Abstract
Via the world-line instanton method, we study electron-positron pair creation by a strong (but sub-critical) electric field of the profile E/ cosh2(kx) superimposed by a weaker pulse E ′ / cosh2(ωt). If the temporal Keldysh parameter γ ω = mω/(qE) exceeds a threshold value γ crit ω which depends on the spatial Keldysh parameter γ k = mk/(qE), we find a drastic enhancement of the pair creation probability — reporting on what we believe to be the first analytic non-perturbative result for the interplay between temporal and spatial field dependences E(t, x) in the Sauter-Schwinger effect. Finally, we speculate whether an analogous effect (drastic enhancement of tunneling probability) could occur in other scenarios such as stimulated nuclear decay, for example.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F. Sauter, Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs, Z. Phys. 69 (1931) 742 [INSPIRE].
F. Sauter, Zum “Kleinschen Paradoxon”, Z. Phys. 73 (1931) 547.
W. Heisenberg and H. Euler, Consequences of Dirac’s theory of positrons, Z. Phys. 98 (1936) 714 [physics/0605038] [INSPIRE].
V. Weisskopf, The electrodynamics of the vacuum based on the quantum theory of the electron, Kong. Dans. Vid. Selsk., Math.-fys. Medd. XIV (1936) 6, reprinted in: Quantum Electrodynamics, J. Schwinger eds., Dover, New York U.S.A. (1958).
J.S. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664 [INSPIRE].
E. Brézin and C. Itzykson, Pair production in vacuum by an alternating field, Phys. Rev. D 2 (1970) 1191 [INSPIRE].
N.B. Narozhnyi and A.I. Nikishov, The Simplist processes in the pair creating electric field, Yad. Fiz. 11 (1970) 1072 [Sov. J. Nucl. Phys. 11 (1970) 596] [INSPIRE].
V.S. Popov, Production of e+e- Pairs in an Alternating External Field, JETP Lett. 13 (1971) 185 [hep-th/0107170].
P. Kennedy, The Woods-Saxon potential in the Dirac equation, J. Phys. A 35 (2002) 689.
D.D. Dietrich, Fermion production in time dependent fields, Phys. Rev. D 68 (2003) 105005 [hep-th/0302229] [INSPIRE].
H. Gies and K. Klingmüller, Pair production in inhomogeneous fields, Phys. Rev. D 72 (2005) 065001 [hep-ph/0505099] [INSPIRE].
S.P. Kim and D.N. Page, Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields, Phys. Rev. D 75 (2007) 045013 [hep-th/0701047] [INSPIRE].
H. Kleinert, R. Ruffini and S.-S. Xue, Electron-Positron Pair Production in Space- or Time-Dependent Electric Fields, Phys. Rev. D 78 (2008) 025011 [arXiv:0807.0909] [INSPIRE].
F. Hebenstreit, R. Alkofer, G.V. Dunne and H. Gies, Momentum signatures for Schwinger pair production in short laser pulses with sub-cycle structure, Phys. Rev. Lett. 102 (2009) 150404 [arXiv:0901.2631] [INSPIRE].
C.K. Dumlu and G.V. Dunne, The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses, Phys. Rev. Lett. 104 (2010) 250402 [arXiv:1004.2509] [INSPIRE].
C.K. Dumlu, Schwinger Vacuum Pair Production in Chirped Laser Pulses, Phys. Rev. D 82 (2010) 045007 [arXiv:1006.3882] [INSPIRE].
S.P. Kim and C. Schubert, Non-adiabatic Quantum Vlasov Equation for Schwinger Pair Production, Phys. Rev. D 84 (2011) 125028 [arXiv:1110.0900] [INSPIRE].
C.K. Dumlu and G.V. Dunne, Interference Effects in Schwinger Vacuum Pair Production for Time-Dependent Laser Pulses, Phys. Rev. D 83 (2011) 065028 [arXiv:1102.2899] [INSPIRE].
E. Akkermans and G.V. Dunne, Ramsey Fringes and Time-domain Multiple-Slit Interference from Vacuum, Phys. Rev. Lett. 108 (2012) 030401 [arXiv:1109.3489] [INSPIRE].
E. Strobel and S.-S. Xue, Semiclassical pair production rate for time-dependent electrical fields with more than one component: WKB-approach and world-line instantons, Nucl. Phys. B 886 (2014) 1153 [arXiv:1312.3261] [INSPIRE].
