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G. Carugno INFN Padova. Casimir effect and the MIR experiment. D. Zanello INFN Roma 1. The quantum vacuum and its microscopic consequences The static Casimir effect: theory and experiments Friction effects of the vacuum and the dynamical Casimir effect The MIR experiment proposal. Summary.

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Casimir effect and the mir experiment l.jpg

G. Carugno

INFN Padova

Casimir effect and the MIR experiment

D. Zanello

INFN Roma 1

Summary l.jpg

The quantum vacuum and its microscopic consequences

The static Casimir effect: theory and experiments

Friction effects of the vacuum and the dynamical Casimir effect

The MIR experiment proposal


The quantum vacuum l.jpg

Quantum vacuum is not empty but is defined as the minimun of the energy of any field

Its effects are several at microscopic level:

Lamb shift

Landè factor (g-2)

Mean life of an isolated atom

The quantum vacuum

The static casimir effect l.jpg
The static Casimir effect the energy of any field

  • This is a macroscopic effect of the quantum vacuum, connected to vacuum geometrical confinement

  • HBG Casimir 1948: the force between two conducting parallel plates of area S spaced by d

Experimental verifications l.jpg
Experimental verifications the energy of any field

  • The first significant experiments were carried on in a sphere-plane configuration. The relevant formula is

R is the sphere radius

Results of the padova experiment 2002 l.jpg
Results of the Padova experiment (2002) the energy of any field

First measurement of the Casimir effect between parallel metallic surfaces

Friction effects of the vacuum l.jpg

Fulling and Davies (1976): effects of the vacuum on a moving mirror

Steady motion (Lorentz invariance)

Uniformly accelerated motion (Free falling lift)

Non uniform acceleration (Friction!): too weak to be detectable

Friction effects of the vacuum

Nph ~ W T (v/c)2

Amplification using an rf cavity l.jpg

GT Moore (1970): proposes the use of an RF EM cavity for photon production

Dodonov et al (1989), Law (1994), Jaeckel et al (1992): pointed out the importance of parametric resonance condition in order to multiply the effect

Amplification using an RF cavity

wm = excitation frequency

w0 = cavity resonance frequency

wm = 2 w0

Parametric resonance l.jpg

The parametric resonance is a known concept both in mathematics and physics

In mathematics it comes from the Mathieu equations

In physics it is known in mechanics (variable length swing) and in electronics (oscillating circuit with variable capacitor)

Parametric resonance

Theoretical predictions l.jpg
Theoretical predictions mathematics and physics

  • Linear growth

A.Lambrecht, M.-T. Jaekel, and S. Reynaud, Phys. Rev. Lett. 77, 615 (1996)

2. Exponential growth

V. Dodonov, et al Phys. Lett. A 317, 378 (2003);

M. Crocce, et al Phys. Rev. A 70, (2004);

M. Uhlmann et alPhys. Rev. Lett. 93, 19 (2004)

t is the excitation time

Is energy conserved l.jpg
Is energy conserved? mathematics and physics










Srivastava (2005):

Resonant rf cavity l.jpg
Resonant RF Cavity mathematics and physics

In a realistic set-up a 3-dim cavity has an oscillating wall.


Cavity with dimensions ~ 1 -100 cm have resonance frequency varying from 30 GHz to 300 MHz. (microwave cavity)

Great experimental challenge: motion of a surface at frequencies extremely large to match cavity resonance and with large velocity (b=v/c)

Surface motion l.jpg

Mechanical motion mathematics and physics. Strong limitation for a moving layer: INERTIA

Very inefficient technique: to move the electrons giving the reflectivity one has to move also the nuclei with large waste of energy

Maximum displacement obtained up to date of the order of 1 nm

Effective motion. Realize a time variable mirror with driven reflectivity (Yablonovitch (1989) and Lozovik (1995)

Surface motion

Resonant cavity with time variable mirror l.jpg

Time variable mirror mathematics and physics

Resonant cavity with time variable mirror

MIR Experiment

The project l.jpg
The Project mathematics and physics

Dino ZanelloRome

Caterina BraggioPadova

Gianni Carugno

Giuseppe Messineo Trieste

Federico Della Valle

Giacomo BressiPavia

Antonio Agnesi

Federico Pirzio

Alessandra Tomaselli

Giancarlo Reali

Giuseppe Galeazzi LegnaroLabs

Giuseppe Ruoso

MIR – RD 2004-2005

R & D financed by National Institute for Nuclear Physics (INFN)


2006 APPROVED AS Experiment.

Our approach l.jpg

Time variable mirror mathematics and physics

Our approach

Taking inspiration from proposals by Lozovik (1995) and Yablonovitch (1989) we produce the boundary change by light illumination of a semiconductor slab placed on a cavity wall

Semiconductors under illumination can change their dielectric properties and become from completely transparentto completely reflective for selected wavelentgh.

