Casimir effect and the MIR experiment

1
Casimir effect and the MIR experiment
G. Carugno INFN Padova

• D. Zanello
• INFN Roma 1

2
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

3
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

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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

5
Experimental verifications

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

R is the sphere radius
Investigators R Range (mm) 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 mm 0.1-0.8 1
Chan et al (2001) 100 mm 0.075-2.2 1
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Results of the Padova experiment (2002)
First measurement of the Casimir effect between
parallel metallic surfaces
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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
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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 excitation frequency w0 cavity resonance
frequency
wm 2 w0
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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)

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Theoretical predictions

1. 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 al Phys. Rev. Lett. 93, 19
(2004)
t is the excitation time
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Is energy conserved?
Eout
Eout
E
E
Ein
Ein
Eout
t
t
Srivastava (2005)
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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 (bv/c)
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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)

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Resonant cavity with time variable mirror
MIR Experiment
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The Project
Dino Zanello Rome Caterina Braggio Padova Giann
i Carugno Giuseppe Messineo
Trieste Federico Della Valle Giacomo
Bressi Pavia Antonio Agnesi Federico
Pirzio Alessandra Tomaselli Giancarlo
Reali Giuseppe Galeazzi Legnaro
Labs Giuseppe Ruoso
MIR RD 2004-2005 R D financed by National
Institute for Nuclear Physics (INFN) MIR 2006
APPROVED AS Experiment.
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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.
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
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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 , ? ? 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 gt 103 per train of shots
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Photon generation plus damping
A0 10 D 2 mm ? b 3 104 cm2/Vs ? 2.5
GHz ? 12 cm (b 7 cm, L 11.6)
? (ps) Z 2?3?F ( )10-4 N (n105pulses) N (n104pulses)
25 0.4 12 9750 7800
28 0.45 8 14600 11800
32 0.5 3 44000 35000
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Measurement set-up
Cryostat wall
The complete set-up is divided into Laser
system Resonant cavity with semiconductor Receiv
er chain Data acquisition and general timing
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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/recombinati
  on 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

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Semiconductor as a reflector
Reflection curves for Si and Cu
Light pulse
Experimental set-up

• Results
• Perfect reflectivity for microwave
  Si, GaAs R1
• Light energy to make a good mirror
  1 mJ/cm2

Time (ms)
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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)
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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
1. Same temperature T 85 K
2. Same dose (7.5E14 N/cm2)
Estimated t 18 ps
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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
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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
QL ???measured 3 106
600 ?m thick slab of GaAs
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Superconducting cavity
Cavity geometry and size optimized after
Dodonovs calculations
Niobium 8 x 9 x 1 cm3
Semiconductor holding top
Antenna hole
Q value 107 for the TE101 mode resonant _at_ 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
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Electronics I
Final goal is to measure about 103 photons _at_ 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
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Electronics II measurements
Motorized control of the pick-up antenna
Superconducting cavity
10 cm
Cryogenic amplifier
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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
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Sensitivity
The power P measured by the FFT is
kB - Boltmanns constant G - total gain B -
bandwidth TN - amplifier noise temperature TR -
50 W real temperature
Results 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
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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
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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 5 GHz, low power
Pulse picker
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)
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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 gt 20 dB Total
energy of the final bunch gt 100 mJ
Flash lamp final amplifier
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Detection scheme

• Steps
• Find cavity frequency nr
• Wait for empty cavity
• Set laser system to 2 nr
• Send burst with gt 1000 pulses
• Look for signal with t Q / 2pnr

Expected number of photons Niobium cavity with
TE101 nr 2.5 GHz (22 x 71 x 110
mm3) Semiconductor GaAs with thickness dx 1
mm Single run with 5000 pulses N 103
photons
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Check list
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

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Conclusions
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

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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.
0
-L
complex dielectric function
transparent background
G
D
Result 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 ? Agt1
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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??)(12 ltN1gt0) thermal photons are
amplified as well
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Surface effective motion II
Generate periodic motion by placing the
reflecting surface in two distinct positions
alternatively Position 1 - metallic
plate Position 2 - microwave mirror with
driven reflectivity USE Semiconductors under
illumination can change their dielectric
properties and become from completely transparent
to completely reflective for microwaves.
Light with photon energy hn gt E band gap of
semiconductor
Enhances electron density in the conduction band
Laser ON - OFF On semiconductor
Time variable mirror