Quantum electromagnetic field in a spherical oscillating cavity

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Quantum electromagnetic field in a spherical
oscillating cavity

• Francisco Diego Mazzitelli
• Universidad de Buenos Aires

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• PLAN OF THE TALK
• Motivations
• Classical description
• Resonant photon creation
• Conservation of angular momentum
• Physical interpretation
• Conclusions

Ximena Orsi FDM 2005
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Dynamical Casimir effect
L(t)
Scalar fields in 11 dimensionsMoore, Fulling
Davies, Lambrecht Reynaud,Dodonov et al,
DalvitFDM, ColeSchieve, Ruser,.... Scalar and
electromagnetic field in 31 dimensions (cubic
and cylindrical cavities) Maia Neto, Dalvit et
al, Schutzhold et al....
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Effective moving mirror
semiconductor
conductor

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This work spherical cavity with time dependent
radius
a(t)
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THEORETICAL MOTIVATIONS

• there is no classical electromagnetic radiation
  with spherical symmetry (not even for an
  oscillating charged sphere)
• another example to compare photon creation in TE
  and TM modes
• any qualitative difference produced by the
  motion of a surface with curvature?

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CLASSICAL DESCRIPTION In the Coulomb gauge
We can describe the TE modes by a potential
and the TM modes by a dual potential
In both cases
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Static boundary conditions (perfect conductivity)
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Dynamic boundary conditions (usual b.c. in the
rest frame)
Time dependent radius
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RESONANT PHOTON CREATION (TE modes)
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For 0 lt t lt T INSTANTANEOUS
BASIS
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At t gtT the radius returns to its initial value
The number of particles is then given by
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Multiple scale analysis resonant conditions
Assume this
0
0
0
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For L 0 the spectrum is equidistant
modes are coupled

• Equivalent to a problem in 11 dimensions
• The number of particles grows quadratically with
  time
• The total energy inside the cavity grows
  exponentially
• (Dodonov-Klimov 96)

THE L 0 MODES ARE NOT PRESENT IN THE
ELECTROMAGNETIC CASE
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For L ? 0 the spectrum is not equidistant
The number of particles in the particular
resonant mode grows exponentially with time
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FOR THE TM MODES
is the
where
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Construction of instantaneous basis Neumann
b.c. (Crocce, Dalvit, FDM Phys Rev A 2002)
For a one dimensional cavity
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New variables
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(No Transcript)
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The situation for L 0 and L ? 0 is similar to
the case of TE modes L 0 ? equidistant
spectrum ? not present in electromagnetic
case L ? 0 ? non equidistant spectrum ?
exponential production of TM photons
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Rate of photon productionTE vs TM
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CONSERVATION OF ANGULAR MOMENTUM
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In the particular case
(TM)
(TE)
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PHYSICAL INTERPRETATION A mechanical analogy -
From Melde to Casimir
Tension T(t)
Resonant amplification
Melde experiment tension T(t). Needs initial
transverse oscillations (see L.Rayleigh, Theory
of sound!)
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L(t)
Havelock 1924, Nicolai 1925 (to illustrate
radiation pressure) Variable length L(t) ??
dynamical Casimir effect in 11 The vacuum
fluctuations act as seeds
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Spherical symmetry Classical fields ? no
radiation
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Spherical symmetry quantum fields ? the moving
shell influences the vacuum
fluctuations ? radiation
Vacuum fluctuations
a(t)
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Spherical symmetry quantum fields ? the moving
mirror influences the vacuum
fluctuations ? radiation
photons
a(t)
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• CONCLUSIONS
• in resonant situations ? exponential growth in
  the number of photons
• no qualitative difference with rectangular
  cavities
• the rate of growth is larger for TM modes than
  for TE modes
• photons are created in singlet states
• vacuum fluctuations with L? 0 act as seeds for
  photon production