casimir effect and the mir experiment d. zanello infn roma 1 g. carugno infn padova
TRANSCRIPT
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