OLLIDERS C ASER L PTICAL O RODUCTION BY P ACUUM Vblaschke/talks/dresden_08.pdf · 3 for a periodic...

VACUUM PAIR PRODUCTION BY OPTICAL LASER COLLIDERS

David Blaschke (Univ. Wroclaw & JINR Dubna)

• Introduction: Schwinger Effect

•Kinetic formulation of pair production

•Application to pair production in subcritical laser fields

•Experimental verification of e+e− pair density

•ELI: towards the Schwinger limit and beyond QED

•Role of Decoherence? Observe π± production in its mu± decay pattern !

Collaboration:

Craig Roberts (Argonne National Laboratory, USA)Sebastian Schmidt (Forschungszentrum Julich, Germany)Alexander Prozorkevich, Stanislav Smolyansky (Saratov State University, Russia)

FZ ROSSENDORF, MAY 9, 2008

1

PAIR CREATION IN STRONG ELECTROMAGNETIC FIELDS

•Magnetars: B∼ 1015G =⇒Problem: unclear conditions!

•Ultra-Peripheral Heavy Ion Coll.

b>R +R

Z

Z

1 2

Problem: extremely short ∼ 10−29 s

ARTIST VIEW OF A MAGNETAR (NASA)

•ELI: Optical → X-Ray @ 1 EW:I0 ∼ 1025 W/cm2 → ICHF ∼ 1036 W/cm2

+ Long lifetime:τ ∼ 10−15 . . . 10−18 s � 10−22 s

+ Condition for pair creation:E2 − B2 6= 0, (crossed lasers)


2

SCHWINGER EFFECT: PAIR CREATION IN STRONG FIELDS

Pair creation as barrier penetrationin a strong constant field

εT

2εT

/E2 ε T2

xE

negative levels

positive levelspositive levels

negative levels

Schwinger result (rate for pair production)

dN

d3xdt=

(eE)2

4π3

∞∑

n=1

1

n2exp

(

−nπEcrit

E

)

•To “materialize” a virtual e+e− pair in aconstant electric field E the separation d must besufficiently large

eEd = 2mc2

•Probability for separation d as quantumfluctuation

P ∝ exp

(

− d

λc

)

= exp

(

−2m2c3

e~E

)

= exp

(

−2Ecrit

E

)

•Emission sufficient for observation when E ∼Ecrit

Ecrit ≡m2c3

e~' 1.3 × 1018V/m

•For time-dependent fields: Kinetic Equationapproach from Quantum Field Theory

J. Schwinger: “On Gauge Invariance and Vacuum Polarization”, Phys. Rev. 82 (1951) 664


3

KINETIC FORMULATION OF PAIR PRODUCTION

Kinetic equation for the single particle distribution function f(P , t) =< 0|a†P(t)aP (t)|0 >

−3 −2 −1 0 1 2 3 4 5τ

0

1

2

3

4

5

f −(τ

)/exp

(−π/

E0)

E0 = 0.7E0 = 1.0E0 = 1.5E0 = 3.0

Schmidt, Blaschke, et al: “Non-Markovian effects

in strong-field pair creation”

Phys. Rev. D 59 (1999) 094005

df±(P , t)

dt=

∂f±(P , t)

∂t+ eE(t)

∂f±(P , t)

∂P‖(t)

=1

2W±(t)

∫ t

−∞dt′W±(t′)[1 ± 2f±(P , t′)] cos[x(t′, t)]

Kinematic momentum P = (p1, p2, p3 − eA(t)),

W−(t) =eE(t)ε⊥ω2(t)

,

where ω(t) =√

ε2⊥ + P 2

‖ (t), with ε⊥ =√

m2 + p2⊥

and x(t′, t) = 2[Θ(t) − Θ(t′)].

