Transcript
University of Ferrara
Measuring the magnetic birefringence of vacuum: status and future perspectives of the PVLAS experiment Guido Zavattini on behalf of the PVLAS collaboration
Università di Ferrara and INFN sezione di Ferrara, Italy
“Hands holding the void” Alberto Giacometti G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
PVLAS collaboration University and INFN - Ferrara G. Di Domenico L. Piemontese G. Zavattini
University and INFN - Trieste F. Della Valle E. Milotti
INFN - Lab. Naz. di Legnaro U. Gastaldi R. Pengo G. Ruoso
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Summary •Short introduction to: •aim of the PVLAS experiment •experimental technique •PVLAS - LNL •Overview of published results •Development phases •Several improvements with respect to PVLAS-LNL •Ferrara Test apparatus •Final experiment G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Classical Electromagnetism in vacuum Classical vacuum has no structure. The superposition principle is valid
¶B ¶t
div D = 0;
rot E = -
div B = 0;
¶D rot H = ¶t
L
EM
2 ö 1 æE 2 = ç 2 -B ÷ 2m 0 è c ø
¶ LEM D= ¶E ¶ LEM H=¶B D = e0 E;
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
m0 H = B
Heisenberg’s Uncertainty Principle
DEDt³
Vacuum is the minimum energy state and can fluctuate into anything compatible with vacuum
2
Vacuum has a structure which can be observed by perturbing it and probing it.
•Evidence of microscopic structure of vacuum is known (Lamb Shift ....)
•Macroscopically observable (small) non linear effects have been predicted since 1936 but have never been directly observed yet. G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Vacuum as a Medium • Scheme: – perturb the vacuum state with an external field – probe the perturbed vacuum state with a polarized laser beam – deduce information on the structure of the vacuum state
- The propagation of light will be affected by the polarized vacuum fluctuations. - Although we consider vacuum, because of the fermion loop the propagation of photons in an external field is now described by Maxwell’s equations like those in material media. Furthermore they are no longer linear G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Aim of PVLAS • We want to study the speed of light in the perturbed vacuum and therefore study changes in the refractive index
nvacuum =1+ (d nr - ik ) field • Absolute changes of nvacuum are too difficult to measure so we study anisotropies due to the perturbing field. • Linear birefringence and linear dichroism G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Linear Birefringence • A birefringent medium has
n|| ¹ n^
• A linearly polarized light beam propagating through a birefringent medium will acquire an ellipticity y ||
a p L(n|| - n^ ) y= = sin 2J b l
a
n || L ||
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
J
Eg
n
b
Linear Dichroism • A dichroic medium has different extinction coefficients: k|| • A linearly polarized light beam propagating through a dichroic medium will acquire an apparent rotation e
p L(k || - k ^ ) e= sin 2J l
Absorption coefficient
=
2p
l
k ||
k^
k
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
¹ k^
Linear dichroism and birefringence BExt
Dichroism
BExt
E
E| |
E
E| |
E^
Ellipticity
E^
before
after
BExt
BExt
E| |
E
E
E| |
E^ before G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
E^ after
apparent rotation e
ellipticity y
Summary of possibile processes •
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Described by the EulerHeisenberg Lagrangian. Should be there. Also includes MCPs
•
Correction 1.45%
•
Hadronic contribution. Difficult to extract from indirect measurements. g-2 open problem.
•
Contribution from hypothetical new particles coupling to two photons.
