Transcript Slide 1

Strong-field physics revealed
through time-domain spectroscopy
George N. Gibson
University of Connecticut
Department of Physics
May 20, 2009
DAMOP
Charlottesville, VA
Grad student: Li Fang
Funding: NSF-AMO
Pump-Probe Spectroscopy

I22+
14
Energy [eV]
12
10
8
I2+ + I
Probe

6
4
2
I1+ + I1+
Pump
0
3
6
9
12
Internuclear separation, R [a.u.]
15
We started doing
transient
spectroscopy on
dissociating
molecules.
While this
worked, we
found a huge
amount of
vibrational
structure.
I2+ + In+ dissociation channels
I1+ + In+ dissociation channels
Questions we can ask:






What kinds of non-dissociating intermediate
states can be populated by the strong laser field?
How do these states couple to the final state?
Do we learn anything about the final state?
Intensity dependence
Wavelength dependence
Geometry or polarization dependence
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, to get the first derivative of
frequency vs. n.
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
hn
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+.
Phase of the motion

If Ipump(R) and Iprobe(R) are the same, as they
would be, to first order, the phase of the signal
is  =  for S() = Socos( + ).
Takes 1/2 an oscillat ion for "hole" to fill in
so that more ionization can occur.
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
n=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(t+) +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 i o t
 2 e
i
2
e iot  ( 2)  12
,



 i iot
f
1
2

2 e
1

2
 f (T )   i
i 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 iot 

1
2

( p1 (T )  p2 (T ))e
1
2
 i o t



R-dependent ionization – assume
only the right well ionizes.
yf = (yg + ye)/2

 14
  1 i o t
4 e
1
4
e
 io t




(1)

Trace() = ½ due to ionization
1
4
What about excited state?

( 2)
 14
  1 i o t
4 e
1
4
e
 i 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( ot )( p1 (T )  p2 (T ))
Lochfrass
Ro

cos(ot )
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 n = 0 - 14
Raman transition
hn
Distortion of potential
curve through bondsoftening
Generalize equations
 (n )
0 0 0 
0 


 U (t , to ) 
0

1




n  nnn /  nn
n
n
 f (T )   pn (T )  (n )
n
DR  2  Rn ,n 1 n ,n 1
n
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 <n> increases with
temperature.
For Lochfrass
 Off diagonal terms are real and have the same
sign. 12(1)  12(2)
 DR increases and <n> 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 <n>
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