The Search for the Schwinger Effect: Non-perturbative Pair - - PowerPoint PPT Presentation
The Search for the Schwinger Effect: Non-perturbative Pair Production from Vacuum Gerald Dunne University of Connecticut DESY Seminar & Physics in Intense Fields: PIF 2013, July 2013 probing the quantum vacuum fundamental physics and
DESY Seminar & Physics in Intense Fields: PIF 2013, July 2013 ✦ probing the quantum vacuum ✦ fundamental physics and the Schwinger effect ✦ QFT methods, optimization and pulse shaping ✦ outlook : conceptual and computational issues
Naturall reason abhorreth vacuum Cranmer, 1550
horror vacui: nature abhors a vacuum Aristotle, c350 BC
Naturall reason abhorreth vacuum Cranmer, 1550
A vacuum is a hell of a lot better than some of the stuff that nature replaces it with Tennessee Williams, “Cat on a Hot Tin Roof”, 1955
horror vacui: nature abhors a vacuum Aristotle, c350 BC
Casimir effect
QED vacuum polarization
Hawking radiation
inherent instability of QED vacuum
Sauter (Bohr), 1931 Heisenberg & Euler, 1936 Feynman, 1949 Schwinger, 1951
probe with an external (laser) electric field
external E field accelerates apart a virtual e+e- pair
inherent instability of QED vacuum
Sauter (Bohr), 1931 Heisenberg & Euler, 1936 Feynman, 1949 Schwinger, 1951
probe with an external (laser) electric field
external E field accelerates apart a virtual e+e- pair
inherent instability of QED vacuum
Sauter (Bohr), 1931 Heisenberg & Euler, 1936 Feynman, 1949 Schwinger, 1951
probe with an external (laser) electric field
external E field accelerates apart a virtual e+e- pair
inherent instability of QED vacuum
Sauter (Bohr), 1931 Heisenberg & Euler, 1936 Feynman, 1949 Schwinger, 1951
probe with an external (laser) electric field
external E field accelerates apart a virtual e+e- pair
2
k
" $
This agrees with the conjecture of N. Bohr that was given in the introduction, that one first obtains the finite probability for the transition of an electron into the region of negative impulse when the potential ramp vh/mc over a distance of the Compton wavelength h/mc has the order of magnitude of the rest energy. k2 =
2 2
2 ( ) mc hc v " ~ 1,
“This case would correspond to around 1016 volt/cm.”
“Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs,” Zeit. f. Phys. 69 (1931), 742-764.
On the behavior of an electron in a homogeneous electric field in Dirac’s relativistic theory
By Fritz Sauter in Munich E cp E cp
2
k
" $
This agrees with the conjecture of N. Bohr that was given in the introduction, that one first obtains the finite probability for the transition of an electron into the region of negative impulse when the potential ramp vh/mc over a distance of the Compton wavelength h/mc has the order of magnitude of the rest energy. k2 =
2 2
2 ( ) mc hc v " ~ 1,
“This case would correspond to around 1016 volt/cm.”
“Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs,” Zeit. f. Phys. 69 (1931), 742-764.
On the behavior of an electron in a homogeneous electric field in Dirac’s relativistic theory
By Fritz Sauter in Munich E cp E cp
*
I would like to thank Herrn Prof. Heisenberg for the friendly tip about this hypothesis of N. Bohr.
vacuum pair production
c ≈ 4 × 1029W/cm2
vacuum pair production
c ≈ 4 × 1029W/cm2
non-perturbative
vacuum pair production
c ≈ 4 × 1029W/cm2
Eion
c
= m2e5 4
= e2 c ⇥3 m2c3 e
Iion
c
= α6Ic ≈ 1016 W/cm2
atomic ionization Eb = m e4 2 2
non-perturbative
vacuum pair production
c ≈ 4 × 1029W/cm2
huge energy & intensity scale difference
Eion
c
= m2e5 4
= e2 c ⇥3 m2c3 e
Iion
c
= α6Ic ≈ 1016 W/cm2
atomic ionization Eb = m e4 2 2
non-perturbative
✦ vacuum energy: mass generation; dark energy ✦ physics beyond the standard model ✦ axion and ALP searches; dark matter ✦ QED and QFT at ultra-high intensity and in strong E & B fields ✦ non-equilibrium QFT: e.g. quark-gluon-plasma, chiral magnetic effect ✦ back-reaction, cascading ✦ astrophysical applications: neutron stars, magnetars, black holes ✦ cosmological particle production (Parker, Zeldovich) ✦ Hawking radiation
Mourou, Tajima
XFEL at DESY Attosecond ? Exawatt? NIF
1024 − 1026 W/cm2 ?
input from: particle physics, laser physics, accelerator physics, plasma physics, ...