A train of laser pulses will produce a frequency controlled variable mirror and thus if the change of the boundary conditions fulfill the parametric resonance condition this will result in the Dynamical Casimir effect with the combined presence of high frequency, large Q and large velocity

Expected results l.jpg
Expected results mathematics and physics

Complete characterization of the experimental apparatus has been done by V. Dodonov et al (see talk in QFEXT07).

V V Dodonov and A V Dodonov

“QED effects in a cavity with time-dependent thin semiconductor slab excited by laser pulses”

J Phys B 39 (2006) 1-18

Calculation based on realistic experimental conditions,

  • t semiconductor recombination time ,   10-30 ps

  •  semiconductor mobility ,   1 m 2 / (V s)

  • () semiconductor light absorption coefficient

  • t semiconductor thickness , t  1 mm

  • laser: 1 ps pulse duration, 200 ps periodicity, 10-4 J/pulse

  • (a, b, L) cavity dimensions

Expected photons N > 103 per train of shots

Photon generation plus damping l.jpg
Photon generation plus damping mathematics and physics

A0 = 10 D = 2 mm  = b = 3 104 cm2/Vs

 = 2.5 GHz  = 12 cm (b = 7 cm, L = 11.6)

Measurement set up l.jpg
Measurement set-up mathematics and physics

Cryostat wall

The complete set-up is divided into

Laser system

Resonant cavity with semiconductor

Receiver chain

Data acquisition and general timing

Experimental issues l.jpg
Experimental issues mathematics and physics

  • Effective mirror

  • the semiconductor when illuminated behaves as a metal (in the microwave band)

  • timing of the generation and recombination processes

  • quality factor of the cavity with inserted semiconductor

  • possible noise coming from generation/recombination of carriers

  • Laser system

  • possibility of high frequency switching

  • pulse energy for complete reflectivity

  • number of consecutive pulses

  • Detection system

  • minimum detectable signal

  • noise from blackbody radiation

Semiconductor as a reflector l.jpg
Semiconductor as a reflector mathematics and physics

Reflection curves for Si and Cu

Light pulse

Experimental set-up

  • Results:

  • Perfect reflectivity for microwave Si, GaAs: R=1;

  • Light energy to make a good mirror ≈ 1 mJ/cm2

Time (ms)

Semiconductor i l.jpg
Semiconductor I mathematics and physics

The search for the right semiconductor was very long and stressful, but we managed to find the right material

Requests: t ~ 10 ps , m ~ 1 m2/ (V s)

Neutron Irradiated GaAs

Irradiation is done with fast neutrons (MeV) with a dose ~ 1015 neutrons/cm2 (performed by a group at ENEA - ROMA). These process while keeping a high mobility decreases the recombination time in the semiconductor

High sensitivity measurements of the recombination time performed on our samples with the THzpump and probe technique by the group of Prof. Krotkus in Vilnius (Lithuania)

Semiconductor ii recombination time l.jpg
Semiconductor II: recombination time mathematics and physics

Results obtained from the Vilnius group on Neutron Irradiated GaAs Different doses and at different temperatures

The technique allows to measure the reflectivity from which one calculate the recombination time

1. Same temperature T = 85 K

2. Same dose (7.5E14 N/cm2)

Estimated t = 18 ps

Semiconductor iii mobility l.jpg
Semiconductor III: mobility mathematics and physics

Mobility can be roughly estimated for comparison with a known sample from the previous measurements and from values of non irradiated samples.

m ~ 1 m2 / (V s)

We are setting up an apparatus for measuring the product mt using the Hall effect.

From literature one finds that little change is expected between irradiated and non irradiated samples at our dose

Cavity with semiconductor wall l.jpg
Cavity with semiconductor wall mathematics and physics

Fundamental mode TE101: the electric field E

Computer model of

a cavity with a semiconductor wafer on a wall

a = 7.2 cm

b = 2.2 cm

l = 11.2 cm

QL= measured ≈3· 106

600 m thick slab of GaAs

Superconducting cavity l.jpg

Cryostats mathematics and physics

old new

Superconducting cavity

Cavity geometry and size optimized after Dodonov’s calculations

Niobium: 8 x 9 x 1 cm3

Semiconductor holding top

Antenna hole

Q value ~ 107 for the TE101 mode resonant @ 2.5 GHz

No changes in Q due to the presence of the semiconductor

The new one has a 50 l LHe vessel

Working temperature 1 - 8 K

Electronics i l.jpg

(Cryogenic) mathematics and physics

Electronics I

Final goal is to measure about 103 photons @ 2.5 GHz

Use a very low noise cryogenic amplifier and then a superheterodyne detection chain at room temperature

