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“ Frontiers in Intense Laser Physics ” , KITP , Santa Barbara, CA, Aug 4, 2014

“ Frontiers in Intense Laser Physics ” , KITP , Santa Barbara, CA, Aug 4, 2014. Pair creation in external electric and magnetic fields Q. Charles Su Intense Laser Physics Theory Unit Department of Physics, Illinois State University. Support: National Science Foundation, NSFC.

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“ Frontiers in Intense Laser Physics ” , KITP , Santa Barbara, CA, Aug 4, 2014

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  1. “Frontiers in Intense Laser Physics”, KITP, Santa Barbara, CA, Aug 4, 2014 Pair creation in external electric and magnetic fieldsQ. Charles Su Intense Laser Physics Theory UnitDepartment of Physics, Illinois State University Support: National Science Foundation, NSFC www.phy.ilstu.edu/ILP

  2. Acknowledgement: Illinois State University www.phy.ilstu.edu/ILP Dr. Wagner Dr. Cheng Dr. Krekora Prof. Grobe Gospodarczyk Lamb Vikartofsky Alexander Graybeal Rogers Ware Shields

  3. Acknowledgement: China Beijing Dr. Y.T. Li Dr. X. Lu Dr. Y.J. Li Dr. M. Jiang W. Su Q.Z. Lv Y. Liu Shanghai W.Y. Wu Dr. F. He Dr. Z.M. Sheng Dr. J. Zhang

  4. e– E e+ Vacuum physics ultra-intense laser development Vacuum breakdown E = mc2 Schwinger limit IZEST Pair creation ELI • Extreme Light Infrastructure • I ～ 1025 W/cm2 • Int. Zetta-Exawatt Sci. & Tech. • I > 1027 W/cm2 CUOS “Zeptotechnology is just around the corner” The Economist, page 77 Feb 28 2004

  5. Relevant experiments heavy ion 1980s，Argonne, GSI pairs observed nuclear triggered laser-electron1997， Stanford, SLAC electron-laser collision indirect pure laser ELI，IZEST, … pure light —> matter

  6. Theoretical exploration goals new concepts threshold estimation possible experiments ? theory Europe (Sweden, ELI, …) US (CA, CT, …) simulation US (ILP) Europe (Heidelberg) Asia (CAS)

  7. Progress obtained with related numerical models Relativistic quantum mechanics (1996–2003) numerical solution to Dirac equation motion in electric and magnetic fields superluminal in barrier tunneling harmonic generation retardation effect resonances in cycloatoms Computational quantum field theory (2003–) resolution of Klein paradox electron-electron correlation transition to negative Dirac sea Zitterbewegung entanglement supercritical bound states interference in charge density pair creation in varying forces Quantum fermion-boson interaction (2008–) numerical solution to Yukawa model virtual boson formation transfer of fermion source correlation to bosons pair creation with Klein-Gordon field

  8. Processes leading to pair creationconnection with ionization? mc2 –mc2 Schwinger tunneling photon transition resonance enhancement dived bound state pair creation = or or or

  9. Outline of my talk  Introduction to the subject ✔  Introduction to numerical approach  Application to the Klein paradox  Time dependent field  Field-induced bound states  Magnetic field influence  Boson versus fermion  Dived bound states  Outlook

  10. QM Dirac equation mc2 0 E=± when A=V=0 –mc2 but <(t)|(t)>=1 How to describe creation ?

  11. QF operator QM state † Quantum field description

  12. Now we know the electron’s quantum field From wave functions to operator solutions time involution of |a> operator J. Braun, Q. Su, R. Grobe, PRA 59, 604 (1999)

  13. † Apply to pair creation Number of created pairs |p> N(t) = <<vac|| (t) (t) ||vac>> |n>

  14. step1: WF start with: |n> the Dirac Sea picture step2: solve to get |n(t)> step3: project |n(t)> on |p>, call it <p|n(t)> How to get pairs step4: repeat steps 1 to 3, … Number of the created pairs step5: add up results N(t) = |p> |p> |p> |p> + + + …… = |n> |n> |n> |n>

  15. The space-time resolved pair creation Phys. Rev. Lett. 92, 040406 (2004) energy e– e+

  16. Klein paradox Oskar Klein (1894-1977) Z Physik 53, 157 (1929)

  17. potential height V “Normal” potential height (V << 2mc2 ) Ekin Classical mechanics predicts: if Ekin< V  ball cannot roll up

  18. Traditional quantum mechanics if Ekin< V  bounces back Movie: Courtesy of Bernd Thaller http://www.kfunigraz.ac.at/imawww/thaller/

  19. height V “Abnormal” potential height (V > 2mc2 ) ? Single-particle quantum mechanics predicts: even if Ekin< V some of the “particle” rolls up ? ?

