Physics Letters B 777 (2018) 406–411
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Pair production by three fields dynamically assisted Schwinger process
Ibrahim Sitiwaldi
a
, Bai-Song Xie
a,b,∗
a
Key Laboratory of Beam Technology of the Ministry of Education, and College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875,
China
b
Beijing Radiation Center, Beijing 100875, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
4 April 2017
Received
in revised form 28 December 2017
Accepted
28 December 2017
Available
online 2 January 2018
Editor: A.
Ringwald
The dynamically assisted Schwinger mechanism for vacuum pair production from two fields to three
fields is proposed and examined. Numerical results for enhanced electron–positron pair production in the
combination of three fields with different time scales are obtained using the quantum Vlasov equation.
The significance of the combination of three fields in the regime of super low field strength is verified.
Although the strengths of each of the three fields are far below the critical field strength, we obtain a
significant enhancement of the production rate and a considerable yields in this combination, where the
nonperturbative field is dynamically assisted by two oscillating fields. The number density depending on
field parameters are also investigated. It is shown that the field threshold to detect the Schwinger effect
can be lowered significantly if the configuration of three fields with different time scales are chosen
carefully.
© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
After Dirac predicted the antiparticle of the electron, the
positron, according to his famous equation, Sauter solved the Dirac
equation for an electron in the Dirac sea in the presence of a static
electric field to find a non-zero probability of electron–positron
pair production from the vacuum under a strong static electric
field [1]. Heisenberg and Euler derived the one-loop effective
Lagrangian accounting for the coupling of a static electromag-
netic
field to the electron vacuum loop [2], according to which
Schwinger calculated the electron–positron pair production rate in
the presence of a static electric field [3]. Since then, vacuum pair
production by electric fields has been usually referred to as the
Schwinger effect.
The
pair production rate in the Schwinger effect has a non-
perturbative
character due to its non-analytic field dependence.
Therefore, it is of fundamental importance for our understand-
ing
of nonperturbative quantum field theories to study vacuum
pair production. Alarge number of investigations are dedicated to
study vacuum pair production, employing different methods such
as proper time [4–6], WKB approximation [7], worldline instan-
*
Corresponding author at: Key Laboratory of Beam Technology of the Ministry of
Education, and College of Nuclear Science and Technology, Beijing Normal Univer-
sity,
Beijing 100875, China.
E-mail
address: bsxie@bnu.edu.cn (B.-S. Xie).
ton techniques [8,9], quantum field theoretical simulation [10–13]
as
well as the quantum kinetic method [14–19]. There is still no
experimental verification of Schwinger pair production since the
threshold field strength is too high to achieve in the laboratory at
present, E
cr
= m
2
c
3
/e
¯
h = 1.32 × 10
18
V/m (m and −e denote mass
and charge of electron, respectively).
In
order to lower the electric field threshold to experimentally
detect the Schwinger effect, various schemes have been proposed
and among them the dynamically assisted Schwinger mechanism
[20] is considered as the most promising one. In this scheme
a greatly enhanced pair production rate is predicted, which also
means a lower field threshold, in a slowly varying electric field
superimposed by a rapidly oscillating one. The dynamically as-
sisted
Schwinger mechanism in a plane-wave x-ray probe beam
superimposed by a strongly focused optical laser pulse [21], in the
superposition of two periodic electric fields with a finite time in-
terval
[22] and in bifrequent fields [23–25] were also studied. The
dynamically assisted Schwinger process in a spatially inhomoge-
neous
field is also studied in [13]. More detailed investigations can
be found in [26–28].
Unlike
these schemes where various types of fields are consid-
ered
but always with the combination of two fields, one fast-weak
field and the other strong-slow/static field, there is an investiga-
tion
where Schwinger process is doubly assisted by a perturbative
weak field and a high energetic photon [29]. It is reasonable to ex-
pect
further lower field threshold due to the combination of three
fields with different time scales with the help of the dynamically
https://doi.org/10.1016/j.physletb.2017.12.060
0370-2693/
© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.