Strong-Field QED and High-Power Lasers

Transcription

1 LC with: O. Schröder (UoP science + computing, Tübingen) B. Liesfeld, K.-U. Amthor, H. Schwörer and A. Wipf (FSU Jena) R. Sauerbrey, FZ Rossendorf

2 Outline Introduction

3 1. Introduction QED basic vertex (interaction): e e γ e + direct on-shell pair production (PP), γ e + e, forbidden by energy-momentum conservation hence, add external e.m. (photon) field: e.g. laser

4 effective/dressed electron lines ( propagators ) absorption/emission of n laser photons γ L (- - -) PP via multi-photon Breit Wheeler: γ + n γ L e + e

5 multi-photon Breit-Wheeler PP: n γ L γ. e e + observed by SLAC E-144 (1997) NL Compton: e + nγ L e + γ multi-photon Breit-Wheeler: γ + nγ L e + e nγ L from Terawatt laser γ = probe photon (29 GeV)

6 important scale: critical electric field E c energy gain of electron traversing distance of one Compton wave length λ e : ee c λ e = m e c 2 E c = m2 e e V/m field required for substantial amount of PP NB: critical intensity I c W/cm 2

7 Keldysh parameter characterises laser background (BG) with 4-momentum (Ω, K): η E/E c Ω/m e = 2E/E c K /m e laser facilities (overview) XFEL XFEL ( goal ) VULCAN POLARIS ELI η

8 Two regimes: η 1 low intensity high BG frequency Ω low-order perturbation theory standard QED regime η 1 high intensity low BG frequency Ω multi-photon (high-order) processes important new QED regime realised by high-power optical lasers!

9 2. Optical Theorem l.h.s.: total PP probability r.h.s.: (Im of) vacuum polarisation modified by laser field

10 central object: (vacuum) polarisation tensor describes both modified light propagation and PP (via Im) low-energy limit (ω, Ω 0) = Heisenberg-Euler for special BGs exact one-loop results available

11 simplest case: crossed fields (CF) (Narozhniy 1969, Ritus 1972) E = B, E B ( frozen plane wave) BG Lorentz invariants vanish: S 1 2 (E 2 B 2 ) = 0, P E B = 0 hence: no PP in single plane wave only two remaining invariants formed form BG fields and probe 4-momentum k = ω(1, n) where n = index of refraction namely...

12 Two kinematic invariants: K Ω (BG) B θ k ω (probe) z LC momenta: k ± = ω(1 ± n) K ± = Ω(1 1) E henceforth: head-on, i.e. θ = π k 2 = k + k = ω 2 (1 n) 2 b 2 = (k + ) 2 I = ω 2 (1 n cos θ) 2 I,

13 3. (hep-ph/ ) Two small parameters: dimensionless probe frequency: dimensionless field: ν ω/m e ɛ E/E c X-ray probe (ω 15 kev) and high-power laser (I = W/cm 2 ): ν 0.03, ɛ 0.01.

14 Parameter Range (schematic): ν standard QED ( ε = 0) 1 strong-field QED Heisenberg-Euler regime 1 ε presently attainable NB: Π µν for CF known in whole range (integral rep.)

15 Theory (CF): Determine eigenvalues Π 0, Π ± of Π µν as functions of invariants k 2, b 2 (Narozhniy 1969, Ritus 1972) Π 0 : trivial dispersion (modifies e.g. Coulomb pot.) Π ± : two nontrivial dispersion relations: birefringence! k 2 Π ± (k 2, b 2 ) = 0 solution: two indices of refraction (Toll 1952) n ± 1 + ± (ɛ, ν) = 1 + α 45π (11 ± 3)ɛ2 + O(ɛ 4 ν 2 )

16 Experiment observable: ellipticity squared δ 2 ( n) 2 (αdɛ 2 /λ) 2 B e linear pol. elliptical pol. λ 45 d z E small λ high I POLARIS: δ ELI: δ experimental challenge! in static B-field non-qed signal recently observed (PVLAS 05)

17 4. (hep-th/ ) small ɛ and ν expansions of ± both asymptotic (ɛ, ν) = k c 2k (ɛ) (ɛν) 2k, r 2k c 2k+2 /c 2k ν r 2k _ ε 2 = 0.1 ε 2 = 1 ε 2 = 100 ε 2 = k asymptotic expansion factorial growth c 2k Γ(2k)

18 Nonperturbative analysis fit large-order factorial growth numerically determine nonperturbative imaginary part of by resummation and dispersion relation define nonperturbative real part of by inverse dispersion relation check analytically by evaluating integral representation derived from Ritus (1972) Im(n) 1 0 dx e a/x x (x x) b speculation: LC wave functions?

19 Results: small-ɛν expansion: normal dispersion large orders: Im(n ± ) exp( 4/3ɛν) ɛν absorption PP Kramers-Kronig: Re(n ± ) shows anomalous dispersion for large ɛν (ε, 0) n current exp. Re (n) _ derivative expansion Re(n) _ Kramers-Kronig Im(n) _ large-o/analytic ν ε = 1

20 theory to-do list cope with advances in laser technology: Π µν for arbitrary BG, in particular Gaussian beams world-line MC (Langfeld, Gies et al. 2001, 2005) QFT with non-standard asymptotic states? LC treatment? (Tajima, Mourou 2002)