Femtosecond Dynamics of Molecules in Intense Laser

Fields

CPC2002T.W. Schmidt1, R.B. López-Martens2, G.Roberts3

University of Cambridge, UK

1. Universität Basel, Confoederatio Helvetica

2. Lunds Universitet, Sverige

3. University of Newcastle, UK

Talk Structure

» Introduction to intense field phenomena» Huge ac-Stark shifts in NO» Time resolved ac-Stark shift experiments

» Intense field manipulation of NO2 photodissociation dynamics

Intense field phenomena

• Characterized by non-perturbative phenomena

• Large ac-Stark shifts

• Multiphoton phenomena predominate

• Above Threshold Ionization

• Over-the-Barrier Ionization

• Tunnel-Ionization

• Light-Induced Potentials

OK, just how Intense is Intense?

109 Wcm-21010 1011 1012 1013 1014 1015 1016

1 VÅ-1 10 VÅ-1

Unfocussed ns dye laser

Focussed ns dye laser

Focussed re-gen fs laser

Fusion + Fissionresearch

Focussed ns Nd:YAG

Perturbative Non-perturbativeIt’s the end of spectroscopy as we know it...

Non-perturbative phenomena:Huge ac-Stark shifts in NO

»Depends on state, can be positive or negative.

»Ground state always negative (energy goes down).

»Excited states depends on neighbouring states &c.

»Rydberg states, = e2E2/4m2=Up - ponderomotive

energy

»How about intermediate states? e.g. Low Rydberg

»Test out the Ã2+ X2r transition of NO...

Experimental Scheme

60000

40000

20000

En

ergy

(cm

-1)

1.0 1.2 1.4 1.6 1.8 2.00

B()

X()

A (3s)

C (3p)D

RNO/Å

» Ã (v = 2) X (v = 0) 2-photon resonance is at 409.8 nm

» Sit above resonance and crank up intensity! (monitor fluorescence)

» Interpret results using semiclassical model of light matter interaction.

Experimental Setup

Ar+ laser fs oscillator

Weak 90 fs, 800 nm pulses (80 MHz)

PC

0.1 m lens

PMT

M/C

scope

Nd: YAG laser Amplifier

Intense 140 fs, 800 nm pulses (10 Hz)

KDP xtal

/2 plate

M400 nm

Static cell, NO 1.6 Torr

Intense 100 fs, 400 nm pulses (10 Hz)

0.2 m lens

M400 nm

Semiclassical Models

Calculate eigenstates as function of field strength

Choose basis set

Interpolate eigenstates and eigenvalues from calculations

Propagate time dependent Schrödinger equation by projecting onto time dependent eigenstates

Evaluate final population in excited state

Semiclassical Models

21800 22890 23980 25070 26160 27250

Sp

atia

lly in

tegr

ated

SF

E0 (a.u.)0.000

0.030

Frequency/cm-1

»Sixteen state model includes v = 0 - 5 for A,C,D states, v = 0 for X state.»Schrödinger Equation propagated by projecting wavefunction onto time dependent eigenstates.»Matrix elements from literature (experimental).

Semiclassical Models

»Four state model includes v = 2 for A,C,D states, v = 0 for X state.»Schrödinger Equation propagated as per 16 state model »Results simpler to interpret...

2448024960

2544025920

26400

0.0000.005

0.0100.015

0.0200.025

0.030

0.00.20.40.60.81.0

frequency (cm-1)

|aA(2) |2

E0 (a.u.)

… in comparison

24480 24960 25440 25920 264000.000

0.0100.020

0.030

00.10.20.30.40.50.60.7

frequency (cm-1 )

E0 (a.u.)

00.20.40.60.8

11.2

frequency (cm-1 )

E0 (a.u.)0.000

0.0100.020

0.030

24416 24852 25288 25724 26160

4 - state model

16 - state model

Results10000

Peak Intensity (1013Wcm-2)

400 nm

0 1 2 3 4 5 6

410 nm

405 nm

S F (

arb.

uni

ts)

»Upper state is shifted into bandwidth of 400 nm laser at about 2×1013Wcm-2.

»16 state semiclassical model not perfect, but confirms intepretation

»state shifts at approximately 50% of ponderomotive energy.

16 state model4 state modelexperimental

The Next Step...

»We want to know exactly what we’re doing to the NO molecules…

»Can we time resolve the shifting states?

»Can we utilise the shift to effect dynamics?

Time-Resolved ac Stark Effect

400 nmprobe

Stark pulse delay

stat

e en

ergy

Unperturbed A state

A state shifted intoresonance by Stark pulse

A state shifted out of resonanceby Stark pulse (strong probe)

Ground state

Experimental Setup

Ar+ laser fs oscillator

Nd:YAG laser Regen. Amp.

