Casimir-Polder forces on atoms near microstructures

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Casimir-Polder forces on atoms near
microstructures
Robert Zietal Physics Astronomy
Department University of Sussex Falmer, Brighton,
BN1 9QH
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Outline

• Casimir-Polder forces
• What are they?
• Why are they important?
• How do we calculate it? Review of theoretical
  methods
• Electrostatic Greens function
• Field quantization by normal-mode expansion
• Perturbation theory
• Asymptotic analysis of integrals
• Results
• Perfect reflectors cylinder and half-plane
• Dielectrics layered half-space
• Outlook
• Absorptive dielectrics half-space
• Metamaterials focusing vacuum fluctuations?

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Casimir-Polder force what is it?
Casimir-Polder force is a force of
electromagnetic origin between a neutral atom and
a neutral macroscopic body.
How is this possible? Consider quantum harmonic
oscillator
Fluctuations!
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Casimir-Polder forces what are they?
Quantized electromagnetic field is like a set of
harmonic oscillators!
Fluctuations!
Fluctuations of the electromagnetic field also
need to satisfy the Maxwell boundary conditions!
Pictorially...
Atomic electron couples to the fluctuating free
electromagnetic field Lamb shift.
Introduce boundaries field fluctuations become
position dependent Lamb shift is position
dependent Casimir-Polder force!
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Casimir-Polder forces why are they important?

• Stability of colloidal systems this is where
  the Casimir-Polder force originated!
• Measurable effects of the quantum vacuum are of
  fundamental interest in Physics.
• Search for the exotic forces beyond the Standard
  Model.
• Casimir-Polder forces play an important role in
  studying the surface effects and devices like
  atomic force microscope. Adsorption of atoms
  onto the surfaces. Measurements of the surface
  electromagnetic fields.
• Casimir-Polder forces can become significant over
  the ranges of sub-micron atom-interface
  separations and therefore significantly alter the
  trapping potentials in cold atom physics.

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Casimir-Polder force how do we calculate it?
No wavefunction overlap!
Purely electrostatic problem! Solve by
generalized method of images
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Casimir-Polder force how do we calculate it?
Greens function of the classical Poisson
equation. What is the electrostatic potential
due to a unit source
?
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Casimir-Polder force how do we calculate it?
Problem requires quantization of the
electromagnetic field! Normal mode expansion
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Casimir-Polder force how do we calculate it?
How do we quantize the electromagnetic field in
the presence of a dielectric?
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Casimir-Polder force how do we calculate it?
Treat the atom non-relativistically using the
Schrödingers perturbation theory
Electric field operator!
Tricky!
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Casimir-Polder force how do we calculate it?
Idealization
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Casimir-Polder force how do we calculate it?
Asymptotic analysis of integrals how to extract
the Physics?
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Casimir-Polder force standard results.
Energy level shift in an atom placed in front of
the perfectly reflecting plane mirror.
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Common microstructures geometry of the problem
Phys. Rev. Lett. 92 050404 (2004)
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Common microstructures - geometry of the problem
For a given degree of freedom the wave-vector is
either discrete or continuous but not both!
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Casimir-Polder force results.
Energy level shift in an atom placed in front of
the perfectly reflecting, infinitely long
cylindrical wire
with
Sum and integral! Asymptotic analysis
non-trivial!
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Casimir-Polder force results.
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Casimir-Polder force results.
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Casimir-Polder force results.
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Casimir-Polder force results.
Energy level shift in an atom in front of the
perfectly reflecting half-plane
Single rapidly converging integral! Asymptotic
analysis easy.
with
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Casimir-Polder force results.
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Casimir-Polder force results.
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Casimir-Polder force results.
Energy level shift in an atom in front of the
layered non-dispersive and non-absorptive
dielectric half-space.
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Casimir-Polder force results.
No other poles around!
Single, compact expression!
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Casimir-Polder force results.
Energy level shift in an atom in front of the
layered non-absorptive and non-dispersive
dielectric half-space
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Casimir-Polder force results.
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Casimir-Polder force results.
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Casimir-Polder force results.
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Casimir-Polder force Outlook.
Energy level shift in an atom in front of the
absorptive and dispersive dielectric half-space
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Casimir-Polder force Outlook.
Interacting quantum fields. The Hamiltonian.
Electromagnetic Field
Polarisation Field
Reservoir Field
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Casimir-Polder force Outlook.
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Casimir-Polder force Outlook.
To leading order dispersion makes no difference
in the retarded regime. The next-to-leading order
has been worked out and is proportional to the
damping constant of the absorption line.
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Casimir-Polder force Outlook.
What is the interaction between two atoms placed
at the focal points of the lens?
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