Euler-Heisenberg Effective Lagrangian For fields much smaller than the critical field (B << 4.4·109 T; E << 1.3·1018 V/m) one can write
W Heisenberg and H Euler, Z. Phys. 98, 714 (1936) H Euler, Ann. Phys. 26, 398 (1936)
2ù 2 é 2 æE ö ö Ae æ E ö 1 æE 2 2 L = Lem + LHE = ç 2 - B ÷ + êç 2 - B ÷ + 7ç × B ÷ ú 2m 0 è c ø m0 êëè c ø è c ø úû 2
2 æ a 2 3e ö -24 -2 Ae = =1.32 ×10 T ç ÷ 45m0 è mec 2 ø Are neglected: a3 terms and higher virtual pairs with particles different from e+ eG. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Induced Magnetic Birefringence of Vacuum •By applying the constitutive relations to LEH one finds
¶ LEH D= ¶E ¶ LEH H=¶B
é æE2 ù ö 2 D = e 0 E + e 0 Ae ê4 ç 2 - B ÷ E +14 E × B Bú êë è c úû ø é æE2 ù ö æ ö E × B m 0 H = B + Ae ê4 ç 2 - B 2 ÷ B -14 ç 2 ÷ Eú êë è c è c ø úû ø
(
)
•Light propagation is still described by Maxwell’s equations in media but they no longer are linear due to EH correction. G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Photon propagating in an external field Study the propagation of the photon in an external field The index of refraction gives information on the nature of the “media”
Considering linearly polarised light traversing an external magnetic field
J Bext
E wave
w, k
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
w << me me2 c 2 B << Bcr = = 4.42 ´10 9 T e ìï E = Ewave and Bext >> Bwave í ïî B = Bext + Bwave
Linearly polarized light passing through a transverse external magnetic field.
ìe|| = 1+10Ae B2Ext ï 2 ím|| = 1+ 4Ae B Ext ï 2 în|| = 1+ 7Ae B Ext
•v ≠ c •anisotropy
ìe^ = 1- 4Ae B2Ext ï 2 ím^ = 1+12Ae B Ext ï 2 în^ = 1+ 4Ae B Ext Ae can be determined by measuring the magnetic birefringence of vacuum.
n = 3AeBExt2 n = 2.5·10-23 for BExt = 2.5 T
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Cotton-Mouton Effect Vacuum behaves like a gas: Cotton-Mouton effect
Gas
CM constant (atm Tesla-2)
vacuum equiv. pressure (mbar)
N2
-2.45·10-13
1.6·10-8
Ar
6.8·10-15
5.8·10-7
Kr
9.9·10-15
4·10-7
Ne
2.8·10-16
1.4·10-5
He
1.8·10-16
2.2·10-5
H2
8.5·10-15
4.7·10-7
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
∆ nCM
P 2 = CM B0 Patm
For N2: Vacuum is ‘equivalent’ to 4.3·108 molecules/cm3
Post-Maxwellian models L pM
2ù 2 é æ 2 æE ö ö x ê E 2 = h1 ç 2 - B ÷ + 4h2 ç × B ÷ ú 2m 0 êë è c ø è c ø úû
1 æ e ö x = 2 = ç 2 2 ÷ = 5·10 -20 T -2 Bcrit è m c ø 7 (QED) a (QED) (QED) h2 = h1 ; h1 = 4 45p 2
The form of LpM is defined by properties of invariance - η1 represents the interaction between parallel fields - η2 represents the interaction between perpendicular fields
∆n
( pM )
= 2x (h2 - h2 ) B
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
2 Ext
Light-Light scattering Very low energy photon-photon scattering is proportional to Ae2. For non polarized light:
s gg
[*]
973m = 20p
2 0
Eg 2 A e 4 4 c 6
(S.I. units)
•For light at 1064 nm this predicts a value of sgg = 1.8·10-65 cm2 •Experimentally Bernard et al.[**] have published sgg < 1.5·10-48 cm2 *Duane et al., Phys Rev. D, vol 57 p. 2443 (1998) **Bernard D. et al., The European Physical Journal D, vol 10, p. 141 (1999) G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