Picture of the room temperature chain

The cryogenic amplifier CA has 37 dB gain allowing to neglect noise coming from the rest of the detector chain

Special care has to be taken in the cooling of the amplifier CA and of the cable connecting the cavity antenna to it



Electronics ii measurements l.jpg
Electronics II: measurements mathematics and physics

Motorized control of the pick-up antenna

Superconducting cavity

~ 10 cm

Cryogenic amplifier

Electronics iii noise measurement l.jpg
Electronics III: noise measurement mathematics and physics

Using a heated 50 W resistor it is possible to obtain noise temperature of the first amplifier and the total gain of the receiver chain

2. Complete chain

1. Amplifier + PostAmplifier

Sensitivity l.jpg
Sensitivity mathematics and physics

The power P measured by the FFT is:

kB - Boltmann’s constant

G - total gain

B - bandwidth

TN - amplifier noise temperature

TR - 50 W real temperature


TN1 = TN2 No extra noise added in the room temperature chain

G1 = 72 dB = 1.6 107

Gtot = 128 dB = 6.3 1012

The noise temperature TN = 7.2 K corresponds to 1 10-22 J

For a photon energy = 1.7 10-24 J

sensitivity ~ 100 photons

Black body photons in cavity at resonance l.jpg
Black Body Photons in Cavity at Resonance mathematics and physics

Noise 50 Ohm Resistor at R.T.

Noise Signal from TE101 Cavity

at R.T.

Cavity Noise vs Temperature

Laser system i l.jpg
Laser system I mathematics and physics

Pulsed laser with rep rate ~ 5 GHz, pulse energy ~100 mJ, train

of 103 - 104 pulses, slightly frequency tunable ~ 800 nm

Laser master oscillator

5 GHz, low power


Optical amplifier

Total number of pulses limited by the energy available in the optical amplifier

Each train repeated every few seconds

Optics Express 13, 5302 (2005)

Laser system ii l.jpg
Laser system II mathematics and physics

Diode preamplifier

Master oscillator

Pulse picker

Current working frequency: 4.73 GHz

Pulse picker: ~ 2500 pulses, adjustable

Diode preamplifier gain: 60 dB

Final amplifier gain: > 20 dB

Total energy of the final bunch: > 100 mJ

Flash lamp final amplifier

Detection scheme l.jpg
Detection scheme mathematics and physics


Find cavity frequency nr

Wait for empty cavity

Set laser system to 2 nr

Send burst with > 1000 pulses

Look for signal witht ~ Q / 2pnr

Expected number of photons:

Niobium cavity with TE101nr = 2.5 GHz (22 x 71 x 110 mm3)

Semiconductor GaAs with thickness dx = 1 mm

Single run with ~ 5000 pulses

N ≥ 103 photons

Check list l.jpg
Check list mathematics and physics

Several things can be employed to disentangle a real signal from a spurious one

Loading of cavity with real photons (is our system a microwave amplifier?)

Change temperature of cavity

Effect on black body photons

Change laser pulse rep. frequency

  • change recombination time of semiconductor

  • change width of semiconductor layer

Conclusions l.jpg

Carry on measurements at different temperatures and extrapolate to T = 0 Kelvin

Loading of cavity with real photons and measure Gain

Change laser pulse rep. frequency


Several things can be employed to disentangle a real signal from a spurious one

We expect to complete assembly Spring this year. First measure is to test the amplification process with preloaded cavity, then vacuum measurements

  • change recombination time of semiconductor

  • change thickness of semiconductor

Frequency shift l.jpg
Frequency shift extrapolate to T = 0 Kelvin

Problem: derivation of a formula for the shift of resonance in the MIR em cavity and compare it with numerical calculations and experimental data.



complex dielectric function

transparent background




a thin film is an ideal mirror (freq shift) even if G  s

MIR experiment: 800 nm light impinging on GaAs +

1 m abs. Length = plasma thickness +

mobility 104 cm2/Vs    mcm  A>1

Slide38 l.jpg

N extrapolate to T = 0 Kelvinb =

n = T/2

  • Nph = sinh2(n) = sinh2(T0) ideal case

  • unphysically large number of photons

  • dissipation effects (instability removed)

  • T  0 non zero temperature experiment?

Nph = sinh2(n)(1+2 <N1>0) thermal photons are amplified as well

Surface effective motion ii l.jpg
Surface effective motion II extrapolate to T = 0 Kelvin

Generate periodic motion by placing the reflecting surface in

two distinct positions alternatively

Position 1 - metallic plate

Position 2 - microwave mirror with driven reflectivity


Semiconductors under illumination can change their dielectric properties and become from completely transparent to completely reflective for microwaves.

Light with photon energy hn > E band gap of semiconductor

Enhances electron density in the conduction band

Laser ON - OFF

On semiconductor

Time variable mirror