Dipole-dipole interaction in quantum logic gates and quantum reflection

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Dipole-dipole interaction in quantum logic gates
and quantum reflection

• Angela M. Guzmán
• Departamento de Física, Universidad Nacional de
  Colombia, Bogotá, Colombia, and visiting
  Professor,
• School of Physics, The Georgia Institute of
  Technology, Atlanta, GA 30332, USA.
• angela.guzman_at_guzgon.com.

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1. Quantum dipole-dipole interaction
2. Controlled collisions between neutral atoms.
s-scattering .vs. dipole-dipole interaction in
a phase gate.
Marco Dueñas, Universidad Nacional de Colombia
3. van der Waals interaction in an external
field Quantum reflection in evanescent-wave
mirrors static .vs. dynamic van der Waals
(dipole-dipole) potential.
Brian Kennedy, Georgia Institute of Technology.
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DIPOLE-DIPOLE INTERACTION
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DIPOLE-DIPOLE INTERACTION
Controlled collisions between adjacent atoms in
an optical lattice
Atom-wall interaction in quantum reflection
Cold atoms
Wannier functions
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s-scattering (Fermi Potential)
D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W.
Gardiner, and P. Zoller. Phys. Rev. Lett. 82,1975
(1999).
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A 1D moving optical lattice (with
polarization gradient)
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Optical potential U,U-
2U0
U0
0
0
1.6
0.8
kLz
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Controlled Collisions
CONTROLLED COLLISION
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DIPOLE-DIPOLE INTERACTION
Atom 1
Atom 2
K2
K1
k
k
VACUUM PHOTONS
Induced dipole -moment.
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Selection rules
Transition probabilities
Elastic collisions
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(No Transcript)
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Elastic collisions, dipole-dipole interaction
Interaction energy
Spatially modulated losses.
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MATRIX ELEMENTS
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Interaction energy
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ImDipole-Dipole interaction potential
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ORDERS OF MAGNITUDE

• The probability losses (probability of having
  the
• atoms in the original two-qubit state)

Adiabatic criterion
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Using a commutation frequency b3
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Remarks

• Long range potentials rather than s-scattering
  determine the table of truth of logic gates based
  on atomic collisions.
• Logic operations based in the dipole-dipole
  interaction can not be performed in a time scale
  shorter than that of the spatially modulated
  losses.
• Dissipation diminishes fidelity and does not
  allow for successive quantum operations.
• Same limitations apply to schemes with enhanced
  dipole-dipole interaction G. K. Brennen, C. M.
  Caves, P. S. Jessen, and I. H. Deutsch, Phys.
  Rev. Lett. 82, 1060 (1999), unless special
  bichromatic engineering is used to balance
  losses.

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Atom-wall interaction in atomic reflection the
dipole-dipole interaction

• J.E. Lennard-Jones, Trans. Faraday Soc. 28,33
  (1932).

Perfect conductor
Perfect conductor
Perfect conductor
r
r
r
r
r
r
r
r
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• H.B. Casimir and D. Polder, Phys. Rev. 73, 360
  (1948). Radiative corrections

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ALKALI ATOMS GOLD SURFACE
Exp. 1 Theor. 2
Cs 1.087 4.143 0.59
Rb 0.938 3.362 0.65
K 0.791 2.877 0.73
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1 A. Shih, V.A. Parsegian , Phys. Rev. A 12,
835 (1975) 2 A. Derevianko, W. R. Johnson, M.
S. Safranova, J. F. Babb Phys. Rev. Lett.
82, 3589 (1999). 3 F. Shimizu, Phys. Rev.
Lett. 86, 987 (2001) (Neon)
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QUANTUM REFLECTION
Na BEC
T. A. Pasquini, Y-I Shin, C. Sanner, M. Saba, A.
Schirotzek, D.E. Pritchard, and W. Ketterle,
arXiv.org/cond-mat/0405530.
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EVANESCENT-WAVE ATOMIC MIRRORS
M. Kasevich, K. Moler, E. Riis, E. Sunderman, D.
Weiss, and S. Chu, Atomic Physics 12, AIP
Conf. Proc. 233, 47 (1991).
A means of measuring atom-surface forces
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DIPOLE-DIPOLE INTERACTION
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Dynamic van der Waals potential between a ground
state atom and a dielectric surface in the
presence of an evanescent wave and the EM vacuum.
Dissipation
Dynamic Potential
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Dissipation due to the interaction through the
vacuum
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Dynamic van der Waals potential
Static van der Waals potential
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Effective potential
Optical potential
Dynamic van der Waals potential
Effect of van der Waals potential
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Quantum reflection

• Evanescent waves. A. Landragin, J.-Y. Courtois,
  G. Labeyrie, N. Vansteenkiste, C. I. Westbrook,
  and A. Aspect, Phys. Rev. Lett. 77, 1464 (1996).

From a solid surface at normal incidence. T. A.
Pasquini, Y-I Shin, C. Sanner, M. Saba, A.
Schirotzek, D.E. Pritchard, and W. Ketterle,
arXiv.org/cond-mat/0405530.
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Quantality of the potentials
q
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Remarks

• Atom-wall and atom-atom van der Waals potential
  in external fields relate to the dynamic rather
  than to the static polarizability.
• The shape of the reflecting potential is not
  controlled by S0 alone. Variations in field
  intensity scale the potential but variations in
  detuning shift the maximum.
• Quantum reflection from solid surfaces occurs
  only for atomic velocities close to zero (heating
  has been observed). Quantum reflection from
  evanescent-wave atomic mirrors occurs at finite
  energies, but the reflectivity will be less than
  one because of dissipative effects.
• Applications in atomic funnels, quantum
  reflection engineering, optical traps for quantum
  gases, Rydberg atoms in optical lattices (a power
  dependent line width of the fluorescence spectrum
  has already been observed, FiO 2004).