  20. Wave packet evolution undersingle particleDirac equation V > 2 mc2 Ekin < V Interpretation of mysterious transmitted portion unclear Braun, Su and Grobe, PRA 59, 604 (1999)

  21. The Klein paradox e– e– e+ e– e– e+ electron affects pair-creation ???? before 2004: simplification: approach: Quantum mechanics no e–- e+ ? ? Quantum field theory no e– ?

  22. 2004: Resolution of the Klein-paradox V > 2 mc2 Ekin < V • Electron cannot move into the barrier • Klein’s state is the amount of suppressed positrons P. Krekora, Q. Su and R. Grobe, Phys. Rev. Lett. 92, 040406 (2004).

  23. ways to create pairs super-critical, large force N Schwinger under-critical, time dependent force multi-field combination EuroPhys. Lett. 86, 13001 (2009)

  24. Lowering the field threshold with 2 subcritical constant fields ? 2 subcritical fields displaced by space D V1 =V2=1.5c2, dash is for V=2.5c2 M. Jiang, et al, Phys. Rev. A 83, 053402 (2011)

  25. Lowering the field threshold with alternating field + constant field ? Different mechanisms for pair creation: 1. Multi-photon transition for an alternating field Key parameter: field frequency Threshold: ωcr> 2c 2 2. Schwinger tunneling for a constant field Key parameter: field strength Threshold: Vcr > 2c 2 [with W ~1/c while E0=V0/(2W )] M. Jiang, et al, Phys. Rev. A 85, 033408 (2012)

  26. Pair creation enhancement due to combined external fields Motivation: Possible solution: · pull out the created pairs Only alternating field: · suppression due to Pauli blocking Model: F1= V1S(z) sin(ωt) with V1=1.5c2and F2= V2S(z) with V2=2.5c2. PRA 85, 033408 (2012)

  27. Pair creation enhanced in combined fields ! Blue lines: both added Red lines: only alternating Black line: only static

  28. Time evolution of the spatial probability F1: creates particles F2: drags the created particles out. For k>0: accelerated (green balls) For k<0: decelerated then accelerated (red balls)

  29. Multiphoton or Schwinger tunneling ?? Perturbation theory Two-level model N(t) for F1 only and F1+F2[W = 5/c ] • For F1only (black line), sudden rise at ω = 2c2, • suggests the start of single photon transition • By addingF2(red line), the region ω < 2c 2 is no longer forbidden, • due to single photon transition and • Schwinger tunneling

  30. Above Threshold Pair-creation M. Jiang, et al, Phys. Rev. A 85, 033408 (2012) (A) (B) (C) Pair production vs energy, for F1 only and with six field strengths. [W = 3/c, ω = 2.5c2, T = 0.002] • > location of the peaks:independent of V1. • peak (A):one-photon transition Einitial(EA) + ω = Efinal(EA); • peak (B) and (C):two and three-photo transitions.

  31. Field-induced bound states enhance pair creation ? Model: a time dependent potential well V (z,t ) = V0 [ S(z–D/2)–S(z+D/2) ] sin(ωt ) Quantum coherent effect Transition from the bound states W ω V0 D Key parameters: V0-depth D-width W-field width ω-frequency PRA 87, 042503 (2013)

  32. Pair creation non-monotonic with D D = 2/c, 4/c, 6/c, 8/c and ∞ (red dashed line). [V0 = 1.5c2, W = 0.5/c and ω=2.5c2] > Supercritical frequency, particles are produced continuously > The slope varies with the well width D, and has an oscillatory behavior

  33. Perturbation theory works The coherent term Momentum distribution at t=0.002 [ V0=1.5c2, W=1/c, ω=4c2, and for D=5/c, D=10/c, and D=82.2/c (∞) ] The N-D plot, at time t=0.004. [V0=1.5c2, ω=3c2]. The inset [V0=0.1c2, W=0.5/c, ω=2.5c2, t=0.002]

