Casimir effect and the MIR experiment

D. Zanello

INFN Roma 1

G. Carugno

INFN Padova

Summary

• 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

• 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 static Casimir effect

• 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

N d

S10 1.3

d 480

S ch F

4

27

4C

Experimental verifications

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

FC 2hcR

720d3

Investigators R Range (m) Precision (%)

Van Blokland and Overbeek (1978)

1 m 0.13-0.67 25 at small distances

50 average

Lamoreaux (1997) 12.5 cm 0.6-6 5 at very small distance, larger elsewhere

Mohideen et al (1998) 200 m 0.1-0.8 1

Chan et al (2001) 100 m 0.075-2.2 1

R is the sphere radius

Results of the Padova experiment (2002)

KC (1.220.18)10 27 N m2

First measurement of the Casimir effect between parallel metallic surfaces

F KC

d4 S

-3000

-2000

-1000

0

0.5 1 1.5 2 2.5 3

Res

idua

l squ

are

freq

uenc

y sh

ift

(Hz

2)

d ( m)

Friction effects of the vacuum

• 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

Nph ~ T v/c2

Amplification using an RF cavity

• 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

m = 2 0

m = excitation frequency

0 = cavity resonance frequency

Parametric resonance

• 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)

Theoretical predictions

N Qt

2v

c

2A.Lambrecht, M.-T. Jaekel, and

S. Reynaud, Phys. Rev. Lett. 77, 615 (1996)

1. Linear growth

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 al Phys. Rev. Lett. 93, 19 (2004)

c

vtsinhN 2

t is the excitation time

Is energy conserved?

t

E Ein

Eout

Eout

t

EEin

Eout

Srivastava (2005): 2nn

dt

dnba

Resonant RF Cavity

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

m

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)

Surface motion

• Mechanical motion. 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)

Resonant cavity with time variable mirror

Time variable mirror

MIR Experiment

The ProjectDino Zanello Rome

Caterina Braggio PadovaGianni Carugno

Giuseppe Messineo TriesteFederico Della Valle

Giacomo Bressi PaviaAntonio AgnesiFederico PirzioAlessandra TomaselliGiancarlo Reali

Giuseppe Galeazzi Legnaro LabsGiuseppe Ruoso

MIR – RD 2004-2005R & D financed by National Institute

for Nuclear Physics (INFN)

MIR 2006 APPROVED AS

Experiment.

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

Time variable mirror

Semiconductors under illumination can change their dielectric properties and become from completely transparent to 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 resultsComplete 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, • 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

N ph 0.85 exp(23 F n)

(ps) Z 23F( )10-4

N (n=105pulses)

N (n=104pulses)

25 0.4 12 9750 7800

28 0.45 8 14600 11800

32 0.5 3 44000 35000

N ph 0.85exp(23 F n)

A0 = 10 D = 2 mm = b = 3 104 cm2/Vs = 2.5 GHz = 12 cm (b = 7 cm, L = 11.6)

Photon generation plus damping

Measurement set-upThe complete set-up is divided into

Laser system

Resonant cavity with semiconductor

Receiver chain

Data acquisition and general timing

Cryostat wall

Experimental issues

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

Detection system

• minimum detectable signal

• noise from blackbody radiation

Laser system

• possibility of high frequency switching

• pulse energy for complete reflectivity

• number of consecutive pulses

Semiconductor as a reflector

Results:• Perfect reflectivity for microwave Si, GaAs: R=1;• Light energy to make a good mirror ≈ 1 J/cm2

Experimental set-up

Reflection curves for Si and Cu

Time (s)

Light pulse

Semiconductor IThe search for the right semiconductor was very long and stressful, but we managed to find the right materialRequests: ~ 10 ps , ~ 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 THz pump and probe technique by the group of Prof. Krotkus in Vilnius (Lithuania)

Semiconductor II: recombination time

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

0

2 10-11

4 10-11

6 10-11

8 10-11

1 10-10

1.2 10-10

0 20 40 60 80 100 120 140

Dose = 1E15 N/cm^2

Dose = 2E15 N/cm^2

Dose = 7.5E14 N/cm^2

Ref

lect

ivit

y (a

.u.)

time (ps)

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

1. Same temperature T = 85 K

0

2 10-11

4 10-11

6 10-11

8 10-11

1 10-10

1.2 10-10

-20 0 20 40 60 80 100

11 K85 K

Re

flec

itiv

ity

(a.u

.)

