Robert E. Wagner

Sophomore

Intense Laser Physics Theory Unit

Illinois State University

What are Cycloatoms?

Support: NSF, Res. Corp., and ISU Honors Program

More Technical:

Use RK4 to solve this

Laser

Magnetic field

d

dt

mv

1 v2

c2

qE t q

c

v

B o

B t V

r

0.20

0.40

0.60

0.80

1.0

0.003 0.004 0.005 0.006

Maximum speed v/c for each

L 0.0043a.u.

E0 0.0500a.u.

non-relativistic

relativistic

L

Can we use classical mechanics to approximate quantum????

realization in terms of classical particles

|(r)|2

High probability

Large density

Can we use classical mechanics to approximate quantum????

? ? ? ?

Summary

1. Pqm(r,t=0) => Pcl(r,t=0)

2. realize Pcl(r,t=0) in terms of 100,000 single trajectories

3. solve time evolution of each trajectory

4. compute a “smoothed” histogram = Pcl(r,t)

choose wisely:Pcl

r , t exp

r

r n (t) 2

22

n1

100,000

too small too large

Non-relativistic Relativistic

Orbits stayin phase

Orbits dephaserelativistically

Time(in 2L

75

150

500

0

y

x

Non-relativistic Movie

=L

QuickTime™ and aGIF decompressor

are needed to see this picture.

Relativistic Movie

=L

QuickTime™ and aGIF decompressor

are needed to see this picture.

relativistic (exact) dephasing model

Time

75

150

500

0

Relativistic 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

replace (V0)

Steady state spatial electron distributionsMultiple resonances

Q. Su, R.E. Wagner, P.J. Peverly & RG, SPIE (in press)

Fractional resonances= 1/2 L = 1/3 L

=L

= 2 L

= 3 L

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

Fractional Resonance

=1/2 L

QuickTime™ and aGIF decompressor

are needed to see this picture.

Fractional Resonance

=1/3 L

QuickTime™ and aGIF decompressor

are needed to see this picture.

SummaryRelativity leads to new phenomena in

the spatial and temporal dynamics

• novel resonances => novel experiments • cycloatoms

• dephasing

[1] R.E. Wagner, Q. Su and R. Grobe, Phys. Rev. Lett. (April, 2000).[2] R.E. Wagner, Q. Su, and R. Grobe, Phys. Rev. A 60, 3233, 1999.[3] P.J. Peverly, R.E. Wagner, Q.Su and R. Grobe, Las. Phys. 10, 303 ( 2000).[4] Q. Su, R.E. Wagner, P.J. Peverly, and R. Grobe, SPIE (in press).[5] R.E. Wagner, P.J. Peverly, Q. Su and R. Grobe, Phys. Rev. A (in press).

www.phy.ilstu.edu/ILP