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

I2+ + In+ dissociation channels

I1+ + In+ dissociation channels

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

Generalize equationsGeneralize equations

10

0

000

),()(ottU

)()()( TpTf

/

1,1,2 RR

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