Light by Light Diffraction in Vacuum at PW lasers
Daniele Tommasini
University of Vigo (Spain)
Presentation of ELI-APS to the Spanish Scientific Community
Villamayor, Salamanca, February 14, 2017
Interaction of laser pulses with the Ideal Vacuum:
QED prediction for γ − γ scattering in vacuum
QED cross section for γ − γ scattering in vacuum
Photon-photon coupling
σ γ −γ
10-30
(cm )
2
10-33
10-36
0.1
σ γ −γ ≈ 10 −63 cm 2
1
10
102
103
ℏω / mc 2
at optical wavelengths
[Figure from Tommasini, Novoa, Roso, 2012]
Effective Lagrangian for the e.m. fields for hν me c 2
(Well below the Schwinger limit
and below the Fedotov, Narozhny, Mourou and Korn limit)
being L0 =
0
2
7
L = L0 + ξL L20 + ξT G 2 ,
4
2
E2 − c 2 B , G = 0 c(E · B).
In QED (Euler - Heisemberg):
ξLQED = ξTQED ≡ ξ =
3
8α2 ~3
−30 m
=
6.7
×
10
.
45me4 c 5
J
Contributions of new virtual particles
10
9
spinless bosons
spin 1 bosons
spin 1/2 fermions
PSALP
SALP
8
7
6
ξT ξ
5
4
3
2
1
QED
0
0
1
2
3
4
5
6
7
8
9
10
ξL ξ
[Tommasini, Ferrando, Michinel, Seco, 2009]
[Figure from Tommasini, Novoa, Roso, 2012]
Nonlinear phase shift of crossing laser pulses
[Tommasini, Ferrando, Michinel, Seco, 2008 & 2009.]
Phase shift of a probe pulse B from a counterpropagating pulse A:
∆φL = 4ξL IA kB τA ,
∆φT = 7ξT IA kB τA
(I = ρc, kA = 2π/λA and kB = 2π/λB ).
This also implies birefringence:
∆φb = ∆φT − ∆φL = (7ξT − 4ξL )IA kB τA
Proposal: Light by light diffraction in vacuum
[Tommasini and Michinel, 2010]
Proposal: Light by light diffraction in vacuum
[Tommasini and Michinel, 2010]
Prediction for the number of diffracted photons
For gaussian pulses, and r0 such that PD (r > r0 ) = 100PU (r > r0 )
NDN
8f N EA2 EB w02
=
π~c λB wA4 wB2
e
−
2r02
w2
D
2
−e
− 2R2
w
D
!
(aξ)2L,T ,
aL = 4 and aT = 7
f = efficiency of the detector
EA = PA τA and EB = PB τB the total energies of the pulses
2
2 −1/2
w0 ≡ (2/w
qA + 1/wB )
wD ≡ w0 1 + (2d/kw02 )2
N = number of repetitions.
Angular constraints and optimization
I
I
Minimal set-up (dividing a single laser pulse)
EA = 2E /3, EB = E /3 (BUT at VEGA EA = 30J, EB = 6J)
p
A must not spread during the crossing → wA & cτB λA /π
I
The center of pulse A must remain close to the central part of
beam B during the interaction.
Safe choice: cτB tan(π − θ) = wA /10.
I
The two beams should be separated by a distance larger (6 or
7 times) than the evolving waist: π − θ ' 6λA /πwA , and we
get
wA =
p
60cτB λA /π.
I
Optimal values of wB > wA and R computed numerically
I
If background level can be neglected (see below):
sensitivity ↔ 10 diffracted photons measured
I
Final sensitivity ∝ fP 3 τ /λ3
Predicted optimal sensitivity for a single shot
Facility
VEGA
ELI 2PW
10 PW
P (PW )
1+0.2
2
10
τ (fs)
30
17
30
λ (nm)
800
800
800
ξTlim /ξ
2.3 × 102
2.3 × 102
8.0
ξ lim /ξ PVLAS
1.0 × 10−1
1.0 × 10−1
3.6 × 10−3
I
wA = 12µm, wB = 59µm.
I
We have used f = 0.5 in all the examples;
I
lim ∝ N −1/2
ξL,T
I
At VEGA and ELI 2PW: To reach QED level, need
N ' 5.2 × 104 shots (few hours), if noise is negligible;
N ' 1.6 × 105 shots if noise at the signal level (2 days at
VEGA, few hours at ELI 2PW);
I
r0 = 0.23cm, R = 0.52cm, π − θ = 7.40 , (for d = 10cm).
Discovery potential for single shot
10
4
1 PW
100 PW 10 PW
10
10
3
2
ξT ξ
10
10
1
QED
0
-1
10
-1
10
10
0
10
1
10
2
10
3
10
4
ξL ξ
(Red line: Current limit form PVLAS experiment)
[Figure from Tommasini, Novoa, Roso, 2012]
Background analysis
I
R
Get rid of backscattered photons for a time ∼ 2R/c ∼ 7ns 1m
.
Background analysis
I
Example: Superconducting Single Photon Detectors (SSPD)
can have a time resolution down to the ns scale keeping a
very high efficiency (f ∼ 0.5 in the near IR!);
I
Detector dark count . 10Hz → . 10−7 per shot;
I
Thermal photons hitting the detector . 10−8 per shot;
I
Vacuum requirements to suppress (relativistic) Thomson
scattered photons below QED signal level:
at VEGA: p . 10−14 Pa ∼ 10−16 Torr
(Using [Paredes, Novoa, Tommasini, 2012, 2014] - !!);
For p ∼ 10−13 Pa (current state of the art vacuum)
I
I
I
At VEGA 1PW (similar result for ELI 2PW)
−→ N ∼ 104 , ξTlim /ξ ∼ 3, ξ lim /ξ PVLAS ∼ 10−3
At 10PW
−→ N ∼ 103 , ξTlim /ξ ∼ 0.3, ξ lim /ξ PVLAS ∼ 10−4
Conclusions
I
In a single shot experiment at PW, ∼ 30J laser (e.g. VEGA or
ELI 2PW): room for detecting new physics or improving the
PVLAS limit (> 2 orders of magnitude in σ, an order of
magnitude in the parameters ξL,T );
I
In a day run VEGA or ELI 2PW can detect QED vacuum
polarization if background can be kept small (p . 10−14 Pa);
with state of art XHV (p ∼ 10−13 Pa), we can improve PVLAS
by more than 2 orders of magnitude in the parameters ξL,T ;
I
For (almost) perfectly counterpropagating pulses, the
single-shot experiment could reach QED level;
I
At a ∼ 10PW laser we can detect the QED vacuum
polarization if background can be kept small (p . 10−12 Pa).