Θ(t) =

∫ t

−∞dt′ω(t′)

Constant field: Schwinger limit reproduced

f(τ → ∞) = exp(−π

E0

)


4

PAIR PRODUCTION IN SUBCRITICAL FIELDS (I)

Kinetic formulation for E(t) = −A(t) inthe Hamiltonian gauge Aµ = (0, 0, 0, A(t))

df(p, t)

dt=

1

2∆(p, t)

t∫

t0

dt′ ∆(p, t′) [1 − 2f(p, t′)]

× cos

2

t∫

t′

dt1 ε(p, t1)

,

where

∆(p, t) = eE(t)

√

m2 + p2⊥

ε2(p, t),

ε(p, t) =√

m2 + p2⊥ + [p3 − eA(t)]2

The particle number density

n(t) = 2

∫

dp

(2π)3f(p, t)

Number of e+e− pairs in the volume λ3 for aweak field (Jena Ti:AlO3 laser, solid line) andfor near-critical field Em/Ecrit = 0.24, λ = 0.15

nm (X-FEL, dashed line).


5

e+e− PAIR PRODUCTION IN SUBCRITICAL LASER FIELDS (II)

Time dependence of the density n(t) fora monochromatic field

E(t) = Em sin ωt, 0 ≤ t ≤ NT, T =2π

ω

Time dependence of the density n(t) for aGaussian wave packet

E(t) = Eme−(t/τL)2 sin ωt.


6

APPLICATION TO SUBCRITICAL LASER FIELDS

Equilibrium-like momentum distribution atthe time of maximal field amplitude t = T/4. Stratum-like structure of the momentum dis-

tribution at the time of zero field amplitudet = T/2, determining the residual density.


7

APPLICATION TO SUBCRITICAL LASER FIELDS (II)

Number of e+e− pairs in the volume λ3 for aweak field (Jena Ti:AlO3 laser, solid line) andfor near-critical field Em/Ecrit = 0.24, λ = 0.15

nm (X-FEL, dashed line).

xz

Off−axis

mirror

Off−axisparabolic mirrorparabolic

BeamsplitterLaser pulse

Heinzl, et al., Opt. Commun. 267, 318 (2006)


8

APPLICATION TO SUBCRITICAL LASER FIELDS (III)

Wavelength dependence of the mean densityof e+e− pairs (solid line) and their annihila-tion rate (dotted line). E = 3 × 10−5Ecr.

Wavelength dependence of the mean densityof e+e− pairs for different E/Ecr


9

PERSPECTIVES FOR e+e− PAIRS @ OPTICAL LASERS (I)

Observable: photon pair (e+ + e− → 2 γ)

xz

Off−axis

mirror

Off−axisparabolic mirrorparabolic


Gamma

(coincidence)detectors

Project: G. Gregori et al. (2008)at RAL Astra-Gemini Laser

γe+

e−p1

2p

γ

dν

dV dt=

∫

dp1dp2 σ(p1,p2)f(p1, t)f(p2, t)

×√

(v1 − v2)2 − |v1 × v2|2,

cross-section σ of two-photon annihilation

σ(p1,p2) =πe4

2m2τ 2(τ − 1)

[

(τ 2 + τ − 1/2)

× ln

{√τ +

√τ − 1√

τ −√

τ − 1

}

− (τ + 1)√

τ (τ − 1)]

,

t-channel kinematic invariant

τ =(p1 + p2)

2

4m2=

1

4m2[(ε1 + ε2)

2 − (p1 + p2)2].


10

PERSPECTIVES FOR e+e− PAIRS @ OPTICAL LASERS (II)

Off−axisparabolic mirror

xz

Off−axis

mirrorparabolic


Interferencefilter

Probebeam

xz

Off−axis

mirror

Off−axisparabolic mirror

parabolic

BeamsplitterLaser pulse Probe beam

filterInterference

Measurement of refraction index by interference with probe beam.Suggestion by R. Sauerbrey; Blaschke, Prozorkevich, Smolyansky, in preparation


11

HOW TO ’SEE’ e+e− PAIRS @ OPTICAL LASERS (III)

nr

quasiparticle EPP

Measurement of refraction index

Interference condition: D = λp/2

Refraction index:n = 1/

√

1 + η2[(2 + η2)/(1 + η2)]

Langmuir frequency ωL:η = ωL/ωp = 104

√

ρe+e−[cm−3]

Probe frequency: ωp = 10 ω0

Condition fulfilled for:ρe+e− = 1023 cm−3, i.e. I ≈ 1023 W/cm2

Angular dependence testable:number of ’pancakes’ crossed varies with incidenceangle: from 3-4 to 20-30

Suggestion: R. Sauerbrey; Estimate: Blaschke, Prozorkevich, Smolyansky, in prep.


