Transcript Slide 1

Strong-field physics revealed through
time-domain spectroscopy
George N. Gibson
Grad student:
University of Connecticut
Department of Physics
Li Fang
Funding:
NSF-AMO
May 30, 2009
XI Cross Border Workshop on Laser Science
University of Ottawa, Ottawa, Canada
Motivation



Vibrational motion in pump-probe experiments
reveals the role of electronically excited
intermediate states.
This raises questions about how the intermediate
states are populated. Also, we can study how
they couple to the final states that we detect.
We observe inner-orbital ionization, which has
important consequences for HHG and quantum
tomography of molecular orbitals.
Pump-probe experiment with
fixed wavelengths.
In these experiments
we used a standard
Ti:Sapphire laser:
I22+
14
Energy [eV]
12
10
8
I2+ + I
800 nm
23 fs pulse duration
1 kHz rep. rate
Probe
6
4
2
I1+ + I1+
Pump
0
3
6
9
12
Internuclear separation, R [a.u.]
15
Pump-probe spectroscopy on I22+
)3,2(
0083
)4,2(
)2,2(
Enhanced
Excitation
)1,2(
)0,2(
0063
thgilf-fo-emiT
)0,2(
]sn[
0073
)1,2(
Enhanced
Ionization at Rc
)4,2(
)3,2(
)2,2(
0053
Internuclear separation of dissociating molecule
0043
Lots of vibrational structure in
pump-probe experiments
Vibrational structure
Depends on:
 wavelength (400 to 800 nm).
 relative intensity of pump and probe.
 polarization of pump and probe.
 dissociation channel.
 We learn something different from each signal.

Will try to cover several examples of
vibrational excitation.
I2+ pump-probe data
(2,0) vibrational signal


Amplitude of vibrations so large that we can
measure changes in KER, besides the signal
strength.
Know final state – want to identify intermediate
state.
I2 potential
energy curves
Simulation of A state
Simulation results
From simulations:
- Vibrational period
- Wavepacket structure
- (2,0) state
What about the dynamics?




How is the A-state populated?
I2  I2+  (I2+)* - resonant excitation?
I2  (I2+)* directly – innershell ionization?
No resonant transition from X to A state in I2+.
From polarization studies



The A state is only produced with the field
perpendicular to the molecular axis. This is
opposite to most other examples of strong field
ionization in molecules.
The A state only ionizes to the (2,0) state!?
Usually, there is a branching ratio between the
(1,1) and (2,0) states, but what is the orbital
structure of (2,0)?
Ionization of A to (2,0) stronger with parallel
polarization.
Implications for HHG and QT



We can readily see ionization from orbitals
besides the HOMO.
Admixture of HOMO-1 depends on angle.
Could be a major problem for quantum
tomography, although this could explain
some anomalous results.
(2,0) potential curve retrieval
It appears that I22+ has a truly bound potential well, as opposed
to the quasi-bound ground state curves. This is an excimer-like
system – bound in the excited state, dissociating in the ground
state. Perhaps, we can form a UV laser out of this.
Wavelength-dependent pump probe scheme
Change inner and outer turning
points of the wave packet by
tuning the coupling wavelength.

Femtosecond laser pulses:
Pump pulse: variable
wavelength. (517 nm, 560 nm
and 600 nm.) Probe pulse: 800
nm.

Vibrational period (fs)
I2+ spectrum: vibrations in signal strength and kinetic energy release
(KER) for different pump pulse wavelength [517nm, 560 nm and 600 nm]
X-B coupling
wavelength (nm)
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.
I2+ + In+ dissociation channels
Neutral ground state
vibrations in I2


Oscillations in the data appear to come from the
X state of neutral I2.
Measured the vibrational frequency and the
revival time.
Power spectrum
[arb. unit]
Dissociation energy (eV)
Revival
structure
1.10
1.08
1.06
FFT of simulation
FFT of data
3
2
1
0
6.20
6.25
6.30
6.35
Freqency [1/ps]
6.40
6.45
1.04
1.02
(a) Data
1.00
2.69 0
5
10
15
20
25
30
35
15
20
25
30
35
R (Å)
2.68
2.67
2.66
2.65
(b) Simulation
2.64
0
5
10
Pump-probe delay (ps)

