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Strong-field physics Strong-field physics revealed through time-revealed through time-domain spectroscopy domain spectroscopy
Grad student: Grad student: Li Li FangFang
FundingFunding: : NSF-NSF-AMOAMO
May 20, 2009May 20, 2009DAMOPDAMOP
Charlottesville, VACharlottesville, VA
George N. George N. GibsonGibsonUniversity of University of ConnecticutConnecticut
Department of Department of PhysicsPhysics
Pump-Probe Pump-Probe SpectroscopySpectroscopy
We started We started doing transient doing transient spectroscopy spectroscopy on dissociating on dissociating molecules.molecules.
While this While this worked, we worked, we found a found a huge huge amount of amount of vibrational vibrational structure.structure.
3 6 9 12 150
2
4
6
8
10
12
14
Ene
rgy
[eV
]
Internuclear separation, R [a.u.]
I22+
I2+ + I
I1+ + I1+Pump
Probe
Questions we can ask:Questions we can ask: What kinds of non-dissociating What kinds of non-dissociating
intermediate states can be populated by intermediate states can be populated by the strong laser field?the strong laser field?
How do these states couple to the final How do these states couple to the final state?state?
Do we learn anything about the final state?Do we learn anything about the final state?
Intensity dependenceIntensity dependence Wavelength dependenceWavelength dependence Geometry or polarization dependenceGeometry or polarization dependence
Neutral Neutral ground state ground state
vibrations in Ivibrations in I22
Oscillations in the data appear to Oscillations in the data appear to come from the X state of neutral Icome from the X state of neutral I22..
Measured the vibrational frequency Measured the vibrational frequency and the revival time, to get the first and the revival time, to get the first derivative of frequency vs. derivative of frequency vs. ..
Revival Revival structurestructure
0 5 10 15 20 25 30 352.64
2.65
2.66
2.67
2.68
2.69 0 5 10 15 20 25 30 351.00
1.02
1.04
1.06
1.08
1.10
6.20 6.25 6.30 6.35 6.40 6.450
1
2
3
(b) SimulationR
(Å
)
Pump-probe delay (ps)
(a) DataDis
soci
atio
n en
ergy
(eV
)
Pow
er s
pect
rum
[ar
b. u
nit]
Freqency [1/ps]
FFT of simulation FFT of data
Vibrational frequencyVibrational frequencyMeasuredMeasured 211.0211.00.7 cm0.7 cm-1-1
KnownKnown 215.1 cm215.1 cm-1-1 Finite tempFinite temp 210.3 cm210.3 cm-1-1
Raman scattering/Bond Raman scattering/Bond softeningsoftening
Raman Raman transitions are transitions are made possible made possible through coupling through coupling to an excited to an excited electronic state. electronic state. This coupling This coupling also gives rise to also gives rise to bond softening, bond softening, which is well which is well known to occur known to occur in Hin H22
++..
h
Raman transition
Distortion of potentialcurve through bond-softening
R-dependentionization
LochfrassLochfrass New mechanism for vibrational excitation: New mechanism for vibrational excitation:
“Lochfrass”“Lochfrass”R-dependent ionization distorts the ground R-dependent ionization distorts the ground state wavefunction creating vibrational motion.state wavefunction creating vibrational motion.
Seen by Ergler Seen by Ergler et et alal. PRL . PRL 9797, , 103004 (2006) in 103004 (2006) in DD22
++..
Phase of the motionPhase of the motion If IIf Ipumppump(R) and I(R) and Iprobeprobe(R) are the same, as (R) are the same, as
they would be, to first order, the phase they would be, to first order, the phase of the signal is of the signal is = = for S( for S() = S) = Soocos(cos( + + ).).
Takes 1/2 an oscillat ion for "hole" to fill in
so that more ionization can occur.
Lochfrass vs. Bond Lochfrass vs. Bond softeningsoftening
Can distinguish these two effects Can distinguish these two effects through the phase of the signal.through the phase of the signal.
