04/18/23

E. Calloni Dip. Scienze Fisiche Federico II NapoliINFN sezione di Napoli

Aladin2: an experiment for the first measurement of variations of

Casimir energy in rigid bodies

SCIENTIFIC MOTIVATIONS• 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

• Measurement of phase transition influenced by vacuum fluctuations

• Long-term R&D on verification of equivalence principle applied to vacuum fluctuations

INSTITUTES PARTICIPATING

• INFN sez. Naples –Italy•INFN sez. Genova –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, F. Gatti, U. Hubner, E. Il’Ichev, L. Milano, L. Rosa, D. Stornaiuolo, F. Tafuri, R. Vaglio

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.

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 problem

120 orders of magnitude Weinberg Rev. Mod. Phys. 61 (1989)

2

1

Rigid Casimir Cavity in weak gravitational field The component of stress-energy tensor in Minkowsky

space-time:

5

3

1

1

1

720 4

2

a

hcT

zza

hcT ˆˆ

4

1

180 4

2

• can be written in a covariant form:

z is the 4-vector space-like orthogonal to the plates L.S. Brown, G.J. Maclay, Phys. Rev. 184 (1969)

x

y

z

a

L

So that, by substituting the metric tensor with g 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

6

d

Tx

gTg

xgf

2

1)det(

det

1

The force is positive (directed upward) : taking into account a system as big as GW detectors’ mirrors made of 106 layers withSeparation of 5 nm (oxide) the total force is about 10-14 N

rec

g

a

hcLF

23

22

720

if 0.5Nec

g

na

cANF r

1423

2

10720

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 factor, which takes into account that real materials are not perfect reflectors)

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)

XComparison with sensitivity of interferometers

F

Visible alsoWith torsionPendulum experiment

Au,Ag

Al2O3

Al

a = 10 nm

D = 10 nm

S = 100 nm

.~~

ALADIN2Experiment 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:

0)()( sc

ncc FFF

Indeed Fc 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)

3

2

720 L

AcE EC

E : modulation factor with respect perfect reflectivity

)2/( ckTx Plot of real part of conducibility normalized to zero frequency Drude conducibilty 0 for different temperatures:

T = Tc (Drude) T/Tc = 0.9 T/Tc = 00.3

610/

Lhc

kT

h

kT

E

E C

C

C

C

CE

N metal

Diel

N/S

Re(

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…

The change in energy can be calculated following the Casimir energy

calculation in case of real plates with complex conductivity

The proposed way to measure Fc consists in placing the cavity in a parallel magnetic field and measuring the critical field that destroys the superconductivity of the film.

Is there a way to measure Fc?

..but also the energy exchanged with the system, besides the vacuum energy, is expected to be small being linked to the condensation energywhich is (roughly) proportional to Tc

2 . Better to use low Tc superconductors.If the two energy variations are comparable then it is expected that vacuum fluctuations modifies the transition

Critical field of superconductors

• Superconductivity is destroyed by a critical magnetic field .

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

)()(8

)(2

TfTfTH

snc

)()()( TeTfTf condsn

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 H c.

2

1)0()(c

cc T

THTH

Hc(T) follows an approximateParabolic law

c

cavc

FEVTH

cond

2)( )(

8

1

Fc causes a shift of critical field Hc: condE2

1 c

c

c F

H

H

erga

cAEF cc 43.0

720 3

2

erg8

cond 103.5E

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 Fc among the Casimir free energies

Expected signal

No theory

)/1( cc TTF

2)/1( ccond TTE

The ratio Fc/Econd diverges TTc

0

10

20

30

40

50

60

70

80

90

100

-0,0020 -0,0015 -0,0010 -0,0005 0,0000

dT (K)

Ap

plie

d F

ield

(G

au

ss)

Upper curve: In-cavity film

Lower curve: stand-alone film

Phys. Rev. Lett. 94-180402 (2005) Nucl. Phys. B 726, 441 (2005)

EXPECTED SIGNAL1) Different theories: TE zero mode contribution ?2) Uncertainties on parameters (Au mean free path-Plasma Frequency)

T < 50 K

T 50 K TE Zero mode contribution & Long mean free pathNo TE Zero mode contribution & Conservative free path T 10 K

2 4 6 8 10

50

100

150

Applied Field (mT)

stand-alone filmin-cavity film

T

NO Theory

TC

0-T

(k

)

0

-

Experimental apparatus

-10 -5 0 5 10

0.9995

1.0000

1.0005

1.0010

1.0015

B(z

,r) / B

(0,0

)

z , r [mm]

B(z, r=0) B(z=0, r)

New Coil (301.67 mT/A)

Based on commercial Oxford Heliox 3He cryostat: base temperature 300 mK

The home-made uniform-field coil is placedUnder vacuum to allow external magnetic screening

Detlef Born

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

radH

H

d

dH

H N

3////

//

101

We estimate that in the same sample

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

ALIGNMENT

C

F

F

C

C

F

c

F

Area of 100x100 m2

And 20x20 m2

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

1.45 1.50 1.55 1.60

0.0

0.2

0.4

0.6

0.8

1.0

R [

a.u

.]

T [K]

Mag. Field [a.u.]

600mA 500mA 0 (n.c.) -100mA 100mA 200mA 300mA 400mA 500mA

The transitionwidth is about50 mK

The applied field are of the order of 10 mT

All the samples are deposited in the same chip and worked in the same way until the last metal covering

Cavities are coveredWith Au or Ag; the differenceis expected to be small

In the scheme is reported the lay out ofA single sample: the distance betweenThe various structures (2 and 3 layers)Are about 2.5 mm

1K plate (T~1.5K)

3He pot (Tmin= 250mK)

5 cm

Measurement with radiation @ 300 K

40

21

10300

1

121

1

121

10

300

10

c

T

T

T

T

e

eM

c

c

c

Preliminary measurement: no isolation from infrared and Microwave radiation

The Casimir energy variation is roughtly proportional to the density of photons of frequency 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 aMagnification factor:

Measurement with real EM @300K

1) As expected it mimics the “Casimir signal”2 T is 300 K

0 150 300 450 600 750 900

0

5

10

15

dT

(mK

)

H (Gauss)

cavity film fit of cavity data fit of film data

Zoom for low applied fields

0 25 50 75 100 125 150 175 200 225 250 275 300

0,0

0,5

1,0

1,5

2,0

d

T(m

K)

H (Gauss)

cavity film fit on the cavity data fit on the film data

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 CasimirSignal T on the conservative side of range T 10 K

Sensitivity to Casimir effect

50are a “big” effect

Zoom

Tc = 1.52 K

EM screened

Expected parabolic behaviour recovered with t 6 K

-10 -8 -6 -4 -2 0 2 4 6 8 10 12

0,0

50,0µ

100,0µ

150,0µ

200,0µ

(K

)

Applied Field (mT)

C

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)

FILM

2 points Measured at 3 days of Distance: theyDiffer for about3 K

T0-

T (

K)

0 10

0,0

20,0µ

40,0µ

60,0µ

80,0µ

100,0µ

Y A

xis

Titl

e

Applied field (mT)

Typical data on cavity

Errors of the same order of magnitude of the signal!!Sensitivity not sufficient to claim for the effect

The uncertainties on cavity are higher: 10 K

T0-

T (

K)

Next experimental steps• Impossible to decrease the gap• Very difficult to improve sensitivity

Major upgrade experimental apparatus: lower the temperature

Presently a 20 mK cryogenic system is under construction

CONCLUSION