Transcript Progress in Casimir engergy variations and supercondutive

Archimedes Experiment
A Feasibility study for the measurement of the
Archimedes force of vacuum

•
•
•
INFN_sezione di Naples – Laboratorio Fisica della Gravitazione Univ. Federico II
INFN sezione di Roma1 – Univ. La Sapienza Roma
Naples Seconda Università
Université de Aix-Marseille Centre de Physique Théorique de Luminy
Institut Universitaire de France
E. Calloni - Rencontres de Moriond 2015-03-25
Scientific motivations and goal of the
experiment
•
The scientific problem addressed is within the interaction of vacuum fluctuations
with gravity -- cosmological constant problem : “why the universe exhibits a vacuum
energy density much smaller than the one resulting from application of quantum
mechanics and equivalence principle?
1
 2 

The first calculation of the radius of the universe as expected by applying general relativity and
a energy density as foreseen by zero point fluctuations - with a cut off to highest
frequencies/wavelenghts equal to the electron radius – dates back to Pauli – 1931 that found
R = 31 km !
Many remarkable and important theoretical attemps since then but not a direct experiment:2
Does vacuum fluctuations gravitate or not?
Does vacuum pressure red-shift ?
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
z
L
a
y
x
1
E   
2
hcL
E
2
If the plates are perfectly reflecting the modes that
can oscillate must have discrete wavenumbers
on vertical axes kz = n/a while all values
are allowed for kx e ky
d k
 n 
2
k 


2

 a 
n   ( 2 )
2 n 
2
2

The regularization is made by determing the Casimir Energy
as the change in energy when the plates are at distance “a” with
respect to the plates having ainfinity
Ereg = E(a) – E()
• Casimir Energy
• Casimir Pressure
Ereg  
 2 L2 hc
720a 3
1 U
 2 hc
PC  2

L a
240a 4
= 1.3x10-3 N/m2 (1mm/a4)
First prediction: Casimir 1948
First measure (force): Sparnay 1956
Presently tested (force) with an accuracy of 0.5% (Mohideen: 2005)
(No problems in QFT in flat space-time)
4
Weighing the vacuum
The idea is to weigh a rigid Casimir cavity when the vacuum energy is
modulated by changing the reflectivity of the plates. The forces along z are
z
L
a
y
Fsup   FC


EC

Finf  FC 1     c 2 g
x
 

EC
Ftot  2 g zˆ
c
g a
c2
difference of gravitational
potential between the plates
The total force is directed upward an it is
equal to the weigh of the vacuum modes
that are removed from the cavity
5
Pressure red-shift
A simple summation of the lower force and upper force on the plates would bring
to a somewhat unespected result:
2 c
Fcas   L
Finf  Fsup  Fcas 1    
EC
c
2
g  Fcas  4
EC
c
2
g
Ecas
240a 4
c
  L2
720a 3
The lower vacuum «photons» must exert a bigger force because the force will be redshifted when reaching the same level of upper plate  in the experiment the sum
must be done taking into account the red-shift becuase the cavity is rigid and hanged
in a unique point - (for this effect our measurement is a null measurement)
Fsup  FC


EC

Finf   FC 1     c 2 g

EC
Ftot  2 g zˆ
c
E. Calloni et.al. Phys. Letters A, 297, 328-333, (2002)
G. Bimonte, E. Calloni , G. Esposito, L. Rosa - Phys. Rev D 74, 085011 (2006)
S. A. Fulling et al. Phys. Rev. D76:025004 (2007)
K.A. Milton et al. J. Phys. A 41:164052 (2008)
G. Bimonte, E. Calloni et. al. Phys.Rev.D76:025008, (2007)
On interpretation of Tolman-Ehrenfest effect:
C. Rovelli, M. Smerlak Class. Quant. Grav. 28 (2011) 075007
Hal M. Haggard and Carlo Rovelli, arXiv:1302.0724
5
6
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.
LASER
The energy E sent to the film is about 5x10^(5) J
The variation of casimir energy DEcas is about 2.5x10^(-19) J
The efficiency is
e = DEcas/E = 10^(-14)
Modulation of Casimir energy with superconductors (type I)
Use of superconductors
• The condensation energy is very small so it can be expected
that the variation of Casimir energy at the transition for a
superconductor inside a cavity can be of the same order, or
even dominates, the total transition energy
N metal
Diel
N/S
8
The change in energy can be calculated following the Casimir energy
calculation in case of real plates with complex conductivity s
c 2 A
DEC  D E
720 L3
N metal
D E : modulation factor with respect
perfect reflectivity
Re(s
Diel
N/S
D E 
DEC kTC
kTC


