International Momiji School for Young Scientists "High Field Science - Kyoto 2012" Nikolay B. Narozhny National Research Nuclear University MEPHI, Russia What is vacuum? In QFT the vacuum is the state with the lowest possible energy (ground state) 1. QED vacuum : No particles ( 2. QCD vacuum : ) An example of a non-perturbative vacuum state Multiple vacuum states can coexist vacuum emptiness QED vacuum Vacuum is “a boiling quantum liquid”! (I.Ya. Pomeranchuk) The size of the loop - Compton length - Compton time An external electromagnetic field polarizes vacuum! Vacuum in the presence of an external e-m field is a non-linear optical medium Experimentally verified effects of vacuum polarization: Spontaneous emission, Casimir effect, Lamb shift The start of “Nonlinear Optics in Vacuum” W. Heisenberg and H. Euler, Zeitschr. Phys. 98, 714 (1936) Hans Heinrich Euler (1909–1941) Werner Karl Heisenberg (1901-1976) F. Sauter, ZS. f. Phys. 69, 742, 1931 “This polarization of the vacuum to be studied below will give rise to a distinction between the vectors on the other” on the one hand and permittivity of vacuum permeability of vacuum Plane wave field ( The result is valid for a weakly variable field ) does not polarize vacuum! Particles also polarize vacuum! no e-m field Real photon does not polarize vacuum in the absence of e-m field e-m field Real photon does polarize vacuum in the presence of e-m field! Vacuum birefringence Crossed field: N.B. Narozhnyi, Zh. Eksp. Teor. Fiz. 55, 714 (1968) [Sov. Phys. JETP 28, 371, 1969] Vacuum is a dispersive, absorptive and dichroic medium at R. Baier, P. Breitenlohner, Acta Phys. Austr. 25, 212, 1967 Constant magnetic field: S.L. Adler, Ann. Phys. (NY) 67 212, 599 (1971) I.A. Batalin, A.E. Shabad, Zh. Eksp. Teor. Fiz. 60, 894 (1971) Constant e-m field of general configuration: [Sov. Phys. JETP 33, 483, 1971] The PVLAS experiment to measure the effect of vacuum birefringence is under way (Ferrara University, Italy) Cherenkov radiation T. Erber, Rev. Mod. Phys. 38, 626, 1966 V.I. Ritus, Zh. Eksp. Teor. Fiz. 57, 2176 (1969) [Sov. Phys. JETP 30, 1181, (1970)] I.M. Dremin, Pis’ma Zh. Eksp. Teor. Fiz. 76, 185 (2002) [JETP Lett. 76, 151, (2002)] The emission angle: The condition for ChR: At: at For and focused to the diffraction limit in the presence of the background due to Compton scattering Harmonics generation 1. A.E. Kaplan and Y.J. Ding, Phys. Rev. A 62, 043805 (2000) Harmonics generation by a laser beam propagating in an external magnetic field 2. A. Di Piazza, K.Z. Hatsagortsyan, C.H. Keitel, Phys. Rev. D 72, 085005 (2005) Harmonics generation by two colliding laser beams in vacuum 3. A.M.Fedotov, N.B. Narozhny, Phys. Lett. A 362, 1 (2007) Harmonics generation by a focused laser beam in vacuum The effect is detectable at ! the effect of stimulated emission of a photon Self-focusing 1. M. Soljacˇic´ and M. Segev, Phys. Rev A, 62, 043817 (2000) A superposition of two plane waves, modified by a slowly varying envelope is considered. It is shown that modified Maxwell equations in vacuum give rise to spatial solitons. The solitons exist because the diffraction, which tends to expand the pulse, is exactly balanced by the nonlinear effect of self-focusing that is trying to shrink the pulse. The peak intensity needed to support the soliton is about ! 2. D. Kharzeev and K. Tuchin, Phys. Rev A, 75, 043807 (2007) Attractive two-photon exchange Since the transverse size of a laser beam is the self-focusing effect must exist! The focusing angle For a laser with (though the estimates of : does not look very reliable!) This diagram dominates at distances t Vacuum is unstable in the presence of very strong electromagnetic field! x x F. Sauter, 1931 W. Heisenberg, H. Euler, 1936 J. Schwinger, 1951 QED scale: length - Compton length energy field laser intensity Existing laser facilities: Question: Is it possible to observe vacuum polarization effects? Most powerful facilities under construction or planning LMJ (France) 240 beams, 2MJ NIF (LLNL, US) UFL-2M (VNIIEF, RF) 192 beams, 1.8MJ 192 beams, 