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

4/29/2020 E. Calloni Dip. Scienze Fisiche Federico II Napoli INFN sezione di Napoli

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 R&D 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. Il’Ichev, L. Milano, L. Rosa, D. Stornaiuolo, F. Tafuri, R. Vaglio

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

• Spiegare lo scopo globale della strategia

y

• Se necessario, utilizzare più punti

x

E

  1 2   If the plates are perfectly reflecting the modes that can oscillate must have discrete wavenumbers on vertical axes k z = n  /a while all values are allowed for k x e k y

E



hcL

2 2

n n

     

d

( 2  2

k

) 2

k

2 

n



a

2  3

• 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

E reg

   2

L

2

hc

720

a

3 E reg = E(a)  •

Casimir Force

F C

 

E



a

   2

L

2

hc

240

a

4 = 1.3x10

-7 N

L

1

cm

2 1 

m a

4 Perfectly reflecting mirrors: long wavelengths are “expelled” from the cavity, so that the internal energy is: a  

E c

  

E c



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 4 S. K. Lamoreaux

Rep. Prog. Phys. 68:201-236 (2005)

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)  1 2    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.

z y

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

L a 

T

    2

hc

720

a

4    1 1 1  3   x •

can be written in a covariant form

: 

T

    2

hc

180

a

4 1 4   

z

ˆ 

z

ˆ 

z

ˆ  is the 4-vector space-like orthogonal to the plates L.S. Brown, G.J. Maclay, Phys. Rev. 184 (1969) 5

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

f

   1  det

g

 

x

  (  det

g

)

T

    1 2 

g

 

x



T

 The force is positive (directed upward) : taking into account a system as big as GW detectors’ mirrors made of 10 6 layers with Separation of 5 nm (oxide) the total force is about 10 -14 N 

F

  2

L

2

hc

720

a

3

g c

2 

e r

d 6

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) 

F

 

N A

 720 2 

na c

3

c g

2

e



r

 10  14

N

if  0.5

F Comparison with Virgo sensitivity Visible also With torsion Pendulum experiment X 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)

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 S = 100 nm

Au,Ag

 a = 10 nm

Al 2 O 3

D = 10 nm

Al

Since the optical properties of the film (in the microwave region) change when it becomes superconducting, and since the Casimir free energy F c 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: 

F c



F c

(

n

) 

F c

(

s

)  0 Indeed  F c 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 F c (s) negative than F c (n) should be more

The change in energy can be calculated following the Casimir energy calculation in case of real plates with complex conductivity  

E C

   

E



c

 2 720

A L

3

N metal

 

E

Re(  : modulation factor with respect perfect reflectivity

Diel N/S

 

E

 

E C E C



kT C h



C



kT C hc

/

L

 10  6 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

x

   /( 2

kT c

) 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 T c …

..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 T c 2 . Better to use low T c superconductors.

If the two energy variations are comparable then it is expected that vacuum fluctuations modifies the transition

Is there a way to measure



F

c

?

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.

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 H c.

The value of H c is obtained by equating the magnetic energy (per unit volume) required to expel the magnetic field with the condensation energy (density) of the superconductor.

2

H

(

T c

8  ) 

f n

(

T

) 

f s

(

T

)

f n

(

T

) 

f s

(

T

) 

e cond

(

T

)

f n/S

(

T

) : density of free energy at zero field in the n/s state H c (T) follows an approximate Parabolic law

H c

(

T

) 

H c

( 0 )    1   

T T c

  2   

Superconducting film as a plate of a Casimir cavity

1 8  When the superconducting film is a plate of the cavity, the condensation energy E cond is augmented by the difference  F c among the Casimir free energies of the film  

H c

(

cav

) (

T

 )   2

V



E

cond  

F c

 F c causes a shift of critical field d H c : d

H c H c

 1 2 

F c

E cond

F c



E c

   2 720 

cA a

3   0 .

43

erg

E cond  3.5

 10  8

erg

100 90 Upper curve: In-cavity film 80 70 Expected signal The ratio  F c /E cond diverges T  T c 60 50 40 No theory 

F c

 ( 1 

T

/

T c

) 30 20 Lower curve: stand-alone film

E cond

 ( 1 

T

/

T c

) 2 10 0 -0,0020 -0,0015 -0,0010 dT (K) -0,0005 0,0000 Phys. Rev. Lett. 94-180402 (2005) Nucl. Phys. B 726, 441 (2005)

EXPECTED SIGNAL

1) Different theories: TE zero mode contribution ?

2) Uncertainties on parameters (Au mean free path-Plasma Frequency) 150 100 stand-alone film in-cavity film 10 < 

T < 50



K

50  T NO Theory 0 2 4 6 Applied Field (mT) 8 TE Zero mode contribution & Long mean free path No TE Zero mode contribution & Conservative free path 10    K  T 10  K

Experimental apparatus

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

Detlef Born

New Coil (301.67 mT/A)

1.0015

B

(

z, r

=0)

B

(

z

=0,

r

) 1.0010

1.0005

1.0000

The home-made uniform-field coil is placed 0.9995

Under vacuum to allow external magnetic screening -10 -5 0

z

,

r

[mm] 5 10

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 c F Area of 100x100  m 2 And 20x20  m 2 F 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 1

H

//

dH d

 // 

H H N

//    < 10  3

rad

We estimate that in the same sample  < 10 4

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 1.0

0.8

0.6

0.4

Mag. Field [a.u.] 600mA 500mA 0 (n.c.) -100mA 100mA 200mA 300mA 400mA 500mA The transition width is about 50 mK 0.2

0.0

1.45

1.50

1.55

T

[K] The applied field are of the order of 10 mT 1.60

All the samples are deposited in the same chip and worked in the same way until the last metal covering 1K plate (

T

~1.5K

)

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 Cavities are covered With Au or Ag; the difference is expected to be small 3 He pot (

T

min = 250mK)

Measurement with radiation @ 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  few times 2KT c /h  v = 10KT c /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:

M

    1 2 1 2   1

e e

10 

T c

300 5

T c T c

1  1  1     300 10 

T c

1 2  40

15

Measurement with real EM @300K

10 cavity film fit of cavity data fit of film data 5 0 0 150 300 450 H (Gauss) 600 750 900

1) As expected it mimics the “Casimir signal”

2 

T is 300



K

2,0 1,5

Zoom for low applied fields

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 1,0 0,5 0,0 0 25 50 75 100 125 150 175 H (Gauss) 200 225 250 275 300 Conclusion from this measurement: we expect the Casimir Signal  T on the conservative side of range    K

Sensitivity to Casimir effect

EM screened Tc = 1.52 K 50 K

are a “big” effect

Expected parabolic behaviour recovered with

d  

K

C 200,0µ 150,0µ 100,0µ 50,0µ FILM 2 points Measured at 3 days of Distance: they Differ for about 3 

K

0,0 -10 -8 -6 -4 -2 0 2 4 Applied Field (mT) 6 8 10 12 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)

After a first analysis on cavity

The uncertainties on cavity are higher: 10  K

The cavity points are a first measurement and are to be Intended as a first preliminar set

Next experimental steps

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

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 (?)

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 R&D of effects of gravitational field on vacuum energy