  34. New peaks in the electron energy spectrum (D/c ~ 2π/ω) D →∞ D=3/c The time evolution of the energy distribution from t=0 to 0.005 (a) D →∞, and (b) D=3/c. [ω=c2, V0=1.5c2, W=0.5/c] E2a~1.2c2, E2b~1.8c2, E2c=E2a+ω and E2d=E2b+ω

  35. New pathways due tofield induced bound states 2b Instantaneous eigenvalues of the potential well in one temporal period [D=3/c, V0=1.5c2, W=0.5/c] 2a The excitations of the three electron (positron) bound states E+2ω=-0.8c2+2c2=1.2c2 E+ ω = 0.8c2+c2=1.8c2 14 14.50 15

  36. Magnetic field influence • J. Schwinger (1951） • considered pure E-field • creation threshold: Bz(x) Ex(x) • magnetic field can not be neglected • model from laser plasma physics • static fields, both change along x • uniform along y, py conserved

  37. Suppression of pair creation due to a steady magnetic field Model: Yellow line: V0=2.5c2, M0=0 Black solid line: V1=2.5c2, M1=0.6c2 Black dashed line: V2=√(V12-M12), M2=0 [WE=WB=0.1/c] PRA 86, 013422 (2012)

  38. Pair creation in unequal width, while WB>WE Time evolution of N for different WB Phys. Rev. Lett. 109, 253202 (2012)

  39. Energy spectrum of the total h vs magnetic field width WB When WB > 1.25/c, continua begin to separate, the system become subcritical. In the gap area new discrete energy levels emerge. Oscillations in N(t): transition between field dressed Landau levels

  40. Why might boson creation work better ? e- e+ • Traditional: • New idea: force p–, p+to return to creation zone B Field B Field p- p+ Dream: stimulated emission amplifies p–, p+creation

  41. #fermions(time) #bosons(time) N(t) ~ a t WWWW Stimulated emission Pair production increases Pauli exclusion principle Pair production stops P. Krekora, K. Cooley, Q. Su and R. Grobe, Phys. Rev. Lett. 95, 070403 (2005) R.E. Wagner, M.R. Ware, Q. Suand R. Grobe, Phys. Rev. A 81, 052104 (2010)

  42. Speculation Number of pairs in a magnetic field e–, e+ attenuation ? p–, p+amplification

  43. Exponential creation confirmed • Four different widths WBof the magnetic field • Inset: log scale shows exponential growth for WB=1.25 V0=2.5c2, WE=0.3=0.0022 a.u., B=0.6c3 and WB=1.25=0.0091 a.u. WB WB = 1.10 1.15 1.25 1.30

  44. suppression for very large widths V0=2.5c2, WE=0.3, B=0.6c3

  45. Multi-channel non-competing mechanism • ways lead to pair creation: • Dirac +/– Sea overlap • bound states dive in the • Dirac Sea • general belief： • when multiple states dive in, • dominant channel matters strength of interaction

  46. 2 states dive in 1 state dive in E = Er – i Ei N(t) = N [ 1 – exp(–Gt) ] G = Ei1 + Ei2 + … PRL, 111, 183204 (2013) PRA 90, 013405 (2014)

  47. Next step: extend our model Dirac field model anti- particle external field particle neglected：（1）inter-particle “forces” （2）particle reaction on external field Maxwell-Dirac field model anti- particle particle Maxwell field

  48. Topics and goals boson yield modification fermion matter correction light field correction Maxwell-Dirac field model energy conservation vacuum correction polarized charge new algorithm 2D/3D（supercomputer） ？ dynamics static

  49. Initial attempts correction on pairs before (no force): external field ＝》 Dirac field now (yes force): Maxwell field 《＝》 Dirac field new formulas： Maxwell field ＝》Dirac field i ∂y(r,t)/∂t=h(V,A)y(r,t) Dirac field ＝》 Maxwell field (c–2∂2/∂t2 –∇2)V(r,t)=4πρ(y) (c–2∂2/∂t2 –∇2)A(r,t)= (4π/c) j(y) correction on width

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