0 200 400 600
2.00
2.01
2.02
2.03
Bond-softening Lochfrass
<R
> [
a.u.
]
Pump-probe delay [fs]
LFLF = = BSBS = = /2./2.
Iodine vs. DeuteriumIodine vs. Deuterium
S/SS/Saveave = 0.60 = 0.60
Iodine better resolved:Iodine better resolved:23 fs pulse/155 fs period = 0.15 (iodine)23 fs pulse/155 fs period = 0.15 (iodine)7 fs pulse/11 fs period = 0.64 7 fs pulse/11 fs period = 0.64
(deuterium)(deuterium) Iodine signal huge:Iodine signal huge:
S/SS/Saveave = 0.10 = 0.10
Variations in kinetic Variations in kinetic energyenergy Amplitude of the Amplitude of the
motions is so large motions is so large we can see we can see variations in KER or variations in KER or <R>.<R>.
2.5 3.0 3.5 4.0
0
1
10
12
14
16
18
18
19
20
21
22
30
35
R-dependentionization
Initialwavefunction
Final vibrational wavepacket
Internuclear separation, R
Pot
enti
al e
nerg
y
Req,ion
R(Å)
I+
2 X
g,3/2
=0
I2+ 2 p
oten
tial
ene
rgy
(eV
)I2+
2 (2,0)
I2 X
gI 2, I+ 2 p
oten
tial
ene
rgy
(eV
)
Req,GES
Probe pulse
Temperature effectsTemperature effects Deuterium vibrationally cold at room Deuterium vibrationally cold at room
temperaturetemperatureIodine vibrationally hot at room temperatureIodine vibrationally hot at room temperature
Coherent control is supposed to get worse at Coherent control is supposed to get worse at high temperatures!!! But, we see a huge high temperatures!!! But, we see a huge effect.effect.
Intensity dependence also unusualIntensity dependence also unusual We fit <R> = We fit <R> = Rcos(Rcos(t+t+) +R) +Raveave
As intensity increases, As intensity increases, R increases, RR increases, Raveave decreases.decreases.
Intensity dependenceIntensity dependence
Also, for Lochfrass signal strength should Also, for Lochfrass signal strength should decrease with increasing intensity, as is decrease with increasing intensity, as is seen.seen.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Internuclear separation, R [atomic units]
Pot
entia
l ene
rgy
[eV
]
v = 1
v = 2
v = 3
v = 4
v = 5
But, RBut, Raveave temperature: temperature:
T T decreasesdecreases while while R R increasesincreases!!!!!!
We have an incoherent sea of We have an incoherent sea of thermally populated thermally populated
vibrational states in which we vibrational states in which we ionize a coherent hole:ionize a coherent hole:
So, we need a density matrix approach.So, we need a density matrix approach.
Density matrix for a 2-Density matrix for a 2-level modellevel model
For a thermal systemFor a thermal system
where where pp11(T)(T) and and pp22(T)(T) are the Boltzmann are the Boltzmann factors. This cannot factors. This cannot be written as a be written as a superposition of superposition of state vectors.state vectors.
e
go
)(0
0)()(
2
1
Tp
TpTi
Time evolution of Time evolution of We can write:We can write:
These we can evolve in time.These we can evolve in time.
10
00,
00
01
,)()()(
)2()1(
)2(2
)1(1
TpTpti
Coherent interaction – use Coherent interaction – use pulse for maximum coherencepulse for maximum coherence
Off diagonal terms have Off diagonal terms have opposite phases. This opposite phases. This means that as the means that as the temperature increases, ptemperature increases, p11 and pand p22 will tend to cancel will tend to cancel out and the coherence will out and the coherence will decrease.decrease.
21
212
21221
21
2
221
)2(
21
2
221
)1(
))()((
))()(()(
,
tii
tii
f
tii
tii
ftii
tii
f
o
o
o
o
o
o
eTpTp
eTpTpT
e
e
e
e
R-dependent ionization – R-dependent ionization – assume only the right well assume only the right well
ionizes.ionizes. ff = ( = (gg + + ee)/2)/2
Trace(Trace() = ½ due to ) = ½ due to ionizationionization
41
41
41
41
)1(ti
ti
o
o
e
e
What about excited state?