What else? QED •photon splitting? Much smaller than birefringence. •higher order corrections are ~ 1% OTHER •low mass, neutral particle search: axion-like •millicharged particles •hadronic contribution
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Higher order
2 2ù é 2 æ ö æ ö Ae æ a ö 90 ê16 E 263 E 2 LR = ç ÷ ç 2 -B ÷ + ç × B÷ ú m0 è p ø 4 êë 81 è c ø 162 è c ø úû
é 90 a æ 263 16 öù 2 2 ∆ nR = 3Ae ê B = 0.0145´ 3A B ç ÷ú 0 e 0 ë 3 p è 648 81 øû G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Axion-like contribution • One can add extra terms [*] to the E-H effective lagrangian to include contributions from hypothetical neutral light particles interacting weakly with two photons
(
1 Lf = f Eg × Bext M
)
pseudoscalar case
Effects on photon propagation Absorption
Dispersion`
M, Ms are inverse coupling constants
(
1 Ls = s Bg × Bext Ms
)
DICHROISM
BIREFRINGENCE
scalar case G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
[L.Maiani, R. Petronzio, E. Zavattini, Phys. Lett B, Vol. 173, no.3 1986] [E. Massò and R. Toldrà, Phys. Rev. D, Vol. 52, no. 4, 1995]
Propagation of the photon in an external field Dichroism k • Photon splitting • Real particle production
Birefringence n • QED dispersion • Virtual particle production • MCPs • Hadrons
Both effect n and k are defined with sign
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Summing up Experimental study of the quantum vacuum with: • magnetic field perturbation • linearly polarised light beam as a probe • changes in the polarisation state are the expected signals
Ellipticity
Key Ingredients
pL y= Dnsin 2J l
• high magnetic field
superconducting dipole magnet or high field permanent magnet
• long optical path
delay line cavity or very-high Q Fabry-Perot resonator
• ellipsometer with heterodyne detection for best sensitivity
periodic change of field amplitude/direction for signal modulation
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Heterodyne detection I0
polariser
y
analyser
ITr
[
Static detection excluded Itr = I0 s 2 + y 2
]
In the heterodyne detection, using a beat with a calibrated effect, we have • Signal linear in the birefringence • Smaller 1/f noise
I0
polariser
mirror
[
Mod
magnetic field
y(t) at 2wMag
Ellipticity modulator
mirror
analyser
ITr
h(t) at wMod
] [
ITr = I0 s 2 + (y (t) + h(t)) = I0 s 2 + (y(t)2 + h(t) 2 + 2y (t)h( t )) 2
Main frequency components at wMod±2wMag and 2wMod
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
]
• Inserting a quarter wave plate before the modulator allows rotation measurements • Ellipticities and rotation do not mix and are independent • In practice, nearly static rotations/ellipticities s generate a 1/f noise around ωMod.
[
ITr = I0 s 2 + (y (t) + h(t) + b s (t))
[
2
]
]
= I0 s 2 + (h(t) 2 + 2y (t)h(t) + 2b s (t)h(t) + ...) ITR(w) a h2 /2
a hY w wMod - 2WMag w Mod + 2WMag wMod 2w Mod G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
signal
noise
Fabry Perot Ferrara test apparatus – High finesse successful The Fabry-Perot cavity is a resonant optical cavity that increases the effective optical path. It is composed of two mirrors placed at a separation d which is an integer multiple of the light half wavelength. To obtain this condition a laser is phase locked to the cavity using a feedback circuit.
