Aladin2: an experiment for the first demonstration of a phase transition influenced by vacuum fluctu

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Aladin2 an experiment for the first
demonstration of a phase transition influenced by
vacuum fluctuation
E. Calloni Dip. Scienze Fisiche Federico II
NapoliINFN sezione di Napoli
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SCIENTIFIC MOTIVATIONS

• First demonstration of a phase transition
  influenced by vacuum fluctuations
• First direct measurement of variation of Casimir
  energy in rigid bodies possibility to open the
  way to measure the debated dependence of Casimir
  energy by geometry
• Long-term RD on verification of equivalence
  principle applied to vacuum fluctuations

INSTITUTES PARTICIPATING

• INFN sez. Naples -Italy
• IPHT (Institute for Physical High Technology) -
  Jena Germany
• Federico II University Naples Italy
• Seconda Università di Napoli Aversa - Italy
  

G. Bimonte, D. Born, E. Calloni, G. Esposito, U.
Hubner, E. IlIchev, L. Milano, L. Rosa, D.
Stornaiuolo, F. Tafuri, R. Vaglio
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The Casimir effect is a macroscopic
manifestation of vacuum fluctuations. It is
derived considering the zero point e.m. energy
contained in a Casimir cavity, i.e. in the volume
defined by two perfectly reflecting parallel
plates

• Spiegare lo scopo globale della strategia
• Indicare l'obiettivo specifico da raggiungere
• Se necessario, utilizzare più punti

If the plates are perfectly reflecting the modes
that can oscillate must have discrete
wavenumbers on vertical axes kz np/a while
all values are allowed for kx e ky
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The regularization is made by determing the
Casimir Energy as the change in energy (in the
same volume) when the plates are at distance a
with respect to the plates having a?infinity

• Casimir Energy

1.3x10-7 N

• Casimir Force

Perfectly reflecting mirrors long wavelengths
are expelled from the cavity, so that the
internal energy is
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History and some open questions
Theory of Casimir effect 1948 First
measurement Sparnay 1954 with 100 error (Force
) Presently tested (Force) with 0.5 error
(?!) Theoretical disagreement on
renormalization procedure in case of different
cavity geometries - no agreement on sign of
expected energies ?Application to MEMS and
NEMS Theoretical debats on zero frequency mode
contribution in case of real material
Dynamic Casimir effect (G. Carugno esperimento
MIR) Cosmological constant problem interaction
of vacuum energy with gravitational field
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S. K. Lamoreaux Rep. Prog. Phys. 68201-236
(2005)
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Cosmological Constant Problem
Problem the universe exhibits a vacuum energy
density much smaller than the one resulting from
application of quantum mechanics and equivalence
principle Cosmological costant problem120
orders of magnitude Weinberg Rev. Mod. Phys. 61
(1989)
First calculation Pauli (1930) Radius of the
Universe 31 Km! This universe would not even
reach to the moon
In spite of enormous theoretical work on
different and deep hypothesis (not solving the
problem even at theoretical level) there is not
even an experiment to study (confirming or
disproving) the application of equivalence
principle for vacuum energy.
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Rigid Casimir Cavity in weak gravitational field
The component of stress-energy tensor in
Minkowsky space-time

• can be written in a covariant form

is the 4-vector space-like orthogonal to the
plates L.S. Brown, G.J. Maclay, Phys. Rev. 184
(1969)
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So that, by substituting the metric tensor hmn
with gnm of the laboratory system fixed on the
earth, it can be easily calculated the force
(density) exterted by the gravitational field on
the Casimir cavity
The force is positive (directed upward) taking
into account a system as big as GW detectors
mirrors made of 106 layers with Separation of 5
nm (oxide) the total force is about 10-14 N
d
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The experiment could not be performed as a sum
of weight of the components it must be carried
in AC, modulating the vacuum energy contained
into the cavities. This in principle could be
done by modulating the plates reflectivities
(i.e.the h factor, which takes into account that
real materials are not perfect reflectors)
if h 0.5
F
Comparison with Virgo sensitivity
Visible also With torsion Pendulum experiment
Experimental problem modulate Casimir energy
without exchanging too much energy with the
system (to not destroy the possibility of
measurement and control) and measure it.
Phys Letters A, 297, 328-333, (2002)
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ALADIN2 Experiment for the direct measurement of
vacuum energy variation in a rigid Casimir
cavity via the modulation of the reflectivity of
one plate, obtained by the normal/superconducting
phase transition
Since the optical properties of the film (in the
microwave region) change when it becomes
superconducting, and since the Casimir free
energy Fc stored in the cavity depends on the
reflectivity of the film, we expect a variation
of energy from the normal (n) to superconducting
(s) states
Indeed DFc is expected to be positive, because,
in the superconducting state, the film should be
closer to an ideal mirror than in the normal
state, and so Fc (s) should be more negative than
Fc (n)
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The change in energy can be calculated following
the Casimir energy calculation in case of real
plates with complex conductivity s
modulation factor with respect perfect
reflectivity
N metal
Re(s)
Diel
N/S
Plot of real part of conducibility s normalized
to zero frequency Drude conducibilty s0 for
different temperatures T Tc (Drude)
T/Tc 0.9
T/Tc 00.3
The conducibility changes only in the very low
frequency region (microwave) so the modulation
depth (if Tc is of the order of 1 K) is expected
to be small for small Tc
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..but also the energy exchanged with the system,
besides the vacuum energy, is expected to be
small being linked to the condensation
energy which is (roughly) proportional to Tc2 .
Better to use low Tc superconductors. If the two
energy variations are comparable then it is
expected that vacuum fluctuations modifies the
transition
Is there a way to measure DFc?
The proposed way to measure DFc consists in
placing the cavity in a parallel magnetic field
and measuring the critical field that destroys
the superconductivity of the film.
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Critical field of superconductors

• Superconductivity is destroyed by a critical
  magnetic field .