Biréfringence Magnétique du Vide (BMV) OSQAR: Optical Search for QED vacuum magnetic birefringence, Axions and photon Regeneration
LIPSS: Light Pseudoscalar and Scalar Search
BELLA laser at LBNL 1 GeV in < 1m; goal: 10 GeV in 10 cm
Physicists are planning lasers powerful enough to rip apart the fabric of space and time. Ed Gerstner is impressed.
NATURE|Vol 446|1 March 2007
NEWS FEATURE
``Physicists are planning lasers powerful enough to rip apart the fabric
Mourou, Tajima
do we really need ?
1029W/cm2
c
c
recall: constant field approximation:
ionization is seen well below the sharp cutoff critical field Eb~15 eV
do we really need ?
1029W/cm2
how critical is the critical field? the constant field approximation only gives a rough estimate there is a lot of interesting physics in going beyond the constant field approximation experimentally necessary and theoretically challenging
Keldysh, 1964; Brézin/Itzykson, 1970; Popov, 1971
“Keldysh” adiabaticity parameter :
new scale : ω
mc2 eE
monochromatic sinusoidal field :
Keldysh, 1964; Brézin/Itzykson, 1970; Popov, 1971
“Keldysh” adiabaticity parameter :
new scale : ω
mc2 eE
monochromatic sinusoidal field :
e E
ω m c
time-dependent WKB:
Keldysh, 1964; Brézin/Itzykson, 1970; Popov, 1971
“Keldysh” adiabaticity parameter :
new scale : ω
mc2 eE
monochromatic sinusoidal field :
e E
ω m c
time-dependent WKB:
Keldysh, 1964; Brézin/Itzykson, 1970; Popov, 1971
“Keldysh” adiabaticity parameter :
new scale : ω
mc2 eE
monochromatic sinusoidal field :
e E
ω m c
time-dependent WKB:
SLAC E-144
VOLUME 79, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 1 SEPTEMBER 1997
Positron Production in Multiphoton Light-by-Light Scattering
Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309
Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996
Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544
Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627
(Received 2 June 1997)
Complete QED Theory of Multiphoton Trident Pair Production in Strong Laser Fields
Huayu Hu,1,2 Carsten Mu ¨ller,1,* and Christoph H. Keitel1
1Max-Planck-Institut fu
¨r Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
2Department of Physics, National University of Defense Technology, Changsha 410073, People’s Republic of China
(Received 12 February 2010; published 16 August 2010)
PRL 105, 080401 (2010) P H Y S I C A L R E V I E W L E T T E R S
week ending 20 AUGUST 2010
tunneling transition to tunneling nonperturbative multiphoton SLAC experiment perturbative fewphoton
1017 1018 1019 1020 1021 1 2 5 10 20 50 100 150 Laser Intensity Wcm2 Electron Energy GeV
trident process could probe across perturbative and non-perturbative regime
why the Schwinger effect is such an interesting, and difficult, QFT problem
we think we understand QED, but: ultra-intense fields, medium effects, back-reaction, non-equilibrium, ...
QED vacuum polarization
dispersive effects: e.g. vacuum birefringence
absorptive effects: e.g. vacuum pair production
encodes nonlinear properties of QED due to vacuum polarization
probability of pair production ≈ 2
vacuum persistence probability
probability of pair production ≈ 2
vacuum persistence probability
E t
Im(−E) t
relativistic analogue of familiar QM:
Heisenberg & Euler
vacuum polarization due to slowly varying [constant] fields
Stückelberg, Feynman, Schwinger, Nambu, Fock, ...
