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estoring frequency (or the shorter the time scale) is. The nonlinearities <strong>of</strong> matter may vary, but this response is universal, ranging over molecular, atomic, plasma electronic and ionic, and even the stiffest <strong>of</strong> all vacuum, nonlinearities. Thus, we have traversed nature’s display <strong>of</strong> the universal behavior <strong>of</strong> the direct correlation between the brevity <strong>of</strong> pulse being generated and the intensity <strong>of</strong> its driving laser over the widest intensity range our laboratory has to ever to <strong>of</strong>fer. For example, we know that the laser self-focuses above the critical power with: χ3 nonlinearity Pcr = λ2/(2πn0n2) ∼ GW (2) relativistic plasma nonlinearity Pcr = mc 5 /e 2 (ω/ωp) 2 ∼ 17(ω/ωp) 2 GW, (3) vacuum nonlinearity [2] Pcr = (90/28)cE 2 Sλ 2 /α ∼ 10 15 (λ/λ1µ) 2 GW, (4) e.g. X-ray <strong>of</strong> 10 keV, Pcr ∼ 10 PW, where ES is the Schwinger field, above which the vacuum becomes sufficiently strongly polarized and divulges electron and positron pairs [31, 32, 33, 34, 35]. If we compare the critical power <strong>of</strong> self-focusing in a gas with the χ3 nonlinearity with that <strong>of</strong> vacuum, we find that the ratio is nearly α 6 with no other parameters involved. On the other hand, the ration <strong>of</strong> the Keldysh power to the Schwinger power is again α 6 (i.e. EK/ES = α 3 ). We know that the Keldysh field is the field to create the potential energy <strong>of</strong> Rydberg energy WB over the Bohr radius aB. On the other hand, the Schwinger field is to create the potential energy <strong>of</strong> 2mc 2 = α −2 WB over the distance <strong>of</strong> the Compton length αaB. See Fig. 2. Figure 2: The exploration <strong>of</strong> vacuum may be learned from that <strong>of</strong> an atom. While the size <strong>of</strong> the atom is <strong>of</strong> aB (the Bohr radius) and the potential depth is <strong>of</strong> the Rydberg energy WB, the size and the potential depth that we wish to explore <strong>of</strong> vacuum is indicated here in this figure, only by a factor <strong>of</strong> the fine structure constant α to its some power. We also know that in atomic physics, there is the Keldysh parameter [36] γK whereas the equivalent in vacuum is γV σ = mσωc/eE = 1/a0.(σ = e, or q, electron or quark) (5) When the Keldysh parameter is smaller than unity, the process <strong>of</strong> ionization is non-perturbative;, while greater than 1, it is multi-photon process [36]. Similarly when γV σ in vacuum is smaller than 1, the vacuum breakdown is non-pertubative QED, while greater than 1, it is perturbative [32, 33, 34]. When we inject an XUV photon to an atom to ionize it and we apply a sufficiently intense CEP-locked laser to accelerate the ejected electron, we can make attosecond resolution streaking by the time<strong>of</strong>-flight detection <strong>of</strong> the electron [19, 37]. An equivalent process in vacuum is the above mentioned Nikishov/Ritus process [32], in which a gamma photon is injected into vacuum while a sufficiently strong enough laser (or XUV) EM fields are applied. Nikishov et al.[32, 33, 34] showed that the Schwinger vacuum breakdown is many orders <strong>of</strong> magnitude reduced. If we take advantage <strong>of</strong> this process, it is conceivable to accomplish electron-positron pair creation from vacuum with a very strong laser field, but still one that is in a realistically achievable intensity regime. With the adoption <strong>of</strong> this process, we see the possibility <strong>of</strong> streaking vacuum with laser (or XUV coherent photons) with zeptosecond time resolution. This should open up a possibility to start the exploration <strong>of</strong> the time-dependent dynamics (in contrast to the spectroscopy) <strong>of</strong> vacuum in that regime. If we become more ambitious, perhaps with higher intensity and shorter time-scale, we might even be able to resolve the dynamics <strong>of</strong> quarks and gluons out <strong>of</strong> vacuum. PROBING THE TEXTURE OF QUANTUM VACUUM WITH ATTOSECOND METROLOGY IN THE PEV ENERGY FRONTIER As discussed above, we can take advantage <strong>of</strong> the process <strong>of</strong> vacuum breakdown with the assistance <strong>of</strong> a highenergy photon under strong coherent fields, as investigated by Nikishov and Ritus some 40 years ago [32]. This is to use the process that an ultrahigh energy gamma-particle can assist to break down the vacuum with a substantially suppressed electric-field threshold compared with the wellknown Schwinger value. This is the nonlinear QED effect. The probability <strong>of</strong> the vacuum breakdown is derived as [ P (E) ∝ exp − 8 3 ES E · mc2 ω where ES the Schwinger field, ω is the gamma energy, E is the applied electric field in vacuum such as a laser. With a PeV gamma-ray particle, the exponent factor <strong>of</strong> (6) is reduced by the ratio <strong>of</strong> MeV to PeV (mc 2 /ω) over the expression <strong>of</strong> Schwinger’s without the presence <strong>of</strong> a ] (6)