A.I. Nikishov and V.I. Ritus, Quantum Processes in the Field of a Plane Electromagnetic Wave and in a Constant Field 1, Sov. Phys. JETP 19 (1964) 529 [INSPIRE].
A.I. Nikishov and V.I. Ritus, Pair production by a photon and photon emission by an electron in the field of an intense electromagnetic wave and in a constant field, Sov. Phys. JETP 25 (1967) 1135.
T.N. Tomaras, N.C. Tsamis and R.P. Woodard, Back reaction in light cone QED, Phys. Rev. D 62 (2000) 125005 [hep-ph/0007166] [INSPIRE].
T.N. Tomaras, N.C. Tsamis and R.P. Woodard, Pair creation and axial anomaly in light cone QED(2), JHEP 11 (2001) 008 [hep-th/0108090] [INSPIRE].
H.M. Fried and R.P. Woodard, The One loop effective action of QED for a general class of electric fields, Phys. Lett. B 524 (2002) 233 [hep-th/0110180] [INSPIRE].
F. Hebenstreit, A. Ilderton and M. Marklund, Pair production: the view from the lightfront, Phys. Rev. D 84 (2011) 125022 [arXiv:1109.3712] [INSPIRE].
V. Dinu, T. Heinzl, A. Ilderton, M. Marklund and G. Torgrimsson, Vacuum refractive indices and helicity flip in strong-field QED, Phys. Rev. D 89 (2014) 125003 [arXiv:1312.6419] [INSPIRE].
A. Ilderton, Localisation in worldline pair production and lightfront zero-modes, JHEP 09 (2014) 166 [arXiv:1406.1513] [INSPIRE].
A. Ilderton, G. Torgrimsson and J. Wardh, Nonperturbative pair production in interpolating fields, Phys. Rev. D 92 (2015) 065001 [arXiv:1506.09186] [INSPIRE].
V.S. Popov, Pair Production in a Variable External Field (Quasiclassical approximation), Sov. Phys. JETP 34 (1972) 709.
V.S. Popov and M.S. Marinov, e+e- pair production in variable electric field, Yad. Fiz. 16 (1972) 809 [INSPIRE].
V.S. Popov, Resonant pair production in a strong electric field, JETP Lett. 18 (1973) 255.
V.S. Popov, The imaginary time method for periodic fields, Sov. J. Nucl. Phys. 19 (1974) 584.
Y. Kluger, E. Mottola and J.M. Eisenberg, The Quantum Vlasov equation and its Markov limit, Phys. Rev. D 58 (1998) 125015 [hep-ph/9803372] [INSPIRE].
F. Hebenstreit, R. Alkofer and H. Gies, Schwinger pair production in space and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory, Phys. Rev. D 82 (2010) 105026 [arXiv:1007.1099] [INSPIRE].
F. Hebenstreit, R. Alkofer and H. Gies, Particle self-bunching in the Schwinger effect in spacetime-dependent electric fields, Phys. Rev. Lett. 107 (2011) 180403 [arXiv:1106.6175] [INSPIRE].
F. Hebenstreit, A. Ilderton, M. Marklund and J. Zamanian, Strong field effects in laser pulses: the Wigner formalism, Phys. Rev. D 83 (2011) 065007 [arXiv:1011.1923] [INSPIRE].
M. Ruf, G.R. Mocken, C. Müller, K.Z. Hatsagortsyan and C.H. Keitel, Pair production in laser fields oscillating in space and time, Phys. Rev. Lett. 102 (2009) 080402 [arXiv:0810.4047] [INSPIRE].
M. Jiang et al., Electron-positron pair creation induced by quantum-mechanical tunneling, Phys. Rev. A 83 (2011) 053402.
M. Jiang et al., Pair creation enhancement due to combined external fields, Phys. Rev. A 85 (2012) 033408.
F.V. Bunkin and I.I. Tugov, Possibility of creating electron-positron pairs in a vacuum by the focusing of laser radiation, Sov. Phys. Dokl. 14 (1970) 678.
V. Ritus, Quantum effects of the interaction of elementary particles with an intense electromagnetic field, J. Sov. Laser Res. 6 (1985) 497.