“We try to represent the amplitude for a particle to get from one point to another as a sum over all trajectories of an amplitude exp(i S) where S is the classical action for a given trajectory. To maintain the relativistic invariance in evidence the idea suggests itself of describing a trajectory in space-time by giving the four variables xμ(u) as functions of some fifth parameter u ... (somewhat analogous to proper time) ...”
aim: extend non-relativistic QM path integral to relativistic QED
“We try to represent the amplitude for a particle to get from one point to another as a sum over all trajectories of an amplitude exp(i S) where S is the classical action for a given trajectory. To maintain the relativistic invariance in evidence the idea suggests itself of describing a trajectory in space-time by giving the four variables xμ(u) as functions of some fifth parameter u ... (somewhat analogous to proper time) ...”
aim: extend non-relativistic QM path integral to relativistic QED but some paths go backwards in time ?!?
Schwinger, 1950-1954 ``Incidentally, the probability of actual pair creation is obtained from the imaginary part of the electromagnetic field action integral.’’ expressed the QED effective action in terms of functional determinants
PH YSI CAL REVIEW
VOLUME
90, NUMBER
4
MA V 25, 2593
Fredholm Theory of Scattering
in a Given Time-Dependent
Field
AaDUS SALAM, St. John's College, Cambridge,
England, and Government
College, Lahore, Pakistan
Laboratory,
Cambrutge,
England (Received October 27, 1952)
It is shown that Feynman's
relativistic solution
for- the scattering
by a given external
Geld is the Fredholm
resolvent
equation and is thus the unique and absolutely convergent solution
for any strength
INTRODUCTION
HE Fredholm
theory
equations has been applied
to the
nonrelativistic theory
scattering by Jost and
Pais.' We here
consider the extension
theory
to the
interaction
quantized electron-positron
field
with
a
prescribed external electromagnetic
has been
considered
by Feynman. ' Feynman's
solution is most simply derived from the 5 matrix in the form given by
matrix
element
for electron scattering
creation is obtained as an expan-
sion in the external field and is normalized
by multi-
plying
by
the vacuum expectation value
matrix.
VVe show that this is identical
with
the Fred-
holm
resolvent
integral equation and is thus absolutely convergent
for any
strength
external
Geld,
for
which
the cross section has any meaning.
ln the first section the Fredholm
theory is stated in
a form given by Plemelj, ' which exhibits the Fredholm
solution
in terms of the iterations
have the advantage
usual form of the theory' that they are either the same
as, or closely related
to, expressions
in the
5 matrix and can be written
down directly by Feynman's
graphical methods.
The
relation
the
Fredholm solution
to the solution
by iteration
is discussed.
The
problem
in a pure
external
field is then
treated
in Secs. 2 and 3, with the result stated above.
The case of a static field is related to the work of Jost
and Pais.'
Consider Fredholm's integral equation
x(s) =y(s)+X
E(s, t)x(t)dt,
(or x=y+XEx), *Now at Department
Physics, University
Birmingham, Birmingham, England.
' R. Jost and A. Pais, Phys. Rev. 82, 840 (1951).
~ R. P. Feynman,
3 F. I. Dyson, Phys. Rev. 75, 486, 1736 (1949}.
4 J. Plemelj, Monatsch. Math. 15, 93 (1904).
' See, for example, E.T. Whittaker
and G. N. Watson, Modern Analysis (Cambridge University
Press, Cambridge,
1940), fourth
edition, Chapter XI.
C,=,r "~E(s, t) tsdsdt&~,
then (1.1) has the unique solution
x(s) =d—
'P.)
D(X, s, t)y(t)dt,
=d—
'(X)A(X, s), for all X for which d(X) WO. Here d()t) =Q d.X",
n=o
(1.
4) D(X, s, t)=g D„(s,t))"
n=o
LD(X, s, t) is called the Fredholrn
resolvent],
where
do= j.,
0'2
S—
1
~ ~ ~Q
(—
1)" ~s
02
e—
2
(1.
6)
~ ~
~0 2
8(s— t) u
~ ~ ~Q
E(s, t)
(—
1)"
D„(s,t) =
E'(s, t)
~ ~e
Q
Oj
0'y
's— 2
'
'
E"(s, t) o„o„i
~ ~ ~(1.7)
E(s, u)E" '(u t)du ' F. Smithies,
Duke Math. J. 8, 107 (1941).
where
the integration may be over a fjxed interval,
. finite or infinite.