12

π+π− PAIR PRODUCTION IN SUBCRITICAL LASER FIELDS (I)

µ µπ π

←µ∗λ

← ∗λ

∗λ

µ µπ π

λ

Time dependence of the pair density (left) and the number of annihilations (right) in the volumeλ3 for a periodic field (T - period) with Em = 1015 V/cm and λ = 800 nm for the different particlespecies. Laser intensity 3 · 1027 W/cm2.


13

COMPARISON WITH IMAGINARY TIME METHOD

V.S. Popov, Phys. Lett. A 298 (2002) 83

• imaginary time method (time indep.)

• number of pairs only after full period T

• no distribution function

γ � 1, γ = ~ωmc2

Ecr

E

N(λ3T ) ∼(m

ν

)4(

E

Ecr

)5/2

exp

[

−πEcr

E

]

γ � 1

N(λ3T ) ≈ 2π(m

ν

)3/2(

e

4γ

)2m/ν

Very large differences for E � Ecr

Here: Grib, Mamaev, Mostepanenko (1988)

•Bogoliubov transformation (time dep.)

• pair number during field evolution

• distribution function

γ � 1

λ3nr ∼(m

ν

)4(

E

Ecr

)2

exp

[

−1.05πEcr

E

]

γ � 1 (mean)

λ3〈n〉 ∼[

(eEm)

m2

]2 [

mλ

2π

]3

,nr

〈n〉 ∼ω2

m2

γ � 1 (residual)

nr ∼(m

ν

)


14

ACCUMULATION EFFECT IN NEAR-CRITICAL FIELDS

Particle number density n(T ; E0) = a0(E0) sin2(2πT ) + ρ(T, E0)T , T = t/λ

0.1 0.2 0.3 0.4 0.5E0/Ecr

10−18

10−17

10−16

10−15

10−14

10−13

10−12

10−11

10−10

ρ (f

m−3

per

iod

−1)

Accumulation rate ρ(0, E0) (solid),Schwinger rate a = 1, b = 1 (dashed),a = 0.305, b = 1.06 (dot-dashed)

Results are nicely fitted with

ρ(T, E0) = ρ(E0) + ρ′(E0)T .

For E = 0.5 E0, a0 = 1.2 × 10−11 fm−3,ρ = 5.4 × 10−12 fm−3/period, ρ′/ρ = 0.0033/period.

Comparison with Schwinger rate

ρ = am4λ

4π3

[

E0

Ecr

]2

e−bπEcr/E0

Attention:E0 ∼ 0.35 Ecr backreactions become important!

Roberts, Schmidt, Vinnik: “Quantum effects with an X-Ray Free-Electron Laser”, Phys. Rev. Lett (2002) 153901


15

CHALLENGES OF ELI FOR THE SCHWINGER EFFECT

•First experimental tests to theories of pair production, e.g. kinetic approach

•Simplest laser field model predicts production of dense electron-positron plasmain the focus of counter-propagating laser fields

•Observable manifestations testable, e.g., at ELI:

– several gamma-pairs per laser pulse

– refraction index measurable by intereference with test beam

– higher harmonics generation, in particular 3rd

•Towards/Beyond Schwinger limit:

– Quantum statistics: Pauli-Blocking/ Bose Condensation; Backreactions

– Pion production limit: signalled by muons

– Pion condensation (?) and quark-gluon-plasma formation

• Laser acceleration of ion beams (see http://eli.jinr.ru)

Thanks to:

D. Habs (Munich), G. Mourou (Paris), R. Sauerbrey (Rossendorf)


16

MORE BRAINSTORMING ELI WORKSHOPS NEEDED ...