)(41
41
41
41
)2( Te
efti
ti
o
o
NOTEMPERATUREDEPENDENCE!
Expectation value of R, Expectation value of R, <R><R>
)()( 2112 oRRTraceR
))()()(sin( 21 TpTptRR oo
Coherent
)cos(2
tR
R ooLochfrass
The expectation values are /2 out of phase for the two interactions as expected.
Comparison of two Comparison of two interactionsinteractions
Coherent Coherent interactionsinteractions::
Off diagonal terms Off diagonal terms are imaginary.are imaginary.
Off diagonal terms Off diagonal terms of upper and lower of upper and lower states have states have opposite signs and opposite signs and tend to cancel out.tend to cancel out.
R-dependent R-dependent ionizationionization
Off-diagonal terms Off-diagonal terms are real.are real.
No sign change, so No sign change, so population in the population in the upper state not a upper state not a problem.problem.
Motion produced by coherent interactions and Lochfrass are /2 out of phase.
““Real” (many level) Real” (many level) molecular systemmolecular system
Include electronic Include electronic coupling to excited coupling to excited state.state.
Use I(R) based on Use I(R) based on ADK rates. Probably ADK rates. Probably not a good not a good approximation but it approximation but it gives R dependence.gives R dependence.
Include Include = 0 - 14 = 0 - 14
h
Raman transition
Distortion of potentialcurve through bond-softening
Same conclusionsSame conclusionsFor bond-softeningFor bond-softening Off-diagonal terms are imaginary Off-diagonal terms are imaginary
and opposite in sign to next higher and opposite in sign to next higher state. state. 1212
(1)(1) - -1212(2)(2)
R decreases and <R decreases and <> increases > increases with temperature.with temperature.
For LochfrassFor Lochfrass Off diagonal terms are real and have Off diagonal terms are real and have
the same sign. the same sign. 1212(1)(1) 1212
(2)(2)
R increases and <R increases and <> decreases > decreases with temperature.with temperature.
Excitation from Lochfrass will always Excitation from Lochfrass will always yield real off diagonal elements with yield real off diagonal elements with the same sign for excitation and the same sign for excitation and deexcitation [f(R) is the survival deexcitation [f(R) is the survival probablility]:probablility]:
dRRfRRc
dRRfRRc
)()()(
)()()(
2*112
1*221
R and R and <<>>
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.00 0.03 0.06 0.09 0.12 0.150.00
0.05
0.10
0.15
0.20
0.25
<v>
<v> - initial <v>
f - bondsoftening
<v>f - Lochfrass
kBT [eV]
R [
a.u.
]
Bondsoftening actual max
Lochfrass actual max
Density matrix elementsDensity matrix elements
1 2 3 4 5
0.00
0.03
0.06
0.09
0.12
0.15
12
345
1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
12
345
1 2 3 4 5
0.00
0.01
0.02
0.03
0.04
0.05
12
345
1 2 3 4 5
0.0
0.2
0.4
0.6
0.8
1.0
12
345
nm
mn
Lochfrass
nm/m
ax
nm
mn
Bond-softening
nm
mn
nm/m
ax
nm
mn
ConclusionsConclusionsCoherent reversible interactionsCoherent reversible interactions Off-diagonal elements are imaginaryOff-diagonal elements are imaginary Excitation from one state to another is out-Excitation from one state to another is out-
of-phase with the reverse process leading of-phase with the reverse process leading to a loss of coherence at high temperatureto a loss of coherence at high temperature
Cooling not possibleCooling not possibleIrreversible dissipative interactionsIrreversible dissipative interactions Off-diagonal elements are realOff-diagonal elements are real Excitation and de-excitation are in phase Excitation and de-excitation are in phase
leading to enhanced coherence at high leading to enhanced coherence at high temperaturetemperature
Cooling is possibleCooling is possible