Strong-field physics revealed
through time-domain
spectroscopy
George N. Gibson
Grad student:
University of Connecticut
Department of Physics
Dr. Li Fang – now at LCLS
Hui Chen, Vincent Tagliamonti
Funding: NSF-AMO
November 7, 2011
Stony Brook University
Stony Brook, New York
What can strong-field physics offer
chemistry?


Time resolution: femtosecond laser pulses can
resolve nuclear motion, R
Can control both R and 
Start with:


End with:
Can look at processes as a function of both
Ultimate goal: Quantum tomography as a
function of R – united atom to separated atom
2-D 1-electron double-well g wavefunctions:
Increasing internuclear separation:
Back to Basics:
Tunneling ionization of a doublewell potential
(All strong field experiments on molecules start here!)
Ionization is dominated by an
effect called “R-critical ”
Basic Tunneling Ionization:
10
5
0
U1 ,
j0
5
10
This separation is called “Rcritical”
(Bandrauk, Seideman, Corkum, Ivanov)
Dynamics of 1 electron in field:
Unified atom limit
Dipole
moment
Separated atom limit.
Intermediate case.
Strongly driven gerade  ungerade transition
creates large dipole moments, compared to
atoms or even-charged ground state molecules.
Data and calculations for H2+:
5
0.30
2x10
0.25
5
Counts/shot/torr/a.u.
2x10
Ionization fraction
0.20
0.15
0.10
5
1x10
4
5x10
0.05
0
0.00
0
2
4
6
8
10
Separation (a.u.)
12
14
0
2
4
6
8
10
12
14
R (Atomic Units)
Better: Zuo and Bandrauk, PRA (1995), Data: Gibson et al., PRL (1997)
End of story? This is from an ion. Also, not pump-probe,
so a number of assumptions were made.
Simple 1-D
1-e
calculation:
Dipole moment, Ionization Probability
4.0
Ionization*50
Final Dipole Moment
Max Dipole Moment
3.5
3.0
1-photon
resonance
2.5
2.0
1.5
3-photon
resonance
1.0
0.5
0.0
0
2
4
6
8
10
Internuclear Separation
12
14
Simple model for Rc
Q
Q
V ( z , R)  

z R/2 zR/2
I p  QI p (neutral )
Find condition where the inner barrier just equals the energy
of the ground state:
2Q
Q

 QI p 
 Rc  3 / I p
Rc / 2
Rc


For H2+, Rc should be 3/(0.5) = 6, which is close.
Want to test in the neutral using pump-probe,
since most experiments start in the neutral species.
Resonant excitation provides a
mechanism for studying the neutral
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
2+
Probe
(2,0)u
14
+
I2, I2 potential energy (eV)
16
I2 potential energy (eV)
(2,0)g
Using pump-probe techniques,
we can control R.
Resonant excitation follows a
cos()2 pattern, producing a
well-aligned and well-defined
sample.
This gives:
<cos()2> = 0.6
at room temperature with
one laser pulse.
[For unaligned samples
<cos()2> = 0.33]
Laser System
• Ti:Sapphire 800 nm Oscillator with a Multipass
•
•
•
Amplifier
750 J pulses @ 1 KHz
Transform Limited, 30 fs pulses
TOPAS Optical Parametric Amplifer:
490nm – 2000nm
Ion Time-of-Flight
Spectrometer
Parabolic Mirror
Drift Tube
MCP
Conical Anode
AMP
Laser
TDC
PC
Discriminator
Nitrogen TOF Spectrum
60000
50000
3+
N TOF Signal
3+
2+
N + NN1+
3+
1+
N +N
40000
30000
30000
20000
20000
2+
N
3+
N
10000
10000
4+
00
0
2500
Zero K.E. TOF
Counts/(shot torr ns)
50000
40000
N
1000
2600
2000 2700 3000
28004000
Time-of-flight
Time-of-flight[ns]
[ns]
5000
2900
6000
3000
Vibrational period (fs)
Wavepacket motion in the B-state of I2 gives <R>(t)
X-B coupling
wavelength (nm)
Ionization vs. R


We know <R(t)> from the motion on the B state.
Can convert from time to R(t).
B-state wavepacket simulation
Wavelength check:
Shorter wavelength:
larger outer turning point
longer vibrational period
Ionization probability
probability [arb.
[arb. units]
units]
Ionization
IpRc = 3.01
1.0
500nm
513nm
500nm
513nm
(a)
(b)
0.8
0.6
0.4
0.4
0.2
0.2
0.0
0.0
-200
5.0 5.5 06.0
200 7.0 400
6.5
7.5
8.06008.5
R [a.u.]
Pump-probe
delay [fs]
800 9.5 1000
9.0
10.0
Really want to study the ground state!
13
(a)
12
11
+
2
I2 : X g,3/2
10
Probe
9
3
2
3
1
+
2
4
3
1
I2:B u (g u g u )
Dump
Pump
+

