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
FC 
 h c S 1.3 10 S
480 d
4

27
d
4
N
Experimental verifications
• The first significant experiments were carried on in a
sphere-plane configuration. The relevant formula is
FC  
 2 hcR
R is the sphere radius
3
720d
Investigators
R
Range (mm)
Precision (%)
Van Blokland and
Overbeek (1978)
1m
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 mm
0.1-0.8
1
Chan et al (2001)
100 mm
0.075-2.2
1
Results of the Padova experiment (2002)
K C  (1.22  0.18) 1027 N m2
2
Residual square frequency shift (Hz
KC
F 4 S
d
)
First measurement of the
Casimir effect between
parallel metallic surfaces
0
-1000
-2000
-3000
0.5
1
1.5
2
d ( mm)
2.5
3
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 ~ W T (v/c)2
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
wm = 2 w0
wm = excitation frequency
w0 = 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
1. Linear growth
A.Lambrecht, M.-T. Jaekel, and
S. Reynaud, Phys. Rev.
Lett. 77, 615 (1996)
2.
2


Wt v
N  Q
 
2 c 
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)
 v
N  sinh  Wt 
 c
2
t is the excitation time
Is energy conserved?
E
Eout
Ein
E
Eout
Ein
Eout
t
t
Srivastava (2005):
dn
 an  bn 2
dt
Resonant RF Cavity
In a realistic set-up a 3-dim cavity has an oscillating wall.
Wm
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
• 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
MIR Experiment
Time variable mirror
The Project
MIR – RD 2004-2005
Dino Zanello
Rome
Caterina Braggio
Gianni Carugno
Padova
R & D financed by National Institute
for Nuclear Physics (INFN)
Giuseppe Messineo
Federico Della Valle
Trieste
MIR
2006 APPROVED AS
Experiment.
Giacomo Bressi
Antonio Agnesi
Federico Pirzio
Alessandra Tomaselli
Giancarlo Reali
Pavia
Giuseppe Galeazzi
Giuseppe Ruoso
Legnaro Labs
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 transparent to
completely reflective for
selected wavelentgh.
Time variable mirror
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
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 , t  10-30 ps
• m semiconductor mobility , m  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
N ph  0.85exp(2  F  n)
3
Expected photons N > 103 per train of shots
Photon generation plus damping
N ph  0.85exp(23 F  n)
A0 = 10 D = 2 mm m = b = 3 104 cm2/Vs
 = 2.5 GHz  = 12 cm (b = 7 cm, L = 11.6)
t (ps)
Z
23F
( )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
Measurement set-up
The 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
Laser system
Detection system
• possibility of high frequency switching
• minimum detectable signal
• pulse energy for complete reflectivity
• noise from blackbody radiation
• number of consecutive pulses
Semiconductor as a reflector
Reflection curves for Si and Cu
Light pulse
Experimental set-up
Results:
• Perfect reflectivity for microwave
• Light energy to make a good mirror
Time (ms)
Si, GaAs: R=1;
≈ 1 mJ/cm2
Semiconductor I
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 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
The technique allows to measure the reflectivity from which one
calculate the recombination time
2. Same dose (7.5E14 N/cm2)
1. Same temperature T = 85 K
1.2 10-10
1.2 10-10
1 10-10
1 10-10
11 K
85 K
Reflecitivity (a.u.)
Reflectivity (a.u.)
Dose = 1E15 N/cm^2
Dose = 2E15 N/cm^2
Dose = 7.5E14 N/cm^2
8 10-11
6 10-11
4 10-11
8 10-11
6 10-11
4 10-11
2 10-11
2 10-11
0
0
20
40
60
time (ps)
80
100
120
140
0
-20
0
20
40
60
Time (ps)
Estimated t = 18 ps
80
100
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.
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
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
2
2
c  1  1
fr 
      2.4899 GHz
2 a l
QL= tmeasured ≈ 3 · 106
600 mm thick slab of GaAs
Superconducting cavity
Cavity geometry and size optimized after
Dodonov’s calculations
Niobium: 8 x 9 x 1 cm3
Antenna hole
Cryostats
old
new
Semiconductor
holding top
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