 106
EC
h C hc / L
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
x   /(2kTc )
The conducibility changes only in the very low frequency region (microwave) so the
9
modulation depth (if Tc is of the order of 1 K) is expected to be small for small Tc…
..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?
Superconductivity is destroyed by a critical magnetic field .
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.
T0- T (mK)
Results and references on energy
modulation – Aladin Experiment
The data are not in contrast
with the theory and the
region of energy of different
behaviour is the expected
one
2008
G. Bimonte et Al. - J. Phys. A: Math. Theor. 41 164023 (2008)
A. Allocca et Al. Jour. Of. Supercond. And Novel Magnetism. 25, 2557-2565 (2012)
Proposal for the weight measurement:
Use of Type II superconductors
1) Use high_Tc layered superconductors as natural multi Casimir-cavities
2) Profit of the fact that in normal state the plane (that will become superconducting)
is a very poor conductor  high variation of Casimir energy at the transition
State of the art in the knowledge of
Casimir energy in superconductors
1) Approximate theory for high_Tc superconductor (plasma sheet no dissipation – zero
temperature) – Kempf hyphotheis (based on order of magnitude estimation): the
contribution to free energy is comparable to condensation energy in particular
layered superconductors like YBCO
2) In the final experiment also if the actual contribution were only of few percent we
could ascertain if it gravitates or not
3) The Casimir Signature: the dependence of the effect from layers separation is
known: the verification of the effect is by changing the layers separation – possible
with standard techniques
12
The key points to be addressed
• Seismic isolation: a seismic isolation of
about 10^(-4) in the 10-30 mHz region
does not yet exist
• A complete theory of the Casimir effect
in type II superconductors does not yet
exist
• An efficient modulation system – by
temperature or external field – is needed
and must be designed from scratch
Archimedes Experiment
13
Present experiment
• 2 years feasibility study : Objectives
 Theoretical implications of the measurement (Naples-Marseille)
 Theoretical evaluation of contribution to condensation energy (NaplesRome)
 Evaluation and choice of best-experimental material (Naples-Roma)
 Design and construction of balance prototype with resonance frequency in
the 10 mHz range (Naples)
 Design and construction of prototype optical read out (Naples)
 Design and test of temperature modulation actuator (Rome - Naples)
 Study of pre-attenuation stage suspension (Pisa)
The Archimedes crew
E. Calloni (Univ. Naples), S. Caprara (Univ. Roma), G. Esposito (INFN Naples),
M. Grilli (Univ. Roma), E. Majorana (INFN Roma), G. P. Pepe (Univ. Naples),
S. Petrarca (Univ. Roma), P. Puppo (INFN Roma), F. Ricci (Univ. Roma),
L. Rosa (Univ. Naples), C. Rovelli (Univ. Marseille), P. Ruggi (EGO-Pisa),
N. Saini (Univ. Roma), C. Stornaiolo (INFN Naples), F. Tafuri (II Univ. Naples)
14
Seismic attenuation
• The experiment is made in the framework of
gravitational wave detectors expertise particularly at
low frequencies and within the improvements in:
- seismic isolation systems
- low loss mirror suspensions systems
- control systems
- low temperatures techniques in small force detectors
• Virgo has reached the best sensitivity at low frequency
during past runs and now LIGO is comparable
The resonance frequency of
the first stage is 30 mHz
Transfer function of the Virgo Super-Attenuator
15
The balance
Scheme of the balance
With suspended samples
Zoom on the flexural joints where
The balance will be suspended
The center of mass must lie within few micron from the flexural rotation point
(bending point).
16
The superconductor
YBCO
Prototype on a 7.5 cm diameter sapphire substrate
(Ceraco)
Transition Temperature : 87 K
Total volume of the superconductor (final
experiment): 30 cm3
Two possibilities under study:
1) deposition on a sapphire substrate
2) Crystals
Gold plated face of YBCO
Frequency of modulation (final): 5-10 mHz
Expected Weight modulation : 4*10-16 N
Differential measurement respect to phononic
contribution: different doping
Other materials are under evaluation: BSCCO
View from the substrate face
17
A side-measurement : the weight of the entropy*T
Difference in internal energy
for a transition at fixed temperature
Difference in entropy for a transition
at fixed temperature valid for BCS –
approximatively for layered type II
Disregarding in this particular discussion
the contribution of Casimir effect the
weight of the entropy (times
Temperature) can be considered as an
interesting side-measurement of the final
experiment. This weight is classical (no
question on it) but never measured
18
Final experiment: balance and local detection
 Seismically isolated balance
 Temperature modulation around Tc
 Balance tilt possibly read with an
optical lever
Signal and Sensitivity: expected signal amplitude under Kempf hypotesis for a
fixed modulation frequency (blue curve) and integration time of 1.5
months - total noise for interferometric detection (black curve) and optical
lever (pink dashed curve) – (seismic noise evaluated from J. Harms et al.
Phys.Rev. D88 (2013) 12, 122003)
E.Calloni, M.De Laurentis, R. De Rosa, F. Garufi, L. Rosa, L, Di Fiore,G. Esposito, C.Rovelli, P.
Ruggi, F. Tafuri: “Towards weighing the condensation energy to ascertain the Archimedes force of
19
vacuum” Phys. Rev. D 90, 022002 (2014)
A curious citation
In the framework of quantum engineering propulsion for the
futures spacecrafts our result has been cited in the paper:
“A gedanken spacecraft that operates using the
quantum vacuum (Dynamic Casimir Effect) “
Foundations of physics 34, pag 477 (2004)
our result is proposed “..to make lighter and modulate the weight of
the future spacecrafts…..”
Is the author of this paper a visionary ?
R. L. Forward – J. Maclay
R. L. Forward realized the first prototype
of interferometric gravitational wave detector !
1972 (Malibu laboratiores – California)
Conclusion
• Archimedes is a two years feasibility study
concerning:
• Theory and on modulation of vacuum
energy in layered Supercondutoring systems
• Experimental Improvement of seismic
performances at low frequency
• Experimental Improvements of high
quality superconductors temperature
modulation
Measure the Archimedes force of vacuum in a
Macroscopic system
The horizontal double-torsion pendulum
in construction at the «Laboratorio di
Fisica della Gravitazione»
The Project is within the «What’s next» activity of INFN – Fundamental Physics
Spares
22
A discussed paper explicitely commenting us
We confirm that suitably
modified ALADIN has the correct
conditions (superconductors,
casimir cavity, measure of
casimir energy contribution) and
that it did not have the sensitivity
to distinguish among the two
theories
(On the gravitational waves vacuum fluctuation contribution to weight
23