Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Effective mass signatures in multiphoton pair production Christian Kohlf¨ urst, Holger Gies , Reinhard Alkofer University of Graz Institute of Physics Non-Perturbative Methods in Quantum Field Theory Balatonf¨ ured , October 8, 2014
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Outline Motivation Theoretical Considerations Model for the Field Numerical Results Concepts Particle Distribution and Spectra Summary & Outlook
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook QED Vacuum Cite: G. Dunne, PIF 2013, July 2013
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook External Field • Strong electric field → charge separation • Particles become measurable
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Dirac Sea Picture • Blue: electron band, Purple: positron band • Measurement: Overcome band gap
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Schwinger Effect • Electron tunneling P ≈ exp ( − π m 2 / eE ) • Relies on field strength E cr = 1 . 3 · 10 18 V / m F. Sauter: Z. Phys. 69(742), 1931 J. S. Schwinger: Phys. Rev. 82(664), 1951
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Photon Absorption � 4 m τ � eE τ • Photon absorption P ≈ 2 m • Relies on photon energy N. Narozhnyi: Sov. J. Nucl. Phys. 11(596), 1970
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Multiphoton Absorption • Absorption of multiple photons C. Kohlfurst et al.: Phys. Rev. Lett. 112(050402), 2014
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Effective Mass • Particle in background field • Apparent mass of a particle in response to a perturbation • Reduction of various interactions into effective mass m ∗ • Treatment of m ∗ as it were a free particle
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Considerations Goal Describe e − and e + in a homogeneous electric field in mean field approximation Requirement • Describe dynamical pair creation • Particle statistics
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Quantum Vlasov Equation Integro-differential equation � t dt ′ W q , t ′ �� q , t ′ �� q , t , t ′ �� � � � � ∂ t F ( q , t ) = W ( q , t ) 1 − F 2 θ cos t Vac (1) W ( q , t ) = eE ( t ) ε ⊥ ( q , t ) ⊥ ( q , t ) = m 2 + q ⊥ 2 , ε 2 , p = q − e A ω 2 ( q , t ) � t ω 2 ( q , t ) = ε 2 q , t , t ′ � q , t ′′ � dt ′′ , ⊥ ( q , t )+( q 3 − eA ( t )) 2 � � θ = t ′ ω • Non-Markovian integral equation, Rapidly oscillating term • Fermions and Pauli statistics S. A. Smolyansky et al. hep-ph/9712377 GSI-97-72, 1997 S. Schmidt et al.: Int.J.Mod.Phys. E7 709-722, 1998
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Differential Equation Auxiliary functions � t dt ′ W q , t ′ �� q , t ′ �� q , t , t ′ �� � � � � G = 1 − F 2 θ (2a) cos t Vac � t dt ′ W q , t ′ �� q , t ′ �� q , t , t ′ �� � � � � H = 1 − F 2 θ (2b) sin t Vac Coupled differential equation ˙ F 0 W 0 F 0 ˙ = − W 0 − 2 ω G + W (3) G ˙ 2 ω 0 0 H 0 H J. C. R. Bloch et al.: Phys. Rev. D 60(116011), 1999
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Pros and Cons of QKT Positive Aspects • Works for arbitrary time-dependent fields • Insight into time evolution of system • Gives particle momentum spectra • Particle density easily calculable Negative Aspects • Works only for spatial homogeneous fields • No magnetic field present • Mean field approximation N.B.: Back-reaction and particle collisions can be included J. C. R. Bloch et al.: Phys. Rev. D 60(116011), 1999
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Outline Motivation Theoretical Considerations Model for the Field Numerical Results Concepts Particle Distribution and Spectra Summary & Outlook
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Characteristic Scales Pair Production • E cr ∼ 10 16 V / cm • τ ∼ 10 − 21 s • I cr ∼ 10 29 W / cm 2 • ω ∼ 1 MeV / c 2 Laser Parameters(Accessible region) • ω γ ∼ 0 . 05 m • E peak ∼ 0 . 001 E cr • τ ∼ 10 − 15 s • ω e ∼ 50 GeV
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Experimental Setup • Two colliding laser fields • Time-dependent electric field in interaction region M. Marklund: Nature Photonics 4, 72-74 2010
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Model for the Field � − t 2 / ( 2 τ 2 ) � • Electric field: E ( t ) = ε E cr exp cos ( ω t ) • Photon energy: ω • Field strength: ε • Pulse duration: τ
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Above Threshold Pair Production • Absorption of photons beyond the “ionization” threshold • Particles produced with non-vanishing momenta • Photon number is intensity dependent ∝ I γ • Likelyhood of creating particles increases with I n P . Agostini et al.: Phys. Rev. Lett. 42(1127-1130), 1979
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Above Threshold Pair Production • Photon absorption beyond the threshold → results in higher net momentum • Two-, three- and higher n -photon absorption processes possible P . Agostini et al.: Phys. Rev. Lett. 42(1127-1130), 1979
Motivation Theoretical Considerations Model for the Field Numerical Results Summary & Outlook Effective Mass • Electric field acts as background field • e − e + interact with background • “Ionization” energy depends on laser field E Kin = n ω − m ∗ � • Effective mass m ∗ = m 1 + ε 2 / ( 2 ω 2 ) � n ω � 2 = m 2 ∗ + q n 2 • AT peak position 2 P . Agostini et al.: Phys. Rev. A 36, 4111, 1987
Recommend
More recommend