Figure 3: The attosecond metrology to detect the arrival time <strong>of</strong> gamma photons within such a time scale is suggested. It utilizes the property <strong>of</strong> vacuum explored by the pioneering works by Schwinger, Nikishov et al. This approach closely parallels with that <strong>of</strong> the atom streaking with a CEP laser with an XUV photon ionization <strong>of</strong> an electron from the atom. Here instead <strong>of</strong> an atom, we simply use the vacuum electron-positron pair. gamma particle. This means that the vacuum breakdown field plummets from the value <strong>of</strong> 10 16 V/cm to 10 10 V/cm. We suggest that by employing time-synchronized somewhat intense laser field (at 10 10 W/cm 2 ) at the “goal line” <strong>of</strong> the gamma-photon arrival (see Fig. 3), we cause sudden breakdown <strong>of</strong> vacuum and its avalanched particles <strong>of</strong> e − e + as soon as one <strong>of</strong> the highenergy gamma particles arrives. The PeV gamma particle triggers the vacuum breakdown. The time scale <strong>of</strong> breakdown is far faster than fs. The exploitation <strong>of</strong> this phenomenon should allow an ultrafast signal <strong>of</strong> the PeV gamma-photon arrival. Since the trigger phenomenon is exponentially sensitive, we could play a game <strong>of</strong> adjusting the value <strong>of</strong> the laser field to see and differentiate different types <strong>of</strong> trigger phenomenology and parameters, depending upon the gamma particle energies. The creation <strong>of</strong> PeV energy gamma particles is a tremendous challenge. For example, Pr<strong>of</strong>. Suzuki [38] has challenged us if this may be accomplished within our life time. Tajima et al. (2011) has ventured and showed to use the Laser Wakefield Acceleration (LWFA) based on a MJ class laser to reach PeV energy electrons. For the probing <strong>of</strong> the quantum vacuum texture such as Ellis has been spearheading can be done with a small number <strong>of</strong> electrons generated gamma particles. Thus we are relieved from the tough luminosity requirements. However, we need to test a precise arrival <strong>of</strong> gamma photons at the ’goal line’ [39]. Here we suggested the exploitation <strong>of</strong> the Schwinger-Nikishov process to see this time resolution. CONCLUSIONS In conclusion, evidences over more than 18 orders <strong>of</strong> magnitude <strong>of</strong> the Pulse Intensity-Duration Conjecture has been accumulated experimentally and through simulation. It shows that the pulse duration goes inversely with the intensity from the millisecond to the attosecond and zeptosecond regimes. Most notably it predicts that the shortest coherent pulse in the zeptosecond-yoctosecond regime should be produced by the largest laser, like ELI or NIF and the Megajoule, if they are reconfigurated [40] into femtosecond pulse systems. This Conjecture may prove to be an invaluable guide for future ultra-intense and ultrashort pulse experiments. It fosters the hope that zeptosecond and perhaps yocto second pulses could be produced using kJ-MJ systems. It opens up the possibility <strong>of</strong> taking snap shots <strong>of</strong> nuclear reactions and <strong>of</strong> peeking into the nuclear interior in the same way that Zewail [41] examined chemical reactions or Corkum and Krausz [42] probed atoms. The other exciting prospect is the possibility <strong>of</strong> studying the nonlinear optical properties <strong>of</strong> vacuum. This Conjecture in short implies: 1. that the shortest coherent pulse will be produced by the largest laser, like the ELI or NIF and The Megajoule pumping a femtosecond Ti: Sapphire or an OPCPA system. 2. that pulses in the zeptosecond-yoctosecond may be produced. 3. that even with modest efficiency, extremely high power rivaling the critical power in vacuum may be produced. It opens up the regime <strong>of</strong> vacuum nonlinearity. It ties the three distinct disciplines <strong>of</strong> science, i.e. ultrafast science, high- field science, and large-energy laser science together with a single stroke. We have also discussed an example <strong>of</strong> the PeV energy frontier using the largest energy laser (e.g. NIF) relaxing the requirement <strong>of</strong> luminosity. In this example, LWFA enables us to reach PeV in a manageable, albeit still large scale, experimental realization [39]. Here again we are utilizing the strong- field vacuum nonlinearity to help achieve ultrafast metrology. ACKNOWLEDGMENTS We would like to acknowledge the fruitful discussions with S. Bulanov, E. Goulielmakis, T. Esirkepov, M. Kando, F. Krausz, A. Suzuki, J. Nees, N. Naumova, E. Moses, S. Iso, K. Itakura and N. Artemiev. T. Tajima was supported in part by the Blaise Pascal Foundation and by DFG Cluster <strong>of</strong> Excellence MAP (Munich Centre for Advanced Photonics). REFERENCES [1] http://www.extreme-light-infrastructure.eu [2] G. A. Mourou, T. Tajima, S. V. Bulanov, Optics in the relativistic regime. Rev. Mod. Phys. 78, 309-371 (2006). [3] T. H. Maiman, Stimulated Optical Radiation in Ruby. Nature 187, 493-494 (1960). [4] R. W. Hellwarth, Advances in Quantum Electronics (Columbia University Press, New York, 1961).