Amplification factor
N=
2F
p
Finesse
F=
pct d
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
PVLAS at Lab. Nazionali Legnaro Focused on a general study of the vacuum in the presence of a magnetic field
Polarizzazione del Vuoto con LASer
Major improvements compared to previous efforts: • Resonant FP cavity (6.4 m) for large amplification factor (> 5 104) • Rotating cryostat allows high modulation frequency (up to 0.4 Hz) • Large magnetic field (magnet tested up to 7 T) • Magnetic system mechanically decoupled from optical system G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
PVLAS at Lab. Nazionali Legnaro
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Present published results - QED n = 3 Ae B02 n1064 < 1.05 10-19 @ 1064 nm n532 < 1.0 10-19 @ 532 nm Ae(LNL) < 6.3 10-21 T-2 Ae(QED) = 1.3 10-24 T-2 sgg < 4.6 10-58 cm2 @ 1064 nm sgg < 2.7 10-56 cm2 @ 532 nm G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Bregant et al, PRD 78, 032006 (2008)
PRESENT published results - ALP
The CAST experiment at CERN has excluded values of M < 1012 GeV Unreachable with present lab techniques G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Some numerical values Main interest is the Euler-Heisenberg birefringence •F = 4·105
•B = 2.5 T ∆n = 2.5·10-23 •L = 2 m
y = 3.7·10-11
If we assume a maximum integration time of 106 s (= 12 days)
Implies a sensitivity of < 3.7·10-8 1/√Hz
e 1 -9 Shot noise limit = = 1·10 for I0 = 100 mW 2I 0 q Hz (I0 = output intensity reaching the analyzer) G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Limitations of the LNL apparatus • Superconducting magnets produce stray field when operated at high fields (saturated iron) • Running time limited due to liquid helium consuption
•Observed correlation between seismic noise and ellipticity noise. The Legnaro apparatus is large and therefore difficult to isolate seismically. • No zero measurement possibile with field turned ON. G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Low finesse – seismic isolation Compact 50 cm long ellipsometer without magnetic field
Flat noise spectrum above ≈ 5 Hz
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
High finesse – seismic isolation
High finesse: F = 414000 Leff = (2F/π)L = 130 km Compact 50 cm long ellipsometer without magnetic field Cavity output power = 25 mW Laser-cavity coupling = 75% Cavity transimission = 25%
Record sensitivity with a cavity Ψ = 3·10-8 1/√Hz Assuming B = 2.3 T: Sensitivity in ∆n = 1.5·10-20 1/√Hz G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Permanent Test Magnets
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Test apparatus in Ferrara
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Ferrara test apparatus - sensitivity No cavity – reached expected noise level with rotating magnets
No electronically induced signals in the readout system G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Ferrara test apparatus - sensitivity With high-finesse cavity > 400000
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Two magnet configuration
In red, magnets at 0 degrees In black, magnets at 90 degrees
With a finesse = 245000 and with the magnets perpendicular to each other we demonstrated a reduction of more than a factor 80 of the Cotton Mouton signal G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Vacuum – perpendicular magnets Finesse ≈ 2·105 (dirty mirrors) Several harmonics at moment under study. Should NOT be there
Second harmonic (red) compared to magnetic probes near two optical enclosures (black – output; blue – input) G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Vacuum – parallel magnets Finesse ≈ 2·105 (dirty mirrors) Several harmonics are again present. Different amplitutdes with respect to the previous configuration. Second harmonic (red) compared to magnetic probes near two optical enclosures (black – output; blue – input). Phase with respect to the probes has changed. G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Vacuum – parallel magnets
• • • •
Integration time = 12400 s Ellipticity = 7·10-9 Clearly systematic Assuming it as limit we obtain
∆n < 4.6·10-20 Ae(exp) < 2.9·10-21 T-2
sgg < 8.9 10-59 cm2 @ 1064 nm
This limit is about a factor 2 better than the published PVLAS value of Ae(LNL) < 6.3·10-21 T-2 G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Present - Future Building final apparatus in clean room in Ferrara. Financed by INFN and MIUR • Magnetic field: 2 x 1 m long magnets with 2.5 T (ordered) • Optical bench with isolation system (installed) • Optical enclosures designed and are in ordering phase • New more powerful laser arrived (2 Watts, 1064 nm) • All optical elements, supports and movements will be non magnetic (ordered) • Getters will be used as vacuum pumps. G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
New granite optical bench Installation in Ferrara clean room
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
New granite optical bench Installation in Ferrara clean room
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Parameter space
G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
Thank you! G. Zavattini, ECT*, Trento, 29 Aug.– 2 Sept. 2011
