e - e + pair production in multiple time scale electric fields - - PowerPoint PPT Presentation

e− - e+ pair production in multiple time scale electric fields

Markus Orthaber

• R. Alkofer, F. Hebenstreit, H. Gies

Institute of Physics - University Graz

March 10, 2010

Motivation QKE Assisted Tunneling Simulations Summary

Schwinger effect

Pair production out of QED vacuum by constant electric field E0. exponentially damped probability (tunnel effect)1 2 W[e+e−] ∝ exp

• −Ecr

E0

• Ecr = 1.3 · 1018 V

m Emax 0.1 · Ecr SOLUTION?

• 1F. Sauter, Z. Phys. 69 (1931)
• 2J. Schwinger, Phys. Rev. 82 (1951)

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Motivation QKE Assisted Tunneling Simulations Summary

1

Motivation

2

QKE

3

Assisted Tunneling

4

Simulations

5

Summary

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Motivation QKE Assisted Tunneling Simulations Summary

What do we learn?

deeper understanding of non-perturbative QED suggest mechanism to verify Schwinger effect experimentally → calculations with time dependent fields: sizeable pair production rate already at 0.4Ecr 3

• 3F. Hebenstreit, Diploma Thesis, University Graz (2008)

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Motivation QKE Assisted Tunneling Simulations Summary

Quantum Kinetic Equation

Boltzmann-like equation for distribution function4 5 6

d dt N(q, t) = S(q, t) + C(q, t) →

d dt N(q, t) = S(q, t) valid for any time dependence of E(t) N contains momentum space distribution information q-space integration gives number of produced pairs W[e+e−] ∝

• N(q, ∞)d3q
• 4Y. Kluger et al., Phys. Rev. D 58 (1998)
• 5S. Schmidt et al., Int. J. Mod. Phys. E7 (1998)
• 6F. Hebenstreit, Diploma Thesis, University Graz (2008)

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Motivation QKE Assisted Tunneling Simulations Summary

Sketch of derivation

L = ¯ Ψ

• i /

D − m

• Ψ − 1

4F µνFµν canonical quantization

classical light field: Aµ = (0, A(t)e3) quantized matter field: Ψ(x, t) = g(q, t)a(q) + g ∗(q, t)b†(−q)

• eiq·x ˜

d3q

equation of motion:

• ∂2

t + ω2(q, t) + ieE(t)

• g(q, t) = 0

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Motivation QKE Assisted Tunneling Simulations Summary

Sketch of derivation

time dependent Bogoliubov transformation a(q) → ˜ a(q, t) b(−q) → ˜ b(−q, t) distribution function: N(q, t) =

• ˜

a†(q, t)˜ a(q, t)

• Particle interpretation ONLY for t → ±∞

source term S =

• ˜

b†(−q, t)˜ a†(q, t)

• Quantum Kinetic equation

˙ N(q, t) = W(q, t) 2 t

−∞

W(q, t′)

• 1 − 2N(q, t′)
• cos
• 2Θ(t, t′)
• dt′

Θ(t, t′) = t

t′ ω(q, τ)dτ 7 / 15 e− - e+ pair production in multiple time scale electric fields

Motivation QKE Assisted Tunneling Simulations Summary

Idea

Combine a strong and slow with a fast and weak laser pulse to get an enhanced pair production rate.7

1 >> ǫ1 >> ǫ2 and ω2 >> ω1 >> 0

→ combination of two scales.

• 7R. Sch¨

utzhold et al., Phys. Rev. Lett. 101 (2008) 8 / 15 e− - e+ pair production in multiple time scale electric fields

Motivation QKE Assisted Tunneling Simulations Summary

Characterization of the system

Essential parameters: ǫ1 ω2 Electric field: E(t) =

ǫEcr cosh2(ωt)

Keldysh parameters: γ1,2 =

ω1,2 mǫ1,2 ,

γ =

ω2 mǫ1

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Motivation QKE Assisted Tunneling Simulations Summary

Keldysh parameter

Determines the adiabaticity of the system. γ =

ω ωT , ωT =

1 τT where τT ... tunnel time

γ << 1....adiabatic (non-perturbative) regime ← Schwinger effect

(enough time to tunnel)

γ >> 1....anti-adiabatic (perturbative) regime ← multiphoton effect

(not enough time to tunnel)

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Motivation QKE Assisted Tunneling Simulations Summary

Simulation setup

Investigate a situation where ǫ2 = 0.1ǫ1 γ1 << 1 γ variable via ω2 Calculate number of produced pairs with q⊥ = 0 to get a qualitative estimate of the multiple time scale effect.

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Motivation QKE Assisted Tunneling Simulations Summary

ǫ1 = 0.09, ǫ2 = 0.009, ω1 ≈ 6 · 1018s−1

5 10 15 20 Γ 1017 1014 1011 108 105 n combined sw9.9 sw9 mp mpsw

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Motivation QKE Assisted Tunneling Simulations Summary

Relative enhancement of produced pairs

1 2 3 4 5 Γ 20 40 60 80 100 ncombnsum Ε10.25 Ε10.15 Ε10.11 Ε10.1 Ε10.09 Ε10.08

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Motivation QKE Assisted Tunneling Simulations Summary

Main Points

Direct verification of Schwinger effect not possible in near future Combine schwinger effect with multi-photon effect → dynamically assisted tunneling Simulations show that pair production is dramatically enhanced

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Motivation QKE Assisted Tunneling Simulations Summary

Outlook

Take whole momentum space into account Simulate several more complicated combined pulses (e. g. high harmonic focusing) Try to find optimal pulse shape (optimization calculation?) Investigate scenarios with an initial particle-density Take also the magnetic field into account

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