Why I never let go of my Ph.D. thesis research!
Rhodes Scholars Symposium
University of Illinois, Chicago
March 28, 2012
Supported by:
National Science Foundation
Research Corporation
The story …
The review …
Major result: Inner-shell ionization
 Common assumption – only the least bound electron is
ionized by tunneling in a strong field and the resulting
ion is left in the ground state.
 Our (Gibson, Rhodes, et al.) result showed inner-shell
ionization and, consequently, excitation of the ion by
the strong laser field. In fact, excitation led to
fluorescence of a previously unobserved state of N 22+.
 Results met with some resistance!
 I continued to pursue this question in different ways as
a postdoc and a professor.
Postdoc work at Bell Labs
Could ionize the 1πu and
2σg electrons, as well.
Dissociation Channels:

N2  N21+  N22+  N1+ 2+
+ N1+ 0+
 N + N (15.1 eV)

N23+  N1+ + N2+

N24+  N2+ 3+
+ N2+ 1+
 N + N (17.8 eV)

N25+  N3+ + N2+

N26+  N3+ 4+
+ N3+ 2+
 N + N (30.1 eV)

N27+  N4+ + N3+
15
Counts/(1k shots)
12
4+
2+
Correlation with Early N
2+
Correlation with Late N
N
9
6
(4,2)
0
1050
125
100
1075
(4,3)
1100
1125
1150
1175
4+
2+
Correlation with Early N
4+
Correlation with Late N
N
(2,2)
75
(2,3)
50
25
(4,2)
(4,3)
3
(2,1)
(2,2)
(2,1)
(2,3)
(2,4)
(2,4)
0
1400
1450
1500
Time of Flight [ns]
1550
0
0
0.010
0.005
0.008
0.002
0.000
0.004
0.000
130
2.0
0.010 601.5
10
0.006
0.5
3
- 2s(2S)2p
2
2
0.0
123.6
100
140
2
2
2
70
-3
10
-4
123.8
0.1
2
3
N III:
2 2s2p - 2p
75
80
150
3
2
4
0
110
Wavelength [nm]
160
0.1
0.0
0.10
124.0 1 124.2 124.4
124.6100 124.8
10
Pressure
(mTorr)
0.00
Wavelength
[nm]
0.05
170
0
2
3
2
2
124.38nm
2
3
2
2
2
3
2N I:22s 2p - 2s 2p (3P)3s
N I: 2s 2p - 2s Plasma
2p (1D)3s
excitation
(124.32nm)
124.31nm
2
N V: 2s - 2p
(124.28nm) 1
100
25
2
3
2
2
2
3
2
2
N II: 2s (1S)2p - 2s(2S)2p
2
N III: 2s (1S)2p - 2s2p
3
High pressure/Late time
110
3
120
180
190
Time (ns)
50
3
N III: 2s (1S)2p - 2s2p
Direct excitation
2
VUV Impulse response
120
130
2
2
2
4
2
2
75
Unidentified
N V: 2s - 2p
3
N V: 2s - 2p
2
2
2
N I: 2s 2p - 2s 2p (1D)3s
3
N I: 2s 2p - 2sN I:2p
- 2s 2p (3P)3s
2s 2p (1D)3s
2
3
N I: 2s 2p - 2s2p
2
N I: 2s 2p - 2s 2p (3P)3s
N I: 2s 2p - 2s 2p (3P)3s
2
N IV: 2s(2S)2p - 2p [23.4 eV]
2
2
N IV: 2s(2S)2p - 2p
2
N II: 2s (1S)2p - 2s(2S)2p
Slope = 0.97
Low pressure/Early time
Slope
1.71= 0.025nm
Step= size
100
N I: 2s 2p - 2s2p
N III: 2s2p - 2p [25.2 eV]
3
90
2
Counts/1K Shot
2
N III: 2s (1S)2p - 2s2p
2
Impulse response
400 nm
115 nm
115 nm fit
N II: 2s (1S)2p - 2s(2S)2p
2
10
N I: 2s 2p - 2s 2p (3P)3s
-2
N II: 2s (1S)2p - 2s 2p(2P°)3s
2
2
N III: 2s (1S)2p - 2s2p
2
N III: 2s (1S)2p - 2s2p
1.0
2
2
2
123.90nm
50
-1
Time
N10V:(ns)2s - 2p
2.5 (123.88nm )
25
2
N II: 2s (1S)2p - 2s 2p(2P°)3s
2
Nitrogen
3.5
Unidentified
0.015
3.0
3
0
2
0.020
N II: 2s (1S)2p
Signal (arb)
2
eV]
1
2
3
Counts/shot/mtorr
N III: 2s2p - 2p [25.2
Signal (arb)
0.025
Unidentified
2
Counts/1K Shot
N IV: 2s(2S)2p - 2p
Intensity [a.u.]
N II: 2s (1S)2p - 2s(2S)2p
2
0.030
VUV Fluorescence Spectrum of N2
2
Plasma excitation
Unidentified
2
3
4
N I: 2s 2p - 2s2p
Molecular Lines?
125.0
200
100
130
Conclusions from VUV Spectra
Coffee and Gibson, PRA 69 (2004)
• Nitrogen shows many fluorescence lines
generated from direct strong field
excitation.
• In all cases, the excitation involves one or
two 2s holes.
• Some upper states consist of multiply
excited states. One is at 25 eV above the
ground state. N2+: 2s2p2 – 2p3.
• Direct lines identified from N4+ - a state not
seen in ion TOF data, until recently.
Theory of Multiphoton Coupling in
Molecules [PRL 89 263001, PRA 67 043401]
• Atoms do not show signs of multiphoton
excitation when exposed to strong laser
fields: at intensities high enough to drive
multiphoton transitions, the ac Stark shift
detunes the laser and ionization sets in.
• So, what is so special about ionized diatomic
molecules?
• They have an excited state structure that is
highly susceptible to multiphoton coupling.
2 electrons in a double well.
Ground state is a
far off-resonant
covalent state.
Above this is a
pair of strongly
coupled ionic
states.
Only a weak
coupling between
them.
3-Level Model System
This system can be solved exactly
for the n-photon Rabi frequency!
N-photon Rabi Frequency:
2-level frequency from Duvall (or Shirley), et al.:
In the 3-level system, multiphoton coupling depends on
R23 while the AC Stark shift depends on R12. In the 2level system, both effects come from the same coupling.
Perfect Floquet Ladder of States:
The pair of ionic states
are strongly modulated
by the laser field and
create a complete
Floquet ladder of states
– with no ac Stark shift!
The ground state
couples to this through
a 1-photon process
which only produces a
small Stark shift.
Example: Population transfer in a
model system: A24+.
1.0
0.4
11-photon
zero field
0.6
Ground
Ionic-u
Ionic-g
Covalent-u
Covalent-g
Ionization
6-photon
zero field
Population
0.8
0.2
0.0
0.114
0.116
0.118
0.120
0.122
Photon Energy [a.u.]
0.124
0.126
Again, a Floquet Ladder of States:
5
4
3
2
1
3
0
2
-1
The pair of strongly
coupled ionic states is
so effective, it can
assist a high-order
multiphoton transition
to a regular covalent
state!
-2
-3
1
Verified through a 5level calculation.
Transition requires R23
to be large.
Can even get adiabatic transfer
on a 10-photon transition!
1.0
0.8
Population
2
0.6
dE/dt = 6/Tn
0.4
0.2
0.0
0.15
0.20
0.25
Field Strength [a.u.]
0.30
Pump-probe experiments in I2
Iodine potential curves
32.0
(2,1) Not to scale
18
31.5
2+
I2
(1,1)
25
12
20
+

