Interacting Ultra Cold Atoms a brief overview

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Interacting Ultra Cold Atomsa 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

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Quantum information Storages and quantum
computers
Many-body physics (condensed matter physics)
Few body physics (Nuclear physics, Atomic
physics)
Ultra Cold atoms
Field theories (emergent gauge fields, color
superconductivity, Neutron star physics)
Cosmology and gravity (Kimble mechanism, Unruh
Radiation etc)
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Topological quantum computer
(Kitaev, 97)
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• Bosons in optical lattices
• S0 bosons
• S1 bosons

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S0 bosons in lattices
Mott states ( t ltlt U)
U
Condensates (t gtgtU)
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).
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Phase diagrams
n
n
Large t
2
Small t
1
m
m
x
E(k,x)
n3
n2
n1
x
Atomic Mott states in a trap
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Interacting S1 bosons
q
f
Stamper-Kurn et al., 98. Ho, 98 Ohmi Machida,
98 Law,98.
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Condensates of S1 bosons (sodium type)(dgt1)
z
q
y
f
x
(Zhou, 01)
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Half vortices in BECs of sodium
atoms In a half vortex, each atom makes a p 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.
p circulation
p spin rotation
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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).
Mott states of Spin-One Bosons
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Nematic-spin singlet transitions (Mott
Insulators)
NMI
SSMI
h10.91

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

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• Fermions
• S1/2 fermions in Optical Lattices
• S3/2 fermions, quintet pairing, exotic vortices
  studied
• (Wu, Hu and Zhang, 2003-2006).
• Feshbach resonances with population difference
• (Experiments MIT group, the Rice
  Universitys 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...

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S1/2 Fermions in optical lattices (small band
width)
Neel Ordered
Spin liquids
Neel ordered only at T0
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S1/2 femions across Feshbach resonances
E (6Li)
F3/2
B
F1/2
Only electron spins shown
Resonances between state 1 of 1/2,1/2gt and state
2 of 1/2,-1/2gt.
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Superfluids near Feshbach Resonances
B
Binding energy
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The Chemical potential and Mol. Fraction at
resonance
Wide resonance (Ho and Diener, 04)
For y ltlt1, 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.
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Energy splitting and population imbalance
A conventional quantum statistical system
Cold atoms
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Energy Landscape 1 Negative Scattering Length
(N fixed) (Gu, Warner and
Zhou, 05)
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Energy Landscape 2 positive scattering length
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Energy Landscape 3 Near resonance
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Phase Separation in a Constrained Subspace(i.e.
population imbalance is conserved)
M
M
1
N
Gapless SF N
SFN
Gapless SF
I
I
Positive scattering length
Negative scattering length
M-H curve for a global ground state
Critical population imbalance
Phase separated states
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Zwierlein et al., 2005 Also studied by the Rice
group.
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Superfluids of polarized fermi gases
Fully polarized F.L.
Splitting between two chemical potentials
Partially polarized F.L.
SF Fermi sea
LOFF
(p, -pQ)
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)
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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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• Quantum Information storage (?)

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A 3-bit Hamming code 3,1,3
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Quantum Error Correction Code
Requirement for a QECC 1) Errors in different
code words are distinguishable 2) Subspace of
errors are indistinguishable so that there will
be no information leakage.
Error Space
Code Space
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The Chemical potential and Mol. Fraction at
resonance
Wide resonance (Ho and Diener, 04)
For y ltlt1, 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.
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Ising symmetries
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A usual superfluid with a thin fermi shell (b)
of qausiparticles is unstable the shell can be
deformed into a crecent (a) by a moving
condensate.
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Absorption images of interference patterns as
the laser intensity is increased (from a to h).
(a-d) BECs and (g-h) Mott insulating states.
(Greiner et al, 2002)