Frontiers in Intense Laser Physics KITP Santa Barbara

“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

Acknowledgement: Illinois State University Prof. Grobe Gospodarczyk Vikartofsky Dr. Wagner Alexander Graybeal Dr. Cheng Rogers Dr. Krekora Ware Shields Lamb

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

ultra-intense laser development Vacuum physics Vacuum breakdown e+ E = mc 2 e– E Pair creation Extreme Light Infrastructure I ～ 1025 W/cm 2 Int. Zetta-Exawatt Sci. & Tech. I > 1027 W/cm 2 “Zeptotechnology is just around the corner” The Economist, page 77 Feb 28 2004 Schwinger limit IZEST ELI CUOS

Relevant experiments heavy ion 1980 s，Argonne, GSI pairs observed nuclear triggered laser-electron 1997， Stanford, SLAC electron-laser collision indirect pure laser ELI，IZEST, … pure light —> matter

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

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

Processes leading to pair creation connection with ionization? mc 2 –mc 2 pair creation = Schwinger tunneling or photon resonance dived or or transition enhancement bound state

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

QM Dirac equation mc 2 when A=V=0 E=± 0 –mc 2 but < (t)| (t)>=1 How to describe creation ?

Quantum field description QM state QF operator †

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

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

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

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

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

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

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

Wave packet evolution under single particle Dirac equation V > 2 mc 2 Ekin < V Interpretation of mysterious transmitted portion unclear Braun, Su and Grobe, PRA 59, 604 (1999)

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

2004: Resolution of the Klein-paradox Ekin < V V > 2 mc 2 • 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).

ways to create pairs super-critical, large force N er g in w h c S under-critical, time dependent force Euro. Phys. Lett. 86, 13001 (2009) multi-field combination

Lowering the field threshold with 2 subcritical constant fields ? 2 subcritical fields displaced by space D M. Jiang, et al, V 1 =V 2=1. 5 c 2, dash is for V=2. 5 c 2 Phys. Rev. A 83, 053402 (2011)

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 > 2 c 2 2. Schwinger tunneling for a constant field Key parameter: field strength Threshold: Vcr > 2 c 2 [with W ~1/c while E 0 =V 0/(2 W )] M. Jiang, et al, Phys. Rev. A 85, 033408 (2012)

Pair creation enhancement due to combined external fields Motivation: Only alternating field: · suppression due to Pauli blocking Possible solution: · pull out the created pairs Model: F 1= V 1 S(z) sin(ωt) F 2= V 2 S(z) with V 1=1. 5 c 2 and with V 2=2. 5 c 2. PRA 85, 033408 (2012)

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

Time evolution of the spatial probability F 1: creates particles F 2: drags the created particles out. For k>0: accelerated (green balls) For k<0: decelerated then accelerated (red balls)

Multiphoton or Schwinger tunneling ? ? Perturbation theory Two-level model N(t) for F 1 only and F 1+F 2 [W = 5/c ] Ø For F 1 only (black line), sudden rise at ω = 2 c 2, suggests the start of single photon transition Ø By adding F 2 (red line), the region ω < 2 c 2 is no longer forbidden, due to single photon transition and Schwinger tunneling

Above Threshold Pair-creation M. Jiang, et al, Phys. Rev. A 85, 033408 (2012) (A) (B) (C) Pair production vs energy, for F 1 only and with six field strengths. [W = 3/c, ω = 2. 5 c 2, T = 0. 002] > location of the peaks: independent of V 1. Øpeak (A): one-photon transition Einitial(EA) + ω = Efinal(EA); Øpeak (B) and (C): two and three-photo transitions.

Field-induced bound states enhance pair creation ? Model: a time dependent potential well V (z, t ) = V 0 [ S(z–D/2)–S(z+D/2) ] sin(ωt ) Quantum coherent effect Transition from the bound states W V 0 ω D Key parameters: V 0 -depth D-width W-field width ω-frequency PRA 87, 042503 (2013)

Pair creation non-monotonic with D D = 2/c, 4/c, 6/c, 8/c and ∞ (red dashed line). [V 0 = 1. 5 c 2, W = 0. 5/c and ω = 2. 5 c 2] > Supercritical frequency, particles are produced continuously > The slope varies with the well width D, and has an oscillatory behavior

Perturbation theory works The coherent term The N-D plot, at time t=0. 004. [V 0=1. 5 c 2, ω=3 c 2]. The inset [V 0=0. 1 c 2, W=0. 5/c, ω=2. 5 c 2, t=0. 002] Momentum distribution at t=0. 002 [ V 0=1. 5 c 2, W=1/c, ω=4 c 2, and for D=5/c, D=10/c, and D=82. 2/c (∞) ]

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=c 2, V 0=1. 5 c 2, W=0. 5/c] E 2 a~1. 2 c 2, E 2 b~1. 8 c 2, E 2 c=E 2 a+ω and E 2 d=E 2 b+ω

New pathways due to field induced bound states 2 b 2 a Instantaneous eigenvalues of the potential well in one temporal period [D=3/c, V 0=1. 5 c 2, W=0. 5/c] The excitations of the three electron (positron) bound states 14 14. 50 15 E+ 2ω =-0. 8 c 2+2 c 2=1. 2 c 2 E+ ω = 0. 8 c 2+c 2=1. 8 c 2

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

Suppression of pair creation due to a steady magnetic field Model: Yellow line: V 0=2. 5 c 2, M 0=0 Black solid line: V 1=2. 5 c 2, M 1=0. 6 c 2 [WE=WB=0. 1/c] Black dashed line: V 2=√(V 12 -M 12), M 2=0 PRA 86, 013422 (2012)

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

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

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

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

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

Exponential creation confirmed WB WB = 1. 10 1. 15 1. 25 1. 30 • Four different widths WB of the magnetic field • Inset: log scale shows exponential growth for WB=1. 25 V 0=2. 5 c 2, WE=0. 3=0. 0022 a. u. , B=0. 6 c 3 and WB=1. 25=0. 0091 a. u.

suppression for very large widths V 0=2. 5 c 2, WE=0. 3, B=0. 6 c 3

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

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

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

Topics and goals ion t a c i f i d o yield m fermion matter correction energy conserv atio n light field correction boson Maxwell-Dirac field model vacuum correction polarized charge dynamics ？ static new algorithm 2 D/3 D（supercomputer）

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

Thank you for your attention! Thank you to the organizers!