Smithies has shown
that, if E(s, t)
is a measurable function
69Q
PH YSI CAL REVIEW
VOLUME
90, NUMBER
4
MA V 25, 2593
Fredholm Theory of Scattering
in a Given Time-Dependent
Field
AaDUS SALAM, St. John's College, Cambridge,
England, and Government
College, Lahore, Pakistan
Laboratory,
Cambrutge,
England (Received October 27, 1952)
It is shown that Feynman's
relativistic solution
for- the scattering
by a given external
Geld is the Fredholm
resolvent
equation and is thus the unique and absolutely convergent solution
for any strength
INTRODUCTION
HE Fredholm
theory
equations has been applied
to the
nonrelativistic theory
scattering by Jost and
Pais.' We here
consider the extension
theory
to the
interaction
quantized electron-positron
field
with
a
prescribed external electromagnetic
has been
considered
by Feynman. ' Feynman's
solution is most simply derived from the 5 matrix in the form given by
matrix
element
for electron scattering
creation is obtained as an expan-
sion in the external field and is normalized
by multi-
plying
by
the vacuum expectation value
matrix.
VVe show that this is identical
with
the Fred-
holm
resolvent
integral equation and is thus absolutely convergent
for any
strength
external
Geld,
for
which
the cross section has any meaning.
ln the first section the Fredholm
theory is stated in
a form given by Plemelj, ' which exhibits the Fredholm
solution
in terms of the iterations
have the advantage
usual form of the theory' that they are either the same
as, or closely related
to, expressions
in the
5 matrix and can be written
down directly by Feynman's
graphical methods.
The
relation
the
Fredholm solution
to the solution
by iteration
is discussed.
The
problem
in a pure
external
field is then
treated
in Secs. 2 and 3, with the result stated above.
The case of a static field is related to the work of Jost
and Pais.'
Consider Fredholm's integral equation
x(s) =y(s)+X
E(s, t)x(t)dt,
(or x=y+XEx), *Now at Department
Physics, University
Birmingham, Birmingham, England.
' R. Jost and A. Pais, Phys. Rev. 82, 840 (1951).
~ R. P. Feynman,
3 F. I. Dyson, Phys. Rev. 75, 486, 1736 (1949}.
4 J. Plemelj, Monatsch. Math. 15, 93 (1904).
' See, for example, E.T. Whittaker
and G. N. Watson, Modern Analysis (Cambridge University
Press, Cambridge,
1940), fourth
edition, Chapter XI.
C,=,r "~E(s, t) tsdsdt&~,
then (1.1) has the unique solution
x(s) =d—
'P.)
D(X, s, t)y(t)dt,
=d—
'(X)A(X, s), for all X for which d(X) WO. Here d()t) =Q d.X",
n=o
(1.
4) D(X, s, t)=g D„(s,t))"
n=o
LD(X, s, t) is called the Fredholrn
resolvent],
where
do= j.,
0'2
S—
1
~ ~ ~Q
(—
1)" ~s
02
e—
2
(1.
6)
~ ~
~0 2
8(s— t) u
~ ~ ~Q
E(s, t)
(—
1)"
D„(s,t) =
E'(s, t)
~ ~e
Q
Oj
0'y
's— 2
'
'
E"(s, t) o„o„i
~ ~ ~(1.7)
E(s, u)E" '(u t)du ' F. Smithies,
Duke Math. J. 8, 107 (1941).
where
the integration may be over a fjxed interval,
. finite or infinite.
Smithies has shown
that, if E(s, t)
is a measurable function
69Q
extremely difficult
QFT problem: compute non-perturbatively for a gauge field corresponding to a realistic laser pulse
Aµ(x) Im Γ[A]
extremely difficult full optimization problem: find that maximizes
Im Γ[A]
so far, prohibitively difficult
QFT problem: compute non-perturbatively for a gauge field corresponding to a realistic laser pulse
Aµ(x) Im Γ[A]
constant E field monochromatic
pulse with sub-cycle structure; carrier phase effect chirped pulse, Gaussian beam, ...
