (r 1 r 2) gF ,
0 1/ 2 4aF
B:( 0 ,φ) 1 ,
R:( ,0 ) 0 . gF , g 2 g0 , F 0,2.
Stamper-Kurn et al., 98.
Ho, 98; Ohmi & Machida, 98; Law,98.
Condensates of S=1 bosons (sodium type)
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.
The vortex is orientated
along the z-direction;
the spin rotation and
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
C C C C
Nematic-spin singlet transitions (Mott Insulators)
vs. h (proportional to hopping) is plotted here.
(Snoek and Zhou, 03; Demler, et al., 03; Demler and Zhou, 02)
• 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)
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
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
Binding energy x ( a s k F ) 1
The Chemical potential and Mol. Fraction at 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
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)
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
chemical Partially polarized
potentials SF + Fermi sea F.L.
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)
• 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.