examples of genuinely relativistic phenomena r. grobe icomp viii, monterey, ca october 1999 intense...
TRANSCRIPT
Examples of genuinely relativistic phenomena
R. Grobe
ICOMP VIII, Monterey, CA October 1999
Intense Laser Physics Theory Unit
Illinois State University
Postdocs Faculty
J.W. BraunB.A. SmetankoJ.J. CsesznegiP.J. PeverlyR.E. WagnerT. ShepherdS.M. MandelA. Bergquist
Undergraduate students
H. Wanare
P. Krekora
G.H. Rutherford
Q. Su
R. Grobe
Support : National Science Foundation, Research Corporation, Illinois State
Tools to explore phenomena that are
genuinely relativistic
Dirac :
iÝ c p
1
cA(r , t)
c2 V(
r )
Ý [H,] with H c4 c2(p
1
cA)2 V(
r )
Liouville:
A flavor of the numerical work
• Discretize:
r 2563 points
t 103-106 points
• Split operator FFT technique
• Supercomputer
r , t 0 integrate
(r , t)
H cp c2 A(r , t)V(
r )
≈ 4 · 2563 · 106 = 1013 complex numbers
Genuinely Relativistic Phenomena
• ZitterbewegungJ.W. Braun, Q. Su & RG, PRA 59, 604 (1999)
• Klein-Paradox (particle pair production)J.W. Braun, Q. Su & RG, PRA 59, 604 (1999)
• Subnatural wave packet spreadingQ. Su, B.A. Smetanko & RG, Opt. Exp. 2, 277 (1998)J.C. Csesznegi, G.H. Rutherford, Q. Su & RG, Las. Phys. 9, 41 (1999)
• Spin-spatial coupling in magnetic fields G.H. Rutherford & RG, PRL 81, 4772 (1998)G.H. Rutherford & RG, JPA 31, 9331 (1998)
• Chaos J. Kim, and H. Lee, PRE 51, 1579 (1995)
• How good is Liouville?R.E. Wagner, P.J. Peverly, Q. Su & RG, PRA (subm.)
• Counterintuitive enhancement of resonancesR.E. Wagner, Q. Su & RG, PRL (subm.)
• Cycloatoms and dephasingP.J. Peverly, R.E. Wagner, Q. Su, & RG, Las. Phys. (in press)
• Scattered light spectraR.E. Wagner, Q. Su & RG, PRA 60, No.4 (1999)
Schrödinger’s Zitterbewegung
small ∆x neg. energy contrib. “Zitter”
position
spin
Zitterbewegung real? controversial issue...
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.0001 0.0002 0.0003
<S z(t
)> [
a.u.
]
time [a.u.]
x=10c
x=c
x=0.1c
-2 10-5
-1 10-5
0
1 10-5
2 10-5
0 0.0001 0.0002 0.0003
<x(
t)>
[a.
u.]
time [a.u.]
x=10c
x=c
x=0.1c
J.W. Braun, Q. Su & RG, PRA 59, 604 (1999).
Time - resolved Klein Paradox
Interpretation still controversial ...
0.2
0.4
position [nm]
1.61 .61
0-0.5
electron
positron
0
voltage barrier
0.2
0.4
position [nm]
1.0
0-0.5
incomingelectron
0
voltage barrier
J.W. Braun, Q. Su & RG, PRA 59, 604 (1999).
voltage > Ekin + 2c2
Stern-Gerlach separation possible for electrons ???
Pauli/Bohr: Lorentz-force “washes out” separation ??
Dirac solution : Spin separation is possible
G.H. Rutherford & RG, PRL 81, 4772 (1998) and JPA 31, 9331(1998).
Position
0
0.02
0.04
0.06
-20 -10 0 10 20
–+
P±(x,t=120a.u.)
0
0.02
0.04
–+
P±(x,t=0)
Sz
SzSz
B (r ) B
0
0
0
x
inhomog. magnetic field:
Subnatural wave packet spreading
Non-relativistic: Spreading independent of
the center of mass motion
• Spreading is suppressed:
Q. Su, B.A Smetanko and RG, Opt. Exp. 2, 277 (1998)
• Spatial profile becomes asymmetrical :
0
0.5
1
1.5
2
0 0.2 0.4 0.6 0.8 1time (a.u.)
x
x NR
y, z
0.00
0.05
0.10
0.15
-40 -20 0 20position (a.u.)
E=1000
E=500
E=2000
x; t
Q. Su, B.A. Smetanko & RG, Las. Phys. 4, 93 (1998)
1
2
3
-10 0 10 20
P(x
,t)
x [a.u.]
t = 0 c
t = 4 c
t = 8 c(b)
0
1
2
3
-10 0 10 20
P(x
,t)
x [a.u.]
t = 0 c
t = 4 c
t = 8 c
(a)
Relativity Induces Chaos
non-relativistic => Liouville = Schrödingerrelativistic => ??? Liouville ≈ Dirac ????
Schrödinger = Newton Dirac ≈ Liouville
What a surprise ...
0
4
8
12
0 20 40 60 80 100
<x
> [
a.u.
]
t [in laser periods]
(a)
2
4
6
8
10
43 44 45 46
<x
> [
a.u.
]
t [in laser periods]
(b)
J. Kim and H. Lee, PRE 51, 1579 (1995):
Ý Ý x 0
2x E sin(t) + relativity => chaos
R.E. Wagner, P.J. Peverly, Q. Su & RG, PRA (subm.)
Relativity enhances resonances
Myth: relativity “heavier mass” slower motion
example: electron in laser and static magnetic field
Maximum speed v/c for each
0.20
0.40
0.60
0.80
1.0
0.003 0.004 0.005 0.006
L 0.0043 a.u.
E0 0.0500a.u.
non-relativistic
relativistic
L
Fact: relativity faster motion
R. Wagner, Q. Su & RG, PRL (submitted)
Novel steady spatial states: Cycloatoms
Non-relativistic Relativistic
Orbits stayin phase
Orbits dephaserelativistically
Time(in 2L
75
150
500
0
y
x
Relativistic dephasing model
relativistic (exact) dephasing model
x(t) x vx
sin t
vy
cos t 1
2 2
cos( t
cos t
y(t) y vy
sin t vx
cos(t) 1
2 2
1
sin t 1
sin t
Time
75
150
500
0
replace (V0)
Q. Su, R.E. Wagner, P.J. Peverly & RG, SPIE (in press)
Steady state spatial electron distributions
Multiple resonances
Fractional resonances
= 3 = 2 =
= 1/2 = 1/3
0
0.4
0.8
1.2
0 0.1 0.2 0.3 0.4 0.5
[a.u.]
= L
= L/2
= 2L
= 3L
= 3L/2
= 2L/3
= L/3
=
L/4
=
L/5
-2.0 104
0.0
2.0 104
-4 104 -2 104 0 2 104
-2.0 104
0.0
2.0 104
-4 104 -2 104 0 2 104
10-8
10-6
10-4
10-2
0 0.05 0.1 0.15 0.210-8
10-6
10-4
10-2
0 0.05 0.1 0.15 0.2
Scattered light spectra
non-relativistic relativistic
x
y
Single orbits
Corresponding spectra
L 0.150 a.u.
E0 1.000a.u.
0.172a.u.
R.E. Wagner, Q. Su & RG, PRA 60, No.4 (1999)
SummaryNumerical solution to the Dirac equation
Relativity leads to new phenomena in the spatial and temporal dynamics
• subnatural spreading
• chaos
• novel resonances => novel experiments
• cycloatoms
• dephasing
• scattered light spectra
www.phy.ilstu.edu/ILP