TwoDimensional Electron Systems in NonAbelian Gauge Potential using Ultracold Atoms

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Two-Dimensional Electron Systems in Non-Abelian
Gauge Potential using Ultracold Atoms
Indu Satija George Mason Univ and National
Institute of Standards and Technology
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Bose-Einstein Condensation in a gas a new form
of matter at the coldest temperatures in the
universe... Predicted 1924...
...Created 1995
Satyendra Nath Bose
Albert Einstein
2001 Nobel Prize
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An optical lattice is simply a set of standing
wave lasers. The electric field of these lasers
can interact with atoms - the atoms see a
potential and therefore congregate in the
potential minima. In the case of a typical
one-dimensional setup, the wavelength of the
opposing lasers is chosen so that the light shift
is negative. This means that the potential minima
occur at the intensity maxima of the standing
wave. Furthermore, the natural beam width
constrains the system to being one-dimensional.
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When atomic physics meets condensed matter

• Mott transition
• Tonk Gas fermionization of bosons
• Disordered system metal-insulator transition in
  two-color lattice
• .........
• Two-dimensional electron systems in a magnetic
  field quantum hall effect, Exotic spectrum,
  localization

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• Creating Artificial magnetic fields using
  ultracold neutral atoms
• Non-Abelian fields ( discovering new phenomena )
• Localization in non-Abelian fields
  delocalization
• Non-Abelian Hamiltonians with time-reversal
  symmetry new localization scenarios for fermions
  and bosons
• Kramers degeneracy and Dirac points new class
  of systems to explore quantum spin-Hall effect

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Particle in a magnetic field
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Artificial magnetic Fields in a lattice
Optical Lattice will provide discrete periodic
structure
Instead of magnetic field, lasers are used to
induce phase for particles hopping around a
closed path in a lattice resembling the effect of
magnetic field
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(ignore color)
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Hofstadter problem Localization
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U(N) gauge fields Vector potential will be a
matrix of order N
Why study non-Abelian gauge fields??
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Gauge Fields, Abelian Non-Abelain
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Non-Abelian U(2) Gauge Fields
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What happens to Landau Levels
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0
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In Abelian case all states localize
No dependence on Ky
Delocalization for fermionic atoms at
half-filling in non-Abelian
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Spectrum for Time Reversal Hamiltonian
fermion at half-filling
bosons
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Time-Reversal system global localization
Localization in fermionic atoms at half-filling
Localization in Bosonic atoms
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Time-Reversal Rational Flux
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fermions at half-filling
bosons
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localization in non-Abelian gauge potentials

• delocalization some states never localize
• Relativistic dispersion
• localization accompanied by loss of relativistic
  dispersion
• localization transition can be tuned by changing
  momentum
• Kramer degeneracy Dirac points in TR systems
• Future Interacting systems, non-Abelian vortices
  quantum spin-Hall effect

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" Metal-Insulator Transition Revisited for Cold
atoms in Non-Abelian Gauge Potentials", Indubala
I Satija, Daniel K Dakin Charles W Clark,
PRL, 97, 216401, 2006
" Two-Dimensional Electron Gas with Cold atoms
in Non-Abelian Gauge Potentials", Indubala I
Satija, Daniel K Dakin , Jay Vaishnav Charles W
Clark, Physics Rev A, 77, 043410, 2008