✦ ensemble of closed spacetime loops: weight ✦ probe with Wilson loop operator ✦ ensemble independent of form of
0 dτ ˙
4
R T
0 dτ ˙
x2
Gies/Klingmüller 2005
imaginary part? exponentially small?
periodic (closed loop) solution = “worldline instanton” classical Euclidean equations of motion
GD, Schubert 2005 GD, Gies, Schubert, Wang, 2006
semiclassical approximation : “instanton dominance”
technically difficult for multi-dimensional fields : complex instantons
computational simplification : scalar QED
temporal variation: over-the-barrier reflection spatial variation: through-the-barrier transmission
⊥) Φ
quantum interference
we can take advantage of this to enhance the Schwinger effect
Multiple Colliding Electromagnetic Pulses: AWay to Lower the Threshold
1FOCUS Center and Center for Ultrafast Optical Science, University of Michigan, Ann Arbor, Michigan 48109, USA 2Institute of Theoretical and Experimental Physics, Moscow 117218, Russia 3National Research Nuclear University MEPhI, 115409 Moscow, Russia
(Received 2 March 2010; published 1 June 2010)
PRL 104, 220404 (2010) P H Y S I C A L R E V I E W L E T T E R S
week ending 4 JUNE 2010
The scheme of interaction
pulses. n Neþe at W ¼ 10 kJ Wth, kJ (Neþe 1) 2 0a 40 4 0b 20 8 4.0 10 16 1:8 103 8 24 4:2 106 5.1
a
colliding beams enhance effect
“mixed” Keldysh parameter significant enhancement of e−Ainst strong, slow field plus weak, fast field large effective γ, but still nonperturbative
2 3 4 5 γ 2.0 2.5 3.0
inst
Dynamically Assisted Schwinger Mechanism
Ralf Schu ¨tzhold,1,2 Holger Gies,3,4 and Gerald Dunne5
1
PRL 101, 130404 (2008) P H Y S I C A L R E V I E W L E T T E R S
week ending 26 SEPTEMBER 2008
dynamically assisted Schwinger mechanism e absorbs weak high ω photon, lowering the effective tunnel barrier strong, slow pulse + weak, fast pulse
Barrier Control in Tunneling eþ-e Photoproduction
¨tstedt,1 A. I. Milstein,1,2 and C. H. Keitel1
1Max-Planck-Institut fu
¨r Kernphysik, Postfach 103980, 69029 Heidelberg, Germany
2Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia
(Received 3 June 2009; published 22 October 2009)
PRL 103, 170403 (2009) P H Y S I C A L R E V I E W L E T T E R S
week ending 23 OCTOBER 2009
quantitative physical explanation: quantum interference
Momentum Signatures for Schwinger Pair Production in Short Laser Pulses with a Subcycle Structure
1
PRL 102, 150404 (2009) P H Y S I C A L R E V I E W L E T T E R S
week ending 17 APRIL 2009
ϕ : carrier phase
quantum interference
0.2 0.4 0.2 0.4 0.6 k MeV 1 10 14 3 10 14 5 10 14
0.2 0.4 0.6 0.2 0.4 0.6 k MeV 1 10 14 3 10 14 5 10 14
Momentum Signatures for Schwinger Pair Production in Short Laser Pulses with a Subcycle Structure
1
PRL 102, 150404 (2009) P H Y S I C A L R E V I E W L E T T E R S
week ending 17 APRIL 2009
ϕ : carrier phase
Stokes: “WKB” solutions are multivalued, even if true solution is not; only LOCAL for many applications we need GLOBAL information
Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
Cesim K. Dumlu and Gerald V. Dunne
Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA (Received 14 April 2010; published 24 June 2010)
PRL 104, 250402 (2010) P H Y S I C A L R E V I E W L E T T E R S
week ending 25 JUNE 2010
+ (p⇥ − A(t))2
t = +∞ t = −∞ local ! we need global information
Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
Cesim K. Dumlu and Gerald V. Dunne
Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA (Received 14 April 2010; published 24 June 2010)
PRL 104, 250402 (2010) P H Y S I C A L R E V I E W L E T T E R S
week ending 25 JUNE 2010
+ (p⇥ − A(t))2
t = +∞ t = −∞ local ! we need global information
Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
Cesim K. Dumlu and Gerald V. Dunne
Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA (Received 14 April 2010; published 24 June 2010)
PRL 104, 250402 (2010) P H Y S I C A L R E V I E W L E T T E R S
week ending 25 JUNE 2010
+ (p⇥ − A(t))2
t = +∞ t = −∞ local ! we need global information quantum interference
1.0 1.5 2.0 2.5
pm
5.109 1.108 1.5108 2.108
N
scalar QED spinor QED
φ = π 2
naive WKB
“Stokes phenomenon”
2 4
2 4
2 4
2 4
2τ2
2τ2
|0 |0 |0 |0 |pairk |pairk |pairk T 1 ω 1 ω
N alternating sign pulses coherent N2 enhancement of certain modes time domain multiple-slit quantum interference effect
Ramsey Fringes and Time-Domain Multiple-Slit Interference from Vacuum
Eric Akkermans1 and Gerald V. Dunne2 PRL 108, 030401 (2012) P H Y S I C A L R E V I E W L E T T E R S
week ending 20 JANUARY 2012
N Npulse
k
< : N 1pulse
k
sin2½Nk=cos2½k; N even N 1pulse
k
cos2½Nk=cos2½k; N odd
|0 |0 |0 |0 |pairk |pairk |pairk T 1 ω 1 ω
N alternating sign pulses coherent N2 enhancement of certain modes time domain multiple-slit quantum interference effect
Ramsey Fringes and Time-Domain Multiple-Slit Interference from Vacuum
Eric Akkermans1 and Gerald V. Dunne2 PRL 108, 030401 (2012) P H Y S I C A L R E V I E W L E T T E R S
week ending 20 JANUARY 2012
N Npulse
k
< : N 1pulse
k
sin2½Nk=cos2½k; N even N 1pulse
k
cos2½Nk=cos2½k; N odd
|0 |0 |0 |0 |pairk |pairk |pairk T 1 ω 1 ω
N alternating sign pulses coherent N2 enhancement of certain modes time domain multiple-slit quantum interference effect
Ramsey Fringes and Time-Domain Multiple-Slit Interference from Vacuum
Eric Akkermans1 and Gerald V. Dunne2 PRL 108, 030401 (2012) P H Y S I C A L R E V I E W L E T T E R S
week ending 20 JANUARY 2012
N Npulse
k
< : N 1pulse
k
sin2½Nk=cos2½k; N even N 1pulse
k
cos2½Nk=cos2½k; N odd
vector potential
t [fs]
2 4
(a)
0.5 1 1.5 2 2.5 10 20 0.5 1 1.5 2 10 20 30 ϕ = 3π / 2 ϕ = π ϕ = π / 2 ϕ = 0
energy [eV] energy [eV] contrast [arb. units]
(b)
Attosecond Double-Slit Experiment
¨tzel,1 H. Walther,1,2 A. Baltus ˇka,1 E. Goulielmakis,1 F. Krausz,1,2,3 D. B. Milos ˇevic ´,4 D. Bauer,5
PRL 95, 040401 (2005) P H Y S I C A L R E V I E W L E T T E R S
week ending 22 JULY 2005
A new scheme for a double-slit experiment in the time domain is presented. Phase-stabilized few-cycle laser pulses open one to two windows (slits) of attosecond duration for photoionization. Fringes in the angle-resolved energy spectrum of varying visibility depending on the degree of which-way information are measured. A situation in which one and the same electron encounters a single and a double slit at the same time is observed. The investigation of the fringes makes possible interferometry on the attosecond time scale. From the number of visible fringes, for example, one derives that the slits are extended over about 500 as.
Much attention has recently been focused on optimal control of quantum systems, and extensive theoretical and numerical work has been performed.1–5 An important case is the desire to achieve a large transition probability from a specific initial state into a final target state by means of a controlling external laser field5 while minimizing the laser
controllin
jective functional
Rapidly convergent iteration methods for quantum optimal control
Wusheng Zhu, Jair Botina, and Herschel Rabitz
Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009
Received 23 May 1997; accepted 24 October 1997
shaped ultra-short pulses: tune time-dependent amplitudes and phases to match characteristic frequencies of quantum system e.g. NMR, selective molecular transformations, ...
