Decoherence protection and quantum logic gates

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Decoherence protection and quantum logic gates
in photonic bandgap structures Sophie
Pellegrin, Gershon Kurizki Chemical Physics
Department Weizmann Institute of Science Rehovot
76100, Israel sophie.pellegrin_at_weizmann.ac.il www
.weizmann.ac.il ?? Quantum information
optically manipulated atoms Challenge protection
of the quantum states from decoherence
spontaneous emission Photonic crystals
photonic bandgap structures Quantum logic gates
dynamical aspects adiabatic / nonadiabatic Period
ic sudden changes
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Photonic crystals
semi conductors - electrons periodic atomic
potential
photonic crystals - light periodic refractive
index
Band structure
1D
3D
K. Lim et al., GaAs and AlGaAs ? 1.8?m, ?4.5 ?m
and 1.5 ?m
2D
Fan et al., Si (dark) and SiO2 (light), large
and complete submicron bandgap.
AIST, Japan, TiO2 pillars of ? 640 nm and height
2 ?m
J. G. Fleming and S. Y. Lin, Opt. Lett. (1999)
S. G. Johnson and J. D. Joannopoulos, APL 77,
3490-3492 (Nov. 2000)
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Defects
Breaking the periodicity

• point like defects cavities

• linear defects waveguide

90? bend 98? of the power transmission (30 ? in
analogous dielectric waveguide)
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Density of modes
Scalar, isotropic approximation

• Neglecting the vectorial nature of the
  electromagnetic field
• analytic scalar dispersion relation
• ? isotropic density of modes (gap sphere) ? (?
  - ?c)-1/2
• ? qualitative results, limited to the
  description of the bandgap neighborhood
• Quantitative results non isotropic density

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Coupling with an atom static aspects
Strong interaction between the atom and its own
photon splitting of the atomic transition one
part is stable, the other one decays.
Static position of the atomic transition inside
the gap.
A. G. Kofman, G. Kurizki, B. Sherman, J. of Mod.
Opt. 41, 353 (1994)
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Dynamic aspects periodic shifts (1)
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Dynamic aspects periodic shifts (2)
control phase gate excited atomic state
phase shift of ? / 2 performed adiabatically
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Conclusion and perspectives

• Periodic modulation of the detuning is able to
  protect the atomic state
• from spontaneous emission more effectively
• than fixing the largest possible detuning value
• Sudden changes outperform the adiabatic
  modulation
• First attempts to apply the results
• to quantum logic gates are very encouraging