17

APPLICATION TO SUPERCRITICAL FIELD STRENGTH

–40–20

020

40p3/m

0

1

2

3

4

pT/m

0.2

0.4

0.6

0.8

f(p3,pT)

Distribution function at t = T/2 (maximal field).

At overcritical field strength:

E = 10 Ec

Pauli blocking in the source term !

’Fermi-momentum’:

p‖ ∼ 40 me ∼ 20 MeV !


18


Extrapolation for CHF focusing

1019

1020

1021

1022

1023

1024

1025

1026

1027

I0 [W/cm

2]

1022

1024

1026

1028

1030

1032

1034

1036

1038

1040

I CH

F [W

/cm

2 ]

1 PW 1 EW

Ie+e-

Iπ+π−Iπo

Numerical scaling of the CHF focal intensityICHF vs. incident laser intensity I0

S. Gordienko et al., PRL 94 (2005) 103903

Critical intensity for π± pair production

Iπ+π− = (mπ±/me)4 IQED

∼ 2.5 1039W/cm2

π0 production, D. Habs, private comm.Iπ0 ∼ 1/4 Iπ+π−

•Bose enhancementin the source term !

•Condensation of pions at zeromomentum

•Overlap of pion wave functionswhen ∼ 1 fm−3

•Quark delocalization:Mott-Anderson transition!

•Color (super) conductivity


19


Condensation effect for Bosons!

m = me (’light’ boson)λ = 0.01 nm

Supercritical field strengths

E = 10 Ec (upper graph)E = 15 Ec (lower graph)

Backreactions already crucial !

Very preliminary !Exploratory calculation


20

A SNAPSHOP OF THE SQGP - ’PERFECT LIQUID’

The Picture: String-flip (Rearrangement) π gas ⇐⇒ Pair correlation

1 2

C. Horowitz et al. PRD (1985), D. B. et al. PLB (1985),G. Ropke et al. PRD (1986)

NNr r

g(r)

1

M. Thoma, Quark Matter ’05;[hep-ph/0509154]

•Strong correlations present: hadronic spectral functions above Tc (lattice QCD)

•Finite width due to rearrangement collisions: liquid-like pair correlation function

http://www.bnl.gov/RHIC/


21

LASER PARAMETERS AND DERIVED QUANTITIES

Laser ParametersOptical X-ray FELFocus: Design Focus: Focus:

Diffraction limit DESY Available GoalWavelength λ 1 µm 0.4 nm 0.4 nm 0.15 nmPhoton energy ~ ω = hc

λ1.2 eV 3.1 keV 3.1 keV 8.3 keV

Peak power P 1 PW 110 GW 1.1 GW 5 TWSpot radius (rms) σ 1 µm 26 µm 21 nm 0.15 nmCoherent spike length (rms) 4t 500 fs ÷ 20 ps 0.04 fs 0.04 fs 0.08 ps

Derived Quantities

Peak power density S = Pπσ2 3 × 1026 W

m2 5 × 1019 Wm2 8 × 1023 W

m2 7 × 1031 Wm2

Peak electric field E =√

µ0 c S 4 × 1014 Vm

1 × 1011 Vm

2 × 1013 Vm

2 × 1017 Vm

Peak electric field/critical field E/Ec 3 × 10−4 1 × 10−7 1 × 10−5 0.1Photon energy/e rest energy ~ω

mec22 × 10−6 0.006 0.006 0.02

Adiabaticity parameter γ = ~ωe Eλ− 9 × 10−3 6 × 104 5 × 102 0.1

A. Ringwald, Phys. Lett. B 510 (2001) 107; hep-ph/0112254


22

OLLIDERS C ASER L PTICAL O RODUCTION BY P ACUUM Vblaschke/talks/dresden_08.pdf · 3 for a periodic...

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