in semiconductors
Fernando Solas, Jennifer M. Ashton, Andreas Markmann,a and Herschel A. Rabitz
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
designer potentials for prescribed 2d scattering
Andreas Markmann1*, Gerald V. Dunne2, Victor S. Batista1
1Department of Chemistry, Yale University, New Haven, CT 06520, *andreas.markmann@yale.edu 2Department of Physics, University of Connecticut, Storrs, CT 06269
✦ OCT has been widely studied for N-level population transfer problems ✦ need: ultra-relativistic extension, QFT formulation: worldline ✦ quantum interference provides guiding principle for optimization Gordon conference 2011
Optimizing the pulse shape for Schwinger pair production
urst,1, ∗ M. Mitter,1, † G. von Winckel,2, 3, ‡ F. Hebenstreit,4, § and R. Alkofer1, ¶
1Institut f¨
ur Physik, Karl-Franzens-Universit¨ at, A-8010 Graz, Austria
2Institut f¨
ur Mathematik und wissenschaftliches Rechnen, Karl-Franzens-Universit¨ at, A-8010 Graz, Austria
3Department of Electrical and Computer Engineering,
University of New Mexico, Albuquerque-NM 87106, USA
4Institut f¨
ur Theoretische Physik, Universit¨ at Heidelberg, D-69120 Heidelberg, Germany (Dated: December 7, 2012)
Simulating fermion production in 1 þ 1 dimensional QED
1Institut fu
¨r Theoretische Physik, Universita ¨t Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
2ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum, Planckstraße 1, 64291 Darmstadt, Germany
(Received 25 February 2013; published 7 May 2013) þ PHYSICAL REVIEW D 87, 105006 (2013)
Quantum Vlasov equation and its Markov limit
Yuval Kluger and Emil Mottola
Theoretical Division, Los Alamos National Laboratory, MS B285, Los Alamos, New Mexico 87545
Judah M. Eisenberg*
School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978 Tel Aviv, Israel Received 20 March 1998; published 16 November 1998, PHYSICAL REVIEW D, VOLUME 58, 125015
✦ created pairs act back on the external electric field ✦ inherently non-equilibrium process ✦ go beyond 1-loop effective action picture ✦ important for heavy ion physics; condensed matter & AMO analogues
Limitations on the Attainable Intensity of High Power Lasers
National Research Nuclear University MEPhI, Moscow 115409, Russia
Institut de la Lumie `re Extre ˆme, UMS 3205 ENSTA, Ecole Polytechnique, CNRS, 91761 Palaiseau, France
PRL 105, 080402 (2010) P H Y S I C A L R E V I E W L E T T E R S
week ending 20 AUGUST 2010
back reaction & radiation reaction; polarization effects
Possibility of Prolific Pair Production with High-Power Lasers
Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom and STFC Central Laser Facility, RAL, Didcot, OX11 0QX, United Kingdom
John G. Kirk
Max-Planck-Institut fu ¨r Kernphysik, Saupfercheckweg, 1, D-69117, Heidelberg, Germany (Received 8 August 2008; published 11 November 2008) Prolific electron-positron pair production is possible at laser intensities approaching 1024 W cm2 at a wavelength of 1 m. An analysis of electron trajectories and interactions at the nodes (B ¼ 0) of two counterpropagating, circularly polarized laser beams shows that a cascade of rays and pairs develops. The geometry is generalized qualitatively to linear polarization and laser beams incident on a solid target.
PRL 101, 200403 (2008) P H Y S I C A L R E V I E W L E T T E R S
week ending 14 NOVEMBER 2008
QED cascades induced by circularly polarized laser fields
1Ludwig-Maximilians Universita
¨t Mu ¨nchen, 80539, Germany
2National Research Nuclear University MEPhI, Moscow, 115409, Russia 3Institute of Applied Physics, Russian Academy of Sciences, 603950, Nizhny Novgorod, Russia
(Received 22 October 2010; published 12 May 2011)
PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 14, 054401 (2011)
Monte-Carlo simulations includes radiation friction fully quantum treatment needed
✦ the ``Schwinger limit’’ is not necessarily a sharp limit ✦ something very interesting is going to happen around 1024 - 1025 W/cm2 ... ✦ experimental challenges : higher intensity, focussing, optics, pulse engineering,
plasma effects in intense fields, control schemes, ...
✦ theoretical challenges : optimal pulse design, non-equilibrium effects, plasma
effects in intense fields, ...
✦ quantum interference is significant; combining e beams with lasers, ... ✦ conceptual and computational problems: non-equilibrium QFT, back-reaction,
cascading, cosmological and gravitational analogues, ...
✦ a new field of high-intensity laser/particle physics is forming