A u,3/2
10
I2
15

X g,3/2

B u
3
Pump
2
1

X g
31.0
+
10
+
5
I2
0
0
4
5
6
7
8
R (a.u.)
9
10
11
12
The (2,0) and (1,1) curves form an
excimer-type system in the
dication!
(2,0) is strictly bound while the
(1,1) is at best quasi-bound.
2+
Probe
(2,0)u
14
+
I2, I2 potential energy (eV)
16
I2 potential energy (eV)
(2,0)g
Many time-resolved pump-probe
experiments are possible. Right
now, we are specifically interested
in the I2+ + I0+ states.
Wanted to see if we could populate
the (2,0) states.
Populating the (2,0) state:
Simulation: trapped population in the (2,0) potential well
pump-probe delay=180 fs
The (2,0) potential curve
measured from the A
state of I2+ in our
previous work:
PRA 73, 023418 (2006)
V ( R)  De 1  exp(   ( R  Re ))   V0
2
De  60meV ,   1.48a.u.1 , Re  6.31a.u.
Asymmetric channels can show spatial
asymmetry in a 12 field


An asymmetric channel like (2,0) actually
consists of two states with gerade and ungerade
symmetry. Then one can form:
(2,0)R ~ (2,0)g + (2,0)u
(2,0)L ~ (2,0)g - (2,0)u
where R and L refer to the 2+ ion going to the
right or the left.
Of course, the (2,0)g and (2,0)u states must be
populated coherently.
I2+ TOF Region with 1ω2ω fields
3850
Time-of-Flight [ns]
3800
3750
3700
3650
0
50
100
150
Pump-probe delay [fs]
200
250
Experimental results
0.45
Fast (2,0)
Slow (2,0)
Amplitude of Right/Left Asymmetry
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
20
40
60
80
100
120
Time Delay [fs]
140
160
180
200
1-D 2-electron model
-2.0
From the asymmetry
measurements, we can show
that the ionization projects
the molecules into the fieldinduced states.
2+
A2
Potential energy [au]
-2.5
(2,0)up field
(2,0)g
-3.0
This has not really been
considered before and
suggests a new form of
strong-field control.
(2,0)u
(2,0)down field
-3.5
(1,1)g
-4.0
0
1
2
3
4
5
6
7
8
Internuclear Separation [au]
9
10
Conclusions
Strong laser fields do a lot more than just ionize the
least bound electron and leave the ion in its ground
state.
Diatomic molecules have a structure that is highly
susceptible to strong field excitation.
High levels of excitation are seen through the
dissociation channels and direct fluorescence from the
excited molecule.
Ionization occurs within the electronic structure
induced by the strong laser field.