A. Nikishov, Problems of intense external-field intensity in quantum electrodynamics, J. Sov. Laser Res. 6 (1985) 619.
A.D. Piazza, Pair production at the focus of two equal and oppositely directed laser beams: The effect of the pulse shape, Phys. Rev. D 70 (2004) 053013 [INSPIRE].
S.S. Bulanov, N.B. Narozhny, V.D. Mur and V.S. Popov, On e + e − pair production by a focused laser pulse in vacuum, Phys. Lett. A 330 (2004) 1 [hep-ph/0403163] [INSPIRE].
N.B. Narozhny, S.S. Bulanov, V.D. Mur and V. S. Popov, On e+e- pair production by colliding electromagnetic pulses, JETP Lett. 80 (2004) 382.
S. Bulanov, N. Narozhny, V. Mur and V. Popov, Electron-positron pair production by electromagnetic pulses, JETP 102 (2006) 9.
G.A. Mourou, T. Tajima and S.V. Bulanov, Optics in the relativistic regime, Rev. Mod. Phys. 78 (2006) 309 [INSPIRE].
G.V. Dunne, New Strong-Field QED Effects at ELI: Nonperturbative Vacuum Pair Production, Eur. Phys. J. D 55 (2009) 327 [arXiv:0812.3163] [INSPIRE].
S.S. Bulanov, T.Z. Esirkepov, A.G.R. Thomas, J.K. Koga and S.V. Bulanov, On the Schwinger limit attainability with extreme power lasers, Phys. Rev. Lett. 105 (2010) 220407 [arXiv:1007.4306] [INSPIRE].
L. Labun and J. Rafelski, Spectra of Particles from Laser-Induced Vacuum Decay, Phys. Rev. D 84 (2011) 033003 [arXiv:1102.5773] [INSPIRE].
R.P. Feynman, Mathematical formulation of the quantum theory of electromagnetic interaction, Phys. Rev. 80 (1950) 440 [INSPIRE].
I.K. Affleck, O. Alvarez and N.S. Manton, Pair Production at Strong Coupling in Weak External Fields, Nucl. Phys. B 197 (1982) 509 [INSPIRE].
S.P. Kim and D.N. Page, Schwinger pair production via instantons in a strong electric field, Phys. Rev. D 65 (2002) 105002 [hep-th/0005078] [INSPIRE].
G.V. Dunne and C. Schubert, Worldline instantons and pair production in inhomogeneous fields, Phys. Rev. D 72 (2005) 105004 [hep-th/0507174] [INSPIRE].
G.V. Dunne, Q.-h. Wang, H. Gies and C. Schubert, Worldline instantons. II. The Fluctuation prefactor, Phys. Rev. D 73 (2006) 065028 [hep-th/0602176] [INSPIRE].
S.P. Kim and D.N. Page, Schwinger pair production in electric and magnetic fields, Phys. Rev. D 73 (2006) 065020 [hep-th/0301132] [INSPIRE].
G.V. Dunne, Worldline instantons, vacuum pair production and Gutzwiller’s trace formula, J. Phys. A 41 (2008) 164041 [INSPIRE].
C.K. Dumlu and G.V. Dunne, Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production, Phys. Rev. D 84 (2011) 125023 [arXiv:1110.1657] [INSPIRE].
C. Schubert, Lectures on the worldline formalism, given at the School on Spinning Particles in Quantum Field Theory: Worldline Formalism, Higher Spins and Conformal Geometry, Morelia Mexico (2012), http://indico.cern.ch/event/206621/.
L.V. Keldysh, Ionization in the field of a strong electromagnetic wave, Sov. Phys. JETP 20 (1965)1307.
D.L. Burke et al., Positron production in multi - photon light by light scattering, Phys. Rev. Lett. 79 (1997) 1626 [INSPIRE].
W. Dittrich and H. Gies, Probing the quantum vacuum. Perturbative effective action approach in quantum electrodynamics and its application, Springer Tracts Mod. Phys. 166 (2000) 1.
J. Avan, H.M. Fried and Y. Gabellini, Nontrivial generalizations of the Schwinger pair production result, Phys. Rev. D 67 (2003) 016003 [hep-th/0208053] [INSPIRE].
G.V. Dunne, The search for the Schwinger effect: Nonperturbative vacuum pair production, Int. J. Mod. Phys. A 25 (2010) 2373 [INSPIRE].