2.8MJ HiPER (GB) Laser Fusion High Field Sciense ELI XCELS (RF) pair creation by a laser field in vacuum becomes observable at intensities ! The probability for vacuum to stay vacuum in a constant electric field: - the Heisenberg-Euler correction to em field Lagrangian J. Schwinger, Phys.Rev., 82, 664 (1951) Focused laser pulse: - focal spot radius, - pulse duration The ideal vacuum is stable in the presence of a laser field until the process of pairs creation starts However, even a single charged particle located in the focal area of an intense laser pulse may lead to vacuum instability Particles are accelerated by the field and … A. R. Bell and J. G. Kirk, Phys. Rev. Lett. 101, 200403 (2008). A.M. Fedotov and N.B. Narozhny, in Extreme Light Infrastructure: Report on the GC Meeting, 27-28 April 2009, Paris, http://www.extreme-light-infrastructure.eu A. M. Fedotov, N. B. Narozhny, G.Mourou and G. Korn, Phys. Rev. Lett. 105, 080402 (2010). Vacuum instability may be caused by: a) A strong focused laser pulse b) A “seed particle” inside a strong focused laser pulse seed particle To describe vacuum instability we should be able to calculate probabilities of elementary processes! 1. Processes initiated by a seed particle a) photon emission b) pair photoproduction The probabilities are known for a monochromatic plane wave field a) b) - classical limit - the process is essentially quantum Domain of formation The space-time area where the functions which determine the probability amplitude for a quantum process are formed The formation length: A.I. Nikishov, V.I. Ritus, 1964 Classically: circular polarization cone of radiation the cone angle PWF: crossed field = constant field with A.I. Nikishov, V.I. Ritus, 1964 Arbitrary configuration of the field : Approximation of locally constant field (LCFA) Let and be the space and time scale of variation of the field, and Then in the domain of formation any field is constant! at A.I. Nikishov, V.I. Ritus, 1964 2. Pair creation by an e-m field in vacuum Constant e-m field: The number of pais created per unit volume and unit time Pairs can be created if A.I. Nikishov, 1969 The formation length (coherence length) for pair production in a constant field A.I.Nikishov, ZhETF, 57, 1210 (1969) formation length and time The formula for the constant field can be applied to a field which is not static and uniform if and are space and time scale of variation of the field. N.B. Narozhny, S.S. Bulanov, V.S. Popov, V.D. Mur, PLA 330, 1 (2004) - local values of field invariants for the laser pulse We can use the static field formula locally if , or Pair creation by laser fields Invariants for a single focused laser pulse (focal plane, t=0) TE- pulse TM-pulse An analytical model for a focused laser pulse was used N.B.Narozhny, M.S.Fofanov, 2000 Pair production by a single focused pulse N.B. Narozhny, S.S. Bulanov, V.S. Popov, V.D. Mur, PLA 330, 1 (2004) A.M. Fedotov, Las. Phys., 19, 214 (2009) Δ=0.1 Δ=0.05 Δ=0.1 4·1027 0.16 4.0·10-11 4.6·10-42 9.6·10-23 1·1028 0.25 24 !! 3.1·10-19 2.0·10-7 2·1028 0.35 3.0·107 1.4·10-7 16 6·1028 0.62 8.4·1013 1.9·105 3.4·109 Number of pairs is growing very fast after the threshold value of intensity Compare the total energy of produced pairs with the energy of the laser pulse COLLAPSE OF THE LASER PULSE PAIR CREATION IMPOSES LIMITATION ON ATTAINABLE LASER INTENSITY Pair production by two colliding S.S. Bulanov, N.B. Narozhny, pulses V.S. Popov, V.D. Mur, ZhETF 129, 14 (2006) Δ=0.05 Δ=0.1 Δ=0.1 1.0·1026 2.5·10-2 4.5·10-12 6.0·10-9 7.1·10-13 2.0·1026 3.6·10-2 5.1·10-2 7.2 1.8·10-2 2.5·1026 4.0·10-2 1.2·103 6.0 5.5·108 1.8·107 5.0·1026 5.7·10-2 14 2.6·107 !! 