PC

scope

800 nm 10 Hz

delay stageNO/Ar mixture

to rotary pump

PMT

M/CMB

400 nm

Results… shifting the state into resonance

-1.0 -0.5 0.0 0.5 1.0time delay (ps)

fluo

resc

ence

(ar

b. u

nits

)

I400nm = 5.3 TWcm-2

2.4 TWcm-2

3.4 TWcm-2

5.8 TWcm-2

7.9 TWcm-2

9.9 TWcm-2

IStark

shifting the state out of resonance

-2.0 -1.0 0.0 1.0 2.0time delay (ps)

fluo

resc

ence

(ar

b. u

nits

)

I400nm = 27 TWcm-2

3.3 TWcm-2

2.5 TWcm-2

1.8 TWcm-2

Semiclassical Models...

-400-200

200400 0.006

0.0070.008

0.0090.010

0.011

0.004

0.0050.006

0.0070.008

ES (a.u.)

ES (a.u.)

0

D (fs)

D (fs)

-400-200

200400

0

ES (a.u.)

ES (a.u.)

D (fs)

D (fs)

400-200

0200

400 0.006

0.007

0.008

0.009

0.010

0.011

0.004

0.005

0.006

0.007

0.008

400-200

0200

400

4 -

stat

e m

odel

3 -

stat

e m

odel

Conclusions...»AC Stark effect is time resolvable

»Can use one laser to shift, another to populate

»Ionization is important

»Is it possible to influence photodissociation dynamics in this way?

Doing it to NO2

NO2

NO2*

(X) NO + O

(A) NO* + O

»Same experimental setup as before

»400 nm acts as 3 photon pump

»monitor fluorescence from particular vibronic state of NO as function of delay between pump and probe

Results?

pump-probe delay (ps) pump-probe delay (ps)

-1.0 0.0 1.0 2.0-1.0 0.0 1.0 2.0

v’ =

0 f

luor

esce

nce

v’ =

1 f

luor

esce

nce

pump = 400 nmprobe = 800 nm

Ipump 5.3 TWcm-2.Iprobe 0.5; 1.0; 2.0; 4.0 TWcm-2.

0.5 TWcm-2

1.0 TWcm-2

2.0 TWcm-2

4.0 TWcm-2

0.5 TWcm-2

1.0 TWcm-2

2.0 TWcm-2

4.0 TWcm-2

Consider the coupled photon-molecule system

Ground state moleculeand n photons

|X,n>

Excited state moleculeand n photons

|A,n>

Excited state moleculeand n-1 photons

|A,n-1>

energy

•Excitation process becomes a curve crossing

•Franck-Condon Principle applies itself through normal curve crossing rules

•Intense laser causes avoided crossing

Ground state moleculeand n photons

|X,n>

Excited state moleculeand n-1 photons

|A,n-1>

energy

The Interpretation

1

2

|A,n>

|3s,n-2>

|3s,n-3> 3

»1. Direct 3 photon absorption

»2. AX then 2 photon absorption

»3. AX, XA dynamics, then 2 photon absorption

|X,n>

1. Direct 3 photon absorption

»Direct 3 photon absorption is FC weak at 400 nm.

»Increased avoided crossing by 800 nm will lessen its importance

»Channel only important at t0

»Will produce more v = 0?

80100

120140

160180 0.5

0.70.9

1.11.3

1.51.7

1.92.1

ON---O Bondlength (Ångströms)O-N-O Angle (degrees)

0

-30000-25000-20000-15000-10000

-50000

5000|X 2A1,n

|3s,n-3

2. AX then 2 photon absorption

»A state populated on leading edge of laser pulse

»Increased avoided crossing by 800 nm will trap population above and below seam.

»Dynamics on A state may lead to preference for v = 0, enhanced by 800 nm irradiation 200 fs after peak of 400 nm pulse...

3. AX , XA dynamics, then 2 photon absorption

»Channel is statistical

»molecules cross as they trickle down from A state.

»Channel important while 400 nm laser is on

»Probably responsible for v = 1 signal.

80100

120140

160180 0.5

0.70.9

1.11.3

1.51.7

1.92.1

05000

1000015000200002500030000

ON---O Bondlength (Ångströms)O-N-O Angle (degrees)

Conclusions and Questions...

» Production of v’ = 1 takes approximately 400 fs.

» Is the second channel responsible for enhanced v’ = 0 at t = 200 fs?

» Other wavelengths produce consistent results

» Need better photoproduct diagnostics to fully understand dynamics

» Theoretical results would be interesting!

» Can intense fields be used to control photodissociation?

Acknowledgements» Research Studentship, Churchill College,

Cambridge

» Eleanora Sophia Wood Travelling Scholarship, University of Sydney

» EPSRC

» Royal Society of London

…. and these guys