G.V. Dunne, The Heisenberg-Euler Effective Action: 75 years on, Int. J. Mod. Phys. A 27 (2012) 1260004 [arXiv:1202.1557] [INSPIRE].
R. Schützhold, H. Gies and G. Dunne, Dynamically assisted Schwinger mechanism, Phys. Rev. Lett. 101 (2008) 130404 [arXiv:0807.0754] [INSPIRE].
G.V. Dunne, H. Gies and R. Schützhold, Catalysis of Schwinger Vacuum Pair Production, Phys. Rev. D 80 (2009) 111301 [arXiv:0908.0948] [INSPIRE].
A. Monin and M.B. Voloshin, Photon-stimulated production of electron-positron pairs in electric field, Phys. Rev. D 81 (2010) 025001 [arXiv:0910.4762] [INSPIRE].
M. Orthaber, F. Hebenstreit and R. Alkofer, Momentum Spectra for Dynamically Assisted Schwinger Pair Production, Phys. Lett. B 698 (2011) 80 [arXiv:1102.2182] [INSPIRE].
C. Fey and R. Schützhold, Momentum dependence in the dynamically assisted Sauter-Schwinger effect, Phys. Rev. D 85 (2012) 025004 [arXiv:1110.5499] [INSPIRE].
H. Kleinert and S.-S. Xue, Electron-positron pair productions in classical electric field and electromagnetic wave, Annals Phys. 333 (2013) 104 [arXiv:1207.0401] [INSPIRE].
S. Gordienko, A. Pukhov, O. Shorokhov and T. Baeva, Coherent Focusing of High Harmonics: A New Way Towards the Extreme Intensities, Phys. Rev. Lett. 94 (2005) 103903 [INSPIRE].
M.F. Linder, C. Schneider, J. Sicking, N. Szpak and R. Schützhold, Pulse shape dependence in the dynamically assisted Sauter-Schwinger effect, Phys. Rev. D 92 (2015) 085009.
M. Büttiker and R. Landauer, Traversal Time for Tunneling, Phys. Rev. Lett. 49 (1982) 1739 [INSPIRE].
G. Gamow, Zur Quantentheorie des Atomkernes, Z. Phys. 51 (1928) 204.
H. Gies and G. Torgrimsson, Critical Schwinger pair production, arXiv:1507.07802 [INSPIRE].
H. Geiger and J.M. Nuttall, The ranges of the α particles from various radioactive substances and a relation between range and period of transformation, Philos. Mag. Ser. 6 22 (1911) 613 [Erratum ibid. 23 (1912) 439].
W. Becker, W.H. Louisell, J.D. McCullen and M.O. Scully, Laser Enhancement of Nuclear β Decay, Phys. Rev. Lett. 47 (1981) 1262.
J.I. Gersten and M.H. Mittleman, Comment on “Laser Enhancement of Nuclear β Decay”, Phys. Rev. Lett. 48 (1982) 651.
H.R. Reiss, Laser Enhancement of Nuclear β Decay, Phys. Rev. Lett. 48 (1982) 652.
W. Becker, W.H. Louisell, J.D. McCullen and M.O. Scully, Becker et al. Respond, Phys. Rev. Lett. 48 (1982) 653.
G.C. Baldwin and S.A. Wender, Effect of Laser Radiation on the Decay of U, Phys. Rev. Lett. 48 (1982) 1461.
H.R. Reiss, Nuclear beta decay induced by intense electromagnetic fields: Basic theory, Phys. Rev. C 27 (1983) 1199 [INSPIRE].
W. Becker, R.R. Schlicher and M.O. Scully, Comment on enhancement of forbidden nuclear beta decay by high-intensity radio-frequency fields, Phys. Rev. C 29 (1984) 1124 [INSPIRE].
H.R. Reiss, Reply to “Comment on enhancement of forbidden nuclear beta decay by high-intensity radio-frequency fields”, Phys. Rev. C 29 (1984) 1132 [INSPIRE].
J.L. Friar and H.R. Reiss, Modification of nuclear β decay by intense low-frequency electromagnetic waves, Phys. Rev. C 36 (1987) 283 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1407.3584
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Schneider, C., Schützhold, R. Dynamically assisted Sauter-Schwinger effect in inhomogeneous electric fields. J. High Energ. Phys. 2016, 164 (2016). https://doi.org/10.1007/JHEP02(2016)164
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)164