Vibrational frequency
Measured
211.00.7 cm-1
Known
215.1 cm-1
Finite temp 210.3 cm-1
Raman scattering/Bond softening

Raman transitions
are made possible
through coupling
to an excited
electronic state.
This coupling also
gives rise to bond
softening, which is
well known to
occur in H2+.
Raman transition
h
Distortion of potential
curve through bondsoftening
Lochfrass

New mechanism for vibrational excitation: “Lochfrass”
R-dependent ionization distorts the ground state
wavefunction creating vibrational motion.

R-dependent
ionization
Seen by Ergler et al.
PRL 97, 103004 (2006)
in D2+.
Lochfrass vs. Bond softening
Can distinguish these two effects through the
phase of the signal.
Bond-softening
Lochfrass
2.03

<R> [a.u.]

2.02

2.01
2.00
0
200
400
Pump-probe delay [fs]
600
LF = 
BS = /2.
Iodine vs. Deuterium
Iodine better resolved:
23 fs pulse/155 fs period = 0.15 (iodine)
7 fs pulse/11 fs period = 0.64 (deuterium)
 Iodine signal huge:
 DS/Save = 0.10
 DS/Save = 0.60

Variations in kinetic energy
18
16
et
+
10
Req,ion
I2 Xg,3/2
22
I2 Xg
21
1
20
19
0
Req,GES
2.5
=0
3.0
R(Å)
3.5
18
4.0
2+
2+
I2 (2,0)
12
I2 potential energy (eV)
30
Probe pulse
14
+
I2, I2 potential energy (eV)
t
n

35
Amplitude of the
motions is so large we
can see variations in
KER or <R>.
Temperature effects
Deuterium vibrationally cold at room temperature
Iodine vibrationally hot at room temperature
 Coherent control is supposed to get worse at high
temperatures!!! But, we see a huge effect.
Intensity dependence also unusual
 We fit <R> = DRcos(wt+) +Rave
As intensity increases, DR increases, Rave decreases.

Intensity dependence

Also, for Lochfrass signal strength should
decrease with increasing intensity, as is seen.

But, Rave  temperature:
5
4.5
4
Potential energy [eV]
3.5
3
2.5
2
v= 5
1.5
v= 4
v= 3
1
v= 2
0.5
v= 1
0
0
0.5
1
1.5
2
2.5
3
3.5
Internuclear separation, R [atomic units]
4
4.5
5
T decreases while DR increases!!!
We have an incoherent sea of thermally
populated vibrational states in which we
ionize a coherent hole:

So, we need a density matrix approach.
Density matrix for a 2-level model

For a thermal system
 p1 (T )
i (T )  
 0
0 

p2 (T )
where p1(T) and p2(T) are
the Boltzmann factors.
This cannot be written as
a superposition of state
vectors.
e
g
o
Time evolution of 

We can write:
i (t )  p1 (T )   p2 (T )  ,
(1)


(1)
( 2)
1 0 ( 2) 0 0

,  


0 0 
0 1 
These we can evolve in time.
Coherent interaction – use /2 pulse for
maximum coherence
 (f1)
 12
  i iw o t
 2 e
i
2
e iwot  ( 2)  12
,



 i iwot
f
1
2

2 e
1

2
 f (T )   i
iw o t

(
p
(
T
)

p
(
T
))
e
2
 2 1

Off diagonal terms have
opposite phases. This means
that as the temperature
increases, p1 and p2 will tend to
cancel out and the coherence
will decrease.
i
2
 2i e iwot 

1
2

( p1 (T )  p2 (T ))e
1
2
 iw o t



R-dependent ionization – assume
only the right well ionizes.
yf = (yg + ye)/2

 14
  1 iw o t
4 e
1
4
e
 iwo t




(1)

Trace() = ½ due to ionization
1
4
What about excited state?

