Casimir forces, surface fluctuations, and thinning of superfluid films Mehran Kardar MIT

1
Casimir forces, surface fluctuations, and
thinning of superfluid films Mehran Kardar
(MIT)

• Roya Zandi
• Joseph Rudnick (UCLA)

Phys. Rev. Lett. 93, 155302 (2004)
2

4He thin film experimentsR. Garcia and M.H.W.
Chan, Phys. Rev. Lett. 83, 1187 (1999)
Superfluid transition
Superfluid
Normal fluid
The film is thinner at the transition, and in the
superfluid phase

Question Why are films thinner in the
superfluid state?
3
Casimir effect
Proc. K. Ned. Akad. Wet. 51, 793 (1948)
Quantum fluctuations of the EM field between
conducting plates in vacuum results in
long-ranged forces

• Normal modes of Electro-Magnetic field between
  plates

• The ground state energy of quantized normal
  modes

• An attractive force between plates

4
Finite-size effects at Criticality

• Analogs in Statistical Mechanics
• Phase diagrams
• Free energy of the long-wavelength fluctuations

C
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Superfluid Helium
Pressure
fluid

• Superfluid He has massless Goldstone modes
  (phonons) associated with the phase of the
  quantum condenstae.
• The interaction resulting from (thermal)
  fluctuations of these modes is
• H. Li and M. Kardar, PRL 67, 3275 (1991)
  PRA 46, 6490 (1992)

C
superfluid
gas
temp
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Wetting by a Superfluid film

• R. Garcia and M.H.W. Chan, Phys. Rev. Lett. 83,
  1187 (1999).
• Question What determines the thickness of the
  wetting layer?

d
He (vapor)
He (liquid)
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Thinning of a Superfluid film
d
h
He (vapor)
He (liquid)

• Thickness of the wetting film is obtained by
  minimizing
• The film is thinner at the transition, and in the
  superfluid phase
• The observed thinning of the film is larger than
  can be accounted by the Casimir forces associated
  with Goldstone modes.

Goldstone modes ?
Critical
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Surface fluctuations

• Normal fluid is clamped due to viscosity
• Superfluid films have a velocity field
  associated with the superfluid phase
• Kinetic energy
• Free energy associated with superfluid flow

• Dzyaloshinskii, Lifshitz, Pitaevskii (1961)
• Mahale and Cole (1986)
• Not a Helfrich interaction which is repulsive

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Thinning of a Superfluid film

• Casimir force due to surface fluctuations
• Total Casimir force

M. Krech Ueno Balibar (2004)
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Summary

• Bulk Goldstone modes surface fluctuations
  suffice to explain the excess thinning of the
  film in the superfluid region.
• Future work
• Effect of surface fluctuations at--and especially
  immediately below--the superfluid transition