Time (ps)

2. Same dose (7.5E14 N/cm2)

Estimated = 18 ps

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

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

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

~ 1 m2 / (V s)

Cavity with semiconductor wallFundamental mode TE101: the electric field E

600 m thick slab of GaAs

Computer model ofa cavity with a semiconductor wafer on a wall

a = 7.2 cmb = 2.2 cml = 11.2 cm

GHz 4899.211

2

22

la

cfr

QL= measured ≈ 3 · 106

Superconducting cavity

Cryostatsold new

Cavity geometry and size optimized after Dodonov’s calculations

Q value ~ 107 for the TE101 mode resonant @ 2.5 GHz No changes in Q due to the presence of the semiconductor

Niobium: 8 x 9 x 1 cm3

The new one has a 50 l LHe vesselWorking temperature 1 - 8 K

Antenna hole Semiconductor holding top

Electronics IFinal goal is to measure about 103 photons @ 2.5 GHz

(Cryogenic)

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

CA PA

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

Picture of the room temperature chain

Electronics II: measurements

Cryogenic amplifier~ 10 cm

Motorized control of the pick-up antenna

Superconducting cavity

Electronics III: noise measurementUsing a heated 50 resistor it is possible to obtain noise temperature of the first amplifier and the total gain of the receiver chain

0

2 10-12

4 10-12

6 10-12

8 10-12

-10 0 10 20 30 40

Mea

su

red

po

we

r (W

)

Temperature of the 50 ohm resistance (K)

Tn = - T0 = 7.2 ± 0.1 K

From slope Total Gain G = 72 dB

0

1 10-6

2 10-6

3 10-6

4 10-6

-10 0 10 20 30 40

Mea

sure

d p

ow

er (

W)

Temperature of the 50 ohm resistance (K)

Tn = -T0 = 7.1 ± 0.2 K

From slope total gain G = 128 dB

50 ohm

FFT

CA PA

heater

1. Amplifier + PostAmplifier 2. Complete chain

50 ohm

FFT

CA PA

heater

LO

SensitivityThe power P measured by the FFT is:

P kBGB(TN TR )

kB - Boltmann’s constantG - total gainB - bandwidthTN - amplifier noise temperatureTR - 50 real temperature

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

For a photon energy = 1.7 10-24 Jsensitivity ~ 100 photons

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

G1 = 72 dB = 1.6 107 Gtot = 128 dB = 6.3 1012

Black Body Photons in Cavity at Resonance

Noise 50 Ohm Resistor at R.T.

Noise Signal from TE101 Cavity at R.T.

Cavity Noise vs Temperature

Laser system I

Laser master oscillator

5 GHz, low power Pulse picker Optical amplifier

Pulsed laser with rep rate ~ 5 GHz, pulse energy ~100 J, trainof 103 - 104 pulses, slightly frequency tunable ~ 800 nm

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

Master oscillator

Pulse picker

Diode preamplifier

Flash lamp final amplifier

Current working frequency: 4.73 GHzPulse picker: ~ 2500 pulses, adjustableDiode preamplifier gain: 60 dBFinal amplifier gain: > 20 dB

Total energy of the final bunch: > 100 mJ

Detection scheme

Steps1. Find cavity frequency r

2. Wait for empty cavity3. Set laser system to 2 r

4. Send burst with > 1000 pulses5. Look for signal with ~ Q / 2r

N pulses

tp = 1/ 2 r Charged cavity.Will decay with itstime constant

Expected number of photons:

Niobium cavity with TE101 r = 2.5 GHz (22 x 71 x 110 mm3)Semiconductor GaAs with thickness x = 1 mmSingle run with ~ 5000 pulses

N ≥ 103 photons

Check list

-change recombination time of semiconductor-change width of semiconductor layer

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

Change temperature of cavityEffect on black body photons

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

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6

Pow

er i

nsi

de

cavi

ty a

t en

d o

f la

ser

pu

lses

(a.

u.)

Power inside cavity at t = t0 (a.u.)

Determine vacuum effect from severalmeasurements with pre-loaded cavity

Change laser pulse rep. frequency

0.6

0.8

1

1.2

1.4

1.6

0.85 0.9 0.95 1 1.05 1.1

Sig

nal

(a.

u.)

Laser pulse frequency (a.u)

Conclusions

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

Loading of cavity with real photons and measure Gain

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6

Pow

er i

nsi

de

cavi

ty a

t en

d o

f la

ser

pu

lses

(a.

u.)

Power inside cavity at t = t0 (a.u.)

Determine vacuum effect from severalmeasurements with pre-loaded cavity

Change laser pulse rep. frequency

0.6

0.8

1

1.2

1.4

1.6

0.85 0.9 0.95 1 1.05 1.1S

ign

al (

a.u

.)Laser pulse frequency (a.u)

- change recombination time of semiconductor- change thickness of semiconductor

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

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

D

-L

G

0

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

Result:a thin film is an ideal mirror (freq shift) even if G s

complex dielectric function transparent background

L D s

A 2GD

s2

, mirror if A 1

MIR experiment: 800 nm light impinging on GaAs + 1 m abs. Length = plasma thickness + mobility 104 cm2/Vs mcm A>1

Frequency shift

Nph = sinh2(n) = sinh2(T0) 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

n = T/2

Nb = kT / h

Generate periodic motion by placing the reflecting surface in two distinct positions alternatively

Position 1 - metallic platePosition 2 - microwave mirror with driven reflectivity

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

Surface effective motion II

Light with photon energy h > E band gap of semiconductor

Enhances electron density in the conduction band

Laser ON - OFFOn semiconductor

Time variable mirror

P1 P2

Variablemirror

Metalplate

Microwave