( 2)
 14
  1 iw o t
4 e
1
4
e
 iw o t
1
4

   f (T )

NO
TEMPERATURE
DEPENDENCE!
Expectation value of R, <R>
R  Trace( R )  Ro ( 12  21 )
R
Coherent
R
 Ro sin( wot )( p1 (T )  p2 (T ))
Lochfrass
Ro

cos(wot )
2
The expectation values are /2 out of
phase for the two interactions as expected.
Comparison of two interactions
Coherent interactions:
 Off diagonal terms are
imaginary.
 Off diagonal terms of
upper and lower states
have opposite signs and
tend to cancel out.
R-dependent ionization
 Off-diagonal terms are
real.
 No sign change, so
population in the upper
state not a problem.
Motion produced by coherent interactions
and Lochfrass are /2 out of phase.
“Real” (many level) molecular system



Include electronic
coupling to excited
state.
Use I(R) based on ADK
rates. Probably not a
good approximation but
it gives R dependence.
Include  = 0 - 14
Raman transition
h
Distortion of potential
curve through bondsoftening
Generalize equations
 ( )
0 0 0 
0 


 U (t , to ) 
0

1




   /  


 f (T )   p (T )  ( )

DR  2  R , 1  , 1

Same conclusions
For bond-softening
 Off-diagonal terms are imaginary and opposite
in sign to next higher state. 12(1)  -12(2)
 DR decreases and <> increases with
temperature.
For Lochfrass
 Off diagonal terms are real and have the same
sign. 12(1)  12(2)
 DR increases and <> decreases with
temperature.

Excitation from Lochfrass will always yield
real off diagonal elements with the same sign
for excitation and deexcitation [f(R) is the
survival probablility]:
c12  y ( R)y 1 ( R) f ( R)dR
*
2
c21  y ( R)y 2 ( R) f ( R)dR
*
1
3.5
DR and <>
3.0
<v>
2.5
2.0
1.5
<v> - initial
<v>f - bondsoftening
1.0
0.5
<v>f - Lochfrass
0.0
DR [a.u.]
0.25
Bondsoftening
actual
0.20
max
Lochfrass
0.15
actual
max
0.10
0.05
0.00
0.00
0.03
0.06
0.09
kBT [eV]
0.12
0.15
Density matrix elements
Bond-softening
0.12
0.04
0.09
0.03
5
1
2
3
0.01
0.00 1
5
m
2 3
n 4
4
0.02
0.8
0.8
0.6
0.4
2 3
n 4
5
1
2
3
5
4
m
0.2
0.0 1
 nm/ nm
max
1.0
 nm/ nm
1.0
2 3
n 4
5
1
2
3
4
5
m
0.06
0.6
0.4
0.2
0.0 1
2 3
4
n
5
1
2
3
4
5
m
 nm
0.05
 nm
0.15
0.03
0.00 1
max
Lochfrass
Conclusions
Coherent reversible interactions
 Off-diagonal elements are imaginary
 Excitation from one state to another is out-of-phase
with the reverse process leading to a loss of coherence
at high temperature
 Cooling not possible
Irreversible dissipative interactions
 Off-diagonal elements are real
 Excitation and de-excitation are in phase leading to
enhanced coherence at high temperature
 Cooling is possible
Conclusions

Excitation of the A-state of I2+
through inner-orbital ionization

Excitation of the B-state of I2 to
populate the bound region of (2,0)
state of I22+

Vibrational excitation through
tunneling ionization.
Laser System
• Ti:Sapphire 800 nm Oscillator
• Multipass Amplifier
• 750 J pulses @ 1 KHz
• Transform Limited, 25 fs pulses
• Can double to 400 nm
• Have a pump-probe setup
Ion Time-of-Flight
Spectrometer
Parabolic Mirror
Drift Tube
MCP
Conical Anode
AMP
Laser
TDC
PC
Discriminator
Phase lag
Ionization geometry
Ionization geometry
2+
I
pump-probe data