1. The effect becomes observable at 2. Small difference between e- and h-pulses The threshold can be lowered essentially at the expense of MULTIPLE PULSES TECHNOLOGY Collision geometry (linear polarization) n=2 n=8 n=4 n=16 The number of created pairs Ne+e- and threshold energy Wth for different number n of colliding pulses S. S. Bulanov, V.D. Mur, N.B. Narozhny, et al., PRL, 104, 220404 (2010) 2. Vacuum instability initiated by a seed particle Acceleration: Cascade can be self-sustained if the field accelerates charged particles It is not the case for PWF or constant electromagnetic field, where is an integral of motion, The self-sustained cascade can arise only in a focused laser field, or for colliding laser pulses The same result is valid for the case of 2 colliding linearly polarized laser pulses I. Kostyukov, 2012 The same result is valid for the case of 2 colliding linearly polarized laser pulses I. Kostyukov, 2012 The electron (positron) radiation lifetime (mean free path/c) The photon lifetime The escape time The following hierarchy of time scales should be respected for occurrence of electromagnetic cascade (for optical frequencies) - determines a natural threshold for electromagnetic cascades. The effect reminds the cosmic-ray air showers The difference: the laser field is not only a target for primary particles, but also an accelerator for slow particles Development of e-m cascade needs a seed particle inside laser pulse seed particle It can be a component of a pair created either i) by a photon, or ii) by the field itself Pairs are created by a focused laser pulse at The theory of e-m cascades works! Fedotov, A. M.; Narozhny, N. B.; Mourou, G.; Korn, G. PRL, 105, 080402 (2010) FIG. 2. Pair production as a function of . The solid curve corresponds to the number Ne of pairs produced by a single cascade process. The dotted curve shows the number of pairs produced by multiple cascades generated by pairs created by two colliding circularly polarized 10 fs laser pulses. The branching point corresponds to the threshold value of where the spontaneous pair production begins. The dash line shows the limit for determined by the energy of the laser pulse. The laser frequency ћω = 1 eV. The inset shows the magnified region of intersection of the curves. These results are supported by N. V. Elkina, A. M. Fedotov, I. Yu. Kostyukov, et a Phys.Rev. ST AB, 14, 054401 (2011) where Monte-Carlo code for simulation of cascades in EM field has been developed The cascade equations for a uniformly rotating homogeneous electric field The μ dependence of the mean values of energy , dynamical quantum parameter χ, and the angle θ between the momentum of an electron and the field, over the estimated values. ћω = 1eV. The increment Γ as a function of the dimensionless field strength µ for two rotation frequencies ћω = 1 eV and ћω = 0:66 eV Pair creation, e-m cascades and their combination are mechanisms for of laser field depletion! BACK REACTION SHOULD BE TAKEN INTO ACCOUNT E.N. Nerush et al., PRL 106, 035001 (2011) The cascade is initiated by a single electron located at x = y = 0 with zero initial momentum for t = 0 (e.g., electron belongs to a pair created by a high-energy photon) seed particle QED cascade stops when the laser energy is almost completely converted into the cascade energy. At the initial stage of the cascade development, the number of created particles is growing exponentially. Then the growth substantially slows down. These results confirm the N. Bohr’s conjecture that the critical QED field strength can be never attained for a pair creating electromagnetic field! e-m cascade can be initiated by ultrarelativistic particles The effect was observed at SLAC E144 experiment D.L.Burke, et al., PRL, 79, 1626 (1997) Laser: Energy of particles: No of steps of the cascade/laser shot Excellent agreement with experiment! Present days PW laser + LWFA - LCFA works! ? NO! Particles loose energy very quickly! Mechanism of acceleration begins to work, if the field is strong enough. Acceleration gives start to cascade development which leads to depletion of the laser field. Depletion of laser field can be observed at intensities lower than the threshold intensity for pair creation! ELI: LCFA, the crossed field, Expansion parameter of perturbation theory at Narozhny, PRD, 1980 Perturbation theory does not work – high energy physics in the presence of extreme laser field is an unexplored branch of science! THANK YOU FOR ATTENTION!