The critical field depends on the shape of the
sample and on the direction of the field. For a
thick flat slab in a paralle field, it is called
thermodynamical field and is denoted as Hc.
The value of Hc is obtained by equating the
magnetic energy (per unit volume) required to
expel the magnetic field with the condensation
energy (density) of the superconductor.
f n/S (T) density of free energy at zero field
in the n/s state
Hc(T) follows an approximate Parabolic law
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Superconducting film as a plate of a Casimir
cavity
When the superconducting film is a plate
of the cavity, the condensation energy Econd of
the film is augmented by the difference DFc
among the Casimir free energies
DFc causes a shift of critical field dHc
Expected signal
The ratio DFc/Econd diverges T?Tc
No theory
Phys. Rev. Lett. 94-180402 (2005) Nucl. Phys.
B 726, 441 (2005)
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EXPECTED SIGNAL

• Different theories TE zero mode contribution ?
• Uncertainties on parameters (Au mean free
  path-Plasma Frequency)

150
stand-alone film
in-cavity film

100
TC0-T (mk)
10 lt DT lt 50 mK
D
T
50
-
NO Theory
0
2
4
6
8
10
Applied Field (mT)
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Experimental apparatus
Based on commercial Oxford Heliox 3He cryostat
base temperature 300 mK
Detlef Born
The home-made uniform-field coil is placed Under
vacuum to allow external magnetic screening
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The measurement consists in placing under vacuum
a sample cointaining a couple of 2 layer
structures (Al film oxide) and a couple of 3
layer structure (Al film oxide metal)The
couples have different areas (like in figure) to
verify that the effect does not depend on area
C
C
F
c
Area of 100x100 mm2 And 20x20 mm2
C
F
F
ALIGNMENT
The constraint is that the angles formed by
cavities and films on the same sample do not
differ with the magnetic field do not differ
more than 10-3 rad
We estimate that in the same sample Dq lt 10-4
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Typical standard measurement on a cavity the
applied magnetic field is fixed and the
transition is obtained by varying the
temperature the shift in transition temperature
is defined by averaging the temperatures in the
linear region
The transition width is about 50 mK
The applied field are of the order of 10 mT
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All the samples are deposited in the same chip
and worked in the same way until the last metal
covering
1K plate (T1.5K)
5 cm
In the scheme is reported the lay out of A single
sample the distance between The various
structures (2 and 3 layers) Are about 2.5 mm
3He pot (Tmin 250mK)
Cavities are covered With Au or Ag the
difference is expected to be small
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Measurement with radiation _at_ 300 K
Preliminary measurement no isolation from
infrared and Microwave radiation
The Casimir energy variation is roughtly
proportional to the density of photons of
frequency n few times 2KTc/h ? v 10KTc/h
(Tc 1.5 K)
In a 300K bath the system is expected to behave
in a similar way with respect to zero point
case except for a Magnification factor
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Measurement with real EM _at_300K

• As expected it mimics the Casimir signal
• DT is 300 mK

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Zoom for low applied fields
The difference derives from the linear
behaviour of film due to EM noise radiation
carried from outside by the cables
Conclusion from this measurement we expect the
Casimir Signal DT on the conservative side of
range DT 10 mK
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Sensitivity to Casimir effect
EM screened
Tc 1.52 K
50 mK are a big effect
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Expected parabolic behaviour recovered with dt
6 mK
2 points Measured at 3 days of Distance
they Differ for about 3 mK
FILM
T0- T (mK)
The parabola it is not a fit on these points it
is the parabola estimated with High fields
measurements (with a single copper-powder Filter
the high field region is not Influenced by EM
noise)
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After a first analysis on cavity
The uncertainties on cavity are higher
10 mK
T0- T (mK)
The cavity points are a first measurement and
are to be Intended as a first preliminar set
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Next experimental steps

• Repeat the measurement on variuos cavities
• Repeat the measurement with cavities having
  different parameters (lower gap to increase the
  signal)

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Current studies for future developments
1) The measurement on rigid cavities could
open the way to test the debated
possibility of positive energy configurations ?
positive force ? real nano-motors 2)
Verification of equivalence principle of vacuum
energy 3)
Contribution in studying gravity effects on
vacuum fluctuations and discriminate between
local/global explanation of Casimir effect
theoretical results? Trace Anomaly (see
L. Rosa talk) Phys. Rev. D 74, 085011 (2006)
4) Upgrade to test the region where
presently the theory lacks (?) useful for
cosmology (?)
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CONCLUSIONS

• Sensitivity seems encouraging for the first
  measurement of variation of Casimir energy in
  rigid bodies
• Demonstrate a phase transition influenced by
  vacuum fluctuations
• Long Term RD of effects of gravitational field
  on vacuum energy