Can we return the wavepacket to the X-state?
Yes, with a pump-dump scheme:
I2, I2 Potential energy [eV]

1
+
2
4
4
I2: X g (g  g )
0
4
5
6
7
R [a.u.]
8
9
10
3900
Depletion of B-state into X-state
3850
(2,1)
TOF [ns]
3800
(2,0)
3750
3700
(2,1)
(2,1) Signal
3650
3600
0.06
0.04
0.02
0.00
0.0
0.1
0.2
0.3
0.4
0.5
Delay [ps]
0.6
0.7
0.8
0.9
1.0
Returning wavefunction in X-state
3900
3900
3850
3850
X-state v=0
"Lochfrass"
TOF [ns]
3800
3800
(2,1)
(2,0)
3750
3750
X-state v= 33!
Returning wavepacket
3700
3700
3650
3650
3600
3600
0
2
0.0
4
6
0.5
8 10 12
1.0
1.5 14 162.0 18 202.522 24
-1
Frequency
[ps ]
Delay [ps]
Single ionization:
+
I2
0.7
0.6
FFT Signal
0.5
0.4
0.3
0.2
0.1
0.0
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
-1
Frequency [ps ]
Diatomic molecules in strong fields:

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
Why is the observation of ChargeAsymmtric Dissociation so important?






It represents direction excitation of states with energies in
the VUV spectral region. (Up to 30eV in N26+).
Excitation involves many photons.
Have seen everything up to I212+  I5+ + I7+.
Optimizing excitation process may lead to amplifiers in
the VUV as inversions are likely occurring.
May be a new high-harmonic source.
CAD is a ubiquitous and robust process:
There must be something generic about the structure of homonuclear
diatomic molecules.
What is so special about (even)
charged diatomic molecules?
Ground state is a
far offresonant
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!
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
Three-level systems:
“V”:
“”:
Now the “”:
Diatomic Dications





How are asymmetric states populated? Is it through
multiphoton transitions in the -system?
(2,0) must have binding. In fact, it is an excimer-like
system, bound in upper state, unbound in lower
state. Can we trap population in this state?
Can we make a multiphoton pumped excimer laser?
We have evidence for bound population.
Evidence for 3- excitation – but is it due to the 
structure???
Need spectroscopic information



Namely, there should be (2,0)g and (2,0)u.
TOF spectroscopy not sensitive enough to
distinguish them.
However, coherent 12 fields provide an
interesting spectroscopic tool.
What are
12 fields?
1.5
Phase = 0
1.0
0.5
0.0
-0.5
-1.0
0
50
100
150
1.5
Spatial direction
If you add a
fundamental laser
frequency and its second
harmonic, you can break
spatial symmetry.
-1.5
200
250
300
250
300
Phase = /4
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
50
100
150
1.5
200
Phase = /2
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
50
100
150
Time
200
250
300
Molecular dissociation

Charge-asymmetric dissociation is generally
spatially symmetric (with a single frequency pulse).
I.e., for I2+ + I, the I2+ goes to the left as much as
to the right.

However, with a spatially-asymmetric laser field can
break the spatial symmetry of the dissociation.
Molecular dissociation,
with a 12 field
Phase = 0
Phase = /2
Eigenstates vs. Observables



Observable: I2+ + I  (2,0) or (0,2) (left or right)
Eigenstates: (2,0)g ~ (2,0) + (0,2)
(2,0)u ~ (2,0) – (0,2)
Eigenstates must dissociate spatially symmetric.
 Therefore, a spatial
asymmetry requires a coherent
superposition of g and u states,
which is only possible in a
spatially asymmetric field.
Simple tunneling model

-2.0
Potential energy [a.u.]
A2
2+
-2.5
(2,0)up field

(2,0)g
-3.0
(2,0)u
(2,0)down field

-3.5
(1,1)g
-4.0
0
1
2
3
4
5
6
R [a.u.]
7
8
9
10
g and u states strongly
coupled – diagonalize
in a dc field.
Assuming ionization
into the lowest lying
(down field) level.
Project back onto
field-free states and
calculate spatial
asymmetry.
Spatial asymmetry as a function of R

We can measure the spatial asymmetry of the (2,0)
dissociation channel by populating the B-state of I2.
What do we learn from 12 fields?




In strong-field ionization, it appears that the field
induced states are populated directly through tunneling
ionization.
It is not the case that ionization populates the ground
state and the asymmetric states are then populated
through the -system. (Very difficult to reproduce the
spatial asymmetry dependence.)
Really must consider the field-induced molecular
structure to understand strong-field ionization.
Also, raises interesting questions about decoherence
and dephasing.
Conclusions




Strong fields offer unprecedented control over t,
R, and .
We also have considerable control over nuclear
wavepackets.
Can measure strong field processes as a function
of these variables.
Can investigate the structure of unusual (highly
ionized) molecules.