Page 1 and 2: Proceedings <stron
Page 3: Conference poster
Page 7: Preface The international conferenc
Page 10: Recent progress of
Page 13: Figure 1: The Pulse Intensity-Durat
Page 18 and 19: THE QED EFFECTIVE ACTION In quantum
Page 20 and 21: Figure 2: Turning points in the com
Page 22 and 23: [5] A. Ringwald, “Pair production
Page 24 and 25: QED IN ULTRA-INTENSE LASER FIELDS
Page 26 and 27: form e + nγL → e ′ + γ where
Page 28 and 29: ection(s) associated with the exter
Page 30 and 31: This is listed in Tab.1. The effect
Page 32 and 33: the spectrum of ph
Page 34 and 35: pf f f pi p x2 x1 k ki p pi Figure
Page 36 and 37: STRONG FIELD DYNAMICS IN HEAVY-ION
Page 38 and 39: Possible effects of</strong
Page 40 and 41: Figure 3: Flux tube structure <stro
Page 42 and 43: Abstract Yoctosecond photon pulse g
Page 44 and 45: emsstrahlung or inelastic pair anni
Page 46 and 47: Abstract Fields, Instantons, and Cu
Page 48 and 49: the dispersion relation p0 = Ep −
Page 50 and 51: CRITICAL BEHAVIOR OF CHARMONIUM: QC
Page 52 and 53: different masses m 0 i ̸= mi only
Page 54 and 55: ON THE UNRUH EFFECT ∗ Ralf Schüt
Page 56 and 57: Abstract Can we detect ”Unruh rad
Page 58 and 59: Equipartition Theorem The stochasti
Page 60 and 61: Abstract Quantum fields and static
Page 62: The relation between acceleration a
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= γ WISP ; ; ALP HP(mγ ′ > 0) .
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Figure 4: Exclusion limit (95% C.L.
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Probing extremely light fields via
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Figure 1: Second harmonic generatio
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Abstract Dynamical view of<
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(a) longitudinal momentum distribut
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Exact solutions of
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Pair production in heat bath Finall
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Table 1: Related ideas in strong fi
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Abstract Non-linear charge transpor
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under the assumption of</st
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Brilliant hardγ-production ande +
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each other. Thus the E field rotate
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ACKNOWLEDGMENTS This work is based
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ϵ is the energy of</strong
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of the sampling eq
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Abstract SCHWINGER LIMIT ATTAINABIL
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To find it we use the integral calc
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cloud with a size of</stron
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A way to quantify the irreversible
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Figure 4: Pair production vs time f
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of the quantum flu
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Phenomena H. Schwarz and H. Hora Ed
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In USA, LLNL has a user’s facilit
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field triggering such phenomena is
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QGP is studied by using the particl
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Fig. (1): Presentation of</
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REFERENCES [1] P.A. Franken, A.E. H
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of electron. When
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splitting, no one has succeeded to
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Abstract WIDE-BAND X-RAY OBSERVATIO
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Radiation from Rotation-Powered Pul
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2 -2 -1 keV (ph cm s keV -1 ) 0.1 0
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Zero temperature case There are sti
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M|, is realized in their case, and
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egime. As analogous to a convention
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With extremely high-peak power lase
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Abstract Flying Mirror as a tool to
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Reflected light intensity (μJ/sr/n
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4-mirror laser stacking cavity for
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CURRENT STATUS OF LFEX LASER AND EX
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which were comparable to those befo
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Abstract X-ray Emission from Magnet
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sometimes exceed the Eddington lumi
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1 0.8 0.6 0.4 0.2 B 2 z E 2 T 0.5 1
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First order quantum correction to t
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dE (1) dt = ¯he4 m 2 12πɛ0p 5 i
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Next, let us consider the origin <s
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Abstract NONCANONICAL LIE PERTURBAT
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with C (2) µ = Γ (2) µ − ˆ L
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log N (PIC particle) When the condi
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Abstract X-RAY GENERATION VIA LASER
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The electron beam is bent to the du
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INVESTIGATING THE ONE-PHOTON ANNIHI
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As a representative characteristics
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the interference terms ⟨ϕIϕh⟩
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P r o g r a m of P
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11:55 lunch & group photo [85] [Rec
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List of Participan
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