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 E 0 . exponentially damped probability (tunnel effect) 1 2 � � − E cr W [ e + e − ] ∝ exp E 0 E cr = 1 . 3 · 10 18 V E max � 0 . 1 · E cr m SOLUTION? 1F. Sauter, Z. Phys. 69 (1931) 2J. Schwinger, Phys. Rev. 82 (1951) e − - e + pair production in multiple time scale electric fields 2 / 15
Motivation QKE Assisted Tunneling Simulations Summary Motivation 1 QKE 2 Assisted Tunneling 3 Simulations 4 Summary 5 e − - e + pair production in multiple time scale electric fields 3 / 15
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 . 4 E cr 3 3F. Hebenstreit, Diploma Thesis , University Graz (2008) e − - e + pair production in multiple time scale electric fields 4 / 15
Motivation QKE Assisted Tunneling Simulations Summary Quantum Kinetic Equation Boltzmann-like equation for distribution function 4 5 6 d d dt N ( q , t ) = S ( q , t ) + C ( q , t ) → 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 , ∞ ) d 3 q 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) e − - e + pair production in multiple time scale electric fields 5 / 15
Motivation QKE Assisted Tunneling Simulations Summary Sketch of derivation Ψ − 1 L = ¯ � � i / D − m 4 F µν F µν Ψ canonical quantization classical light field: A µ = (0 , A ( t ) e 3 ) quantized matter field: e i q · x ˜ g ( q , t ) a ( q ) + g ∗ ( q , t ) b † ( − q ) � � � d 3 q Ψ( x , t ) = equation of motion: ∂ 2 t + ω 2 ( q , t ) + ieE ( t ) � � g ( q , t ) = 0 e − - e + pair production in multiple time scale electric fields 6 / 15
Motivation QKE Assisted Tunneling Simulations Summary Sketch of derivation time dependent Bogoliubov transformation a ( q ) → ˜ a ( q , t ) b ( − q ) → ˜ b ( − q , t ) � a † ( q , t )˜ � distribution function: N ( q , t ) = ˜ a ( q , t ) Particle interpretation ONLY for t → ±∞ source term � � ˜ b † ( − q , t )˜ a † ( q , t ) S = Quantum Kinetic equation � t N ( q , t ) = W ( q , t ) ˙ W ( q , t ′ ) 1 − 2 N ( q , t ′ ) 2Θ( t , t ′ ) dt ′ � � � � cos 2 −∞ � t Θ( t , t ′ ) = t ′ ω ( q , τ ) d τ e − - e + pair production in multiple time scale electric fields 7 / 15
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 >> ǫ 1 >> ǫ 2 and ω 2 >> ω 1 >> 0 → combination of two scales. 7R. Sch¨ utzhold et al., Phys. Rev. Lett. 101 (2008) e − - e + pair production in multiple time scale electric fields 8 / 15
Motivation QKE Assisted Tunneling Simulations Summary Characterization of the system Essential parameters: ǫ 1 ω 2 ǫ E cr Electric field: E ( t ) = cosh 2 ( ω t ) ω 1 , 2 ω 2 Keldysh parameters: γ 1 , 2 = m ǫ 1 , 2 , γ = m ǫ 1 e − - e + pair production in multiple time scale electric fields 9 / 15
Motivation QKE Assisted Tunneling Simulations Summary Keldysh parameter Determines the adiabaticity of the system. γ = ω T , ω 1 ω T = τ T where τ T ... 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) e − - e + pair production in multiple time scale electric fields 10 / 15
Motivation QKE Assisted Tunneling Simulations Summary Simulation setup Investigate a situation where ǫ 2 = 0 . 1 ǫ 1 γ 1 << 1 γ variable via ω 2 Calculate number of produced pairs with q ⊥ = 0 to get a qualitative estimate of the multiple time scale effect. e − - e + pair production in multiple time scale electric fields 11 / 15
Motivation QKE Assisted Tunneling Simulations Summary ǫ 1 = 0 . 09 , ǫ 2 = 0 . 009 , ω 1 ≈ 6 · 10 18 s − 1 n mp � sw 10 � 5 mp 10 � 8 sw9 sw9.9 10 � 11 combined 10 � 14 10 � 17 Γ 0 5 10 15 20 e − - e + pair production in multiple time scale electric fields 12 / 15
Motivation QKE Assisted Tunneling Simulations Summary Relative enhancement of produced pairs n comb � n sum Ε 1 � 0.08 100 Ε 1 � 0.09 Ε 1 � 0.1 80 Ε 1 � 0.11 60 Ε 1 � 0.15 Ε 1 � 0.25 40 20 0 Γ 1 2 3 4 5 e − - e + pair production in multiple time scale electric fields 13 / 15
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 e − - e + pair production in multiple time scale electric fields 14 / 15
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 e − - e + pair production in multiple time scale electric fields 15 / 15
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