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
CA
PA
(Cryogenic)
Electronics II: measurements
Motorized control
of the pick-up
antenna
Superconducting
cavity
Cryogenic amplifier
~ 10 cm
Electronics III: noise measurement
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
LO
5 0 ohm
5 0 ohm
FFT
CA
FFT
CA
PA
8 10-12
4 10-6
6 10-12
3 10-6
Measured power (W)
Measured power (W)
heat er
Tn = - T0 = 7.2 ± 0.1 K
4 10-12
From slope Total Gain G = 72 dB
2 10-12
0
-10
PA
heat er
0
10
20
30
Temperature of the 50 ohm resistance (K)
40
Tn = -T0 = 7.1 ± 0.2 K
2 10-6
From slope total gain G = 128 dB
1 10-6
0
-10
0
10
20
30
Temperature of the 50 ohm resistance (K)
40
Sensitivity
The power P measured by the FFT is:
P  kBGB(TN  TR )
Results:
TN1 = TN2
kB - Boltmann’s constant
G - total gain
B - bandwidth
TN - amplifier noise temperature
TR - 50 W real temperature
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
Noise 50 Ohm Resistor at R.T.
Noise Signal from TE101 Cavity
at R.T.
Cavity Noise vs Temperature
Laser system I
Pulsed laser with rep rate ~ 5 GHz, pulse energy ~100 mJ, train
of 103 - 104 pulses, slightly frequency tunable ~ 800 nm
Laser master oscillator
Pulse picker
Optical amplifier
5 GHz, low power
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
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
N pulses
Steps
1. Find cavity frequency r
2. Wait for empty cavity
3. Set laser system to 2 r
4. Send burst with > 1000 pulses
5. Look for signal with t ~ Q / 2r
t p = 1 / 2 r
Expected number of photons:
Niobium cavity with TE101 r = 2.5 GHz (22 x 71 x 110 mm3)
Semiconductor GaAs with thickness dx = 1 mm
Single run with ~ 5000 pulses
N ≥ 103 photons
Charg ed cavit y.
Will decay wit h it s
t ime co nst ant
Check list
Several things can be employed to disentangle a real signal from a
spurious one
Change temperature of cavity
Effect on black body photons
Loading of cavity with real photons (is
our system a microwave amplifier?)
Change laser pulse rep. frequency
1.6
1.4
12
10
8
6
4
Determine vacuum effect from several
measurements with pre-loaded cavity
2
0
1.2
Signal (a.u.)
Power inside cavity at end of laser pulses (a.u.)
14
0
1
2
3
4
Power inside cavity at t = t0 (a.u.)
5
6
1
0.8
0.6
0.85
0.9
0.95
Laser pulse frequency (a.u)
1
1.05
1.1
-change recombination time of semiconductor
-change width of semiconductor layer
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
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
Change laser pulse rep. frequency
1.6
1.4
12
10
1.2
Signal (a.u.)
Power inside cavity at end of laser pulses (a.u.)
14
8
6
4
1
0.8
Determine vacuum effect from several
measurements with pre-loaded cavity
0.6
0.85
2
0.9
0.95
Laser pulse frequency (a.u)
1
1.05
1.1
0
0
1
2
3
4
Power inside cavity at t = t0 (a.u.)
5
6
- change recombination time of semiconductor
- change thickness of semiconductor
Frequency shift
Problem: derivation of a formula for the shift of resonance in the MIR em
cavity and compare it with numerical calculations and experimental data.
-L
complex dielectric
function
0
G
transparent background
D
Result:
a thin film is an ideal mirror (freq shift) even if G  ds L  D  d
A2
GD
ds2
s
, mirror if A  1
MIR experiment: 800 nm light impinging on GaAs
+
1 mm abs. Length = plasma thickness +
mobility 104 cm2/Vs
   mWcm  A>1
n = WT/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)
Nb = kT / h
thermal photons are amplified as well
Surface effective motion II
Met al
plat e
Generate periodic motion by placing the reflecting surface in
two distinct positions alternatively
Position 1
Position 2
Variab le
mirror
Micro wave
- metallic plate
- microwave mirror with driven reflectivity
USE
P1
P2
Semiconductors under illumination can change their dielectric properties and become
from completely transparent to completely reflective for microwaves.
Light with photon energy
h > E band gap of semiconductor
Enhances electron density in the conduction band
Laser ON - OFF
On semiconductor
Time variable mirror