Strong-field physics Strong-field physics revealed through time-revealed through time-domain spectroscopydomain spectroscopy

Grad student:Grad student:Dr. Li Fang – now at Dr. Li Fang – now at

LCLSLCLSHui Chen, Vincent Hui Chen, Vincent

TagliamontiTagliamonti

FundingFunding: : NSF-AMONSF-AMONovember 7, 2011November 7, 2011Stony Brook UniversityStony Brook UniversityStony Brook, New YorkStony Brook, New York

George N. George N. GibsonGibsonUniversity of University of ConnecticutConnecticutDepartment of Department of PhysicsPhysics

What can strong-field What can strong-field physics offer chemistry?physics offer chemistry?

Time resolution: femtosecond laser pulses Time resolution: femtosecond laser pulses can resolve nuclear motion, Rcan resolve nuclear motion, R

Can control both R and Can control both R and

Can look at processes as a function of bothCan look at processes as a function of both Ultimate goal: Quantum tomography as a Ultimate goal: Quantum tomography as a

function of R – united atom to separated function of R – united atom to separated atomatom

Start with: End with:

Increasing internuclear separation:

2-D 1-electron double-well g wavefunctions:

Back to Basics:Back to Basics:Tunneling ionization of a Tunneling ionization of a

double-well potentialdouble-well potential((All strong field experiments on All strong field experiments on

molecules start here!molecules start here!))

Ionization is dominated Ionization is dominated by an effect called “by an effect called “R-R-

critical critical ””

Basic Tunneling Basic Tunneling Ionization:Ionization:

U1j 0

10 5 0 5 10

This separation is called “Rcritical”(Bandrauk, Seideman, Corkum, Ivanov)

Dynamics of 1 electron in Dynamics of 1 electron in field:field:

Dipole moment

Unified atom limit

Separated atom limit.Separated atom limit.

Intermediate case.Intermediate case.

Strongly driven gerade ungerade transition creates large dipole moments, compared to atoms or even-charged ground state molecules.

Data and calculations for Data and calculations for HH22

++::

0 2 4 6 8 10 12 140

5x104

1x105

2x105

2x105

Cou

nts/

shot

/torr

/a.u

.

R (Atomic Units)

End of story? This is from an ion. Also, not pump-probe,so a number of assumptions were made.

0 2 4 6 8 10 12 140.00

0.05

0.10

0.15

0.20

0.25

0.30

Ioni

zatio

n fr

actio

n

Separation (a.u.)

Better: Zuo and Bandrauk, PRA (1995), Data: Gibson et al., PRL (1997)

Simple 1-D 1-eSimple 1-D 1-e-- calculation:calculation:

0 2 4 6 8 10 12 140.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

1-photonresonance

3-photonresonance

Dip

ole

mom

ent,

Ioni

zatio

n Pr

obab

ility

Internuclear Separation

Ionization*50 Final Dipole Moment Max Dipole Moment

Simple model for RSimple model for Rcc

For HFor H22++, R, Rcc should be 3/(0.5) = 6, which is close. should be 3/(0.5) = 6, which is close.

Want to test in the neutral using pump-probe, since Want to test in the neutral using pump-probe, since most experiments start in the neutral species.most experiments start in the neutral species.

2/2/),(

RzQ

RzQRzV

)(neutralQII pp

pcc

pc

IRRQQI

RQ /3

2/2

Find condition where the inner barrier just equals the energy of the ground state:

Resonant excitation Resonant excitation provides a mechanism for provides a mechanism for

studying the neutralstudying the neutralUsing pump-probe Using pump-probe

techniques, we can techniques, we can control R.control R.

Resonant excitation Resonant excitation follows a cos(follows a cos())22 pattern, producing a pattern, producing a well-aligned and well-well-aligned and well-defined sample.defined sample.

This gives:This gives: <cos(<cos())22> = 0.6> = 0.6

at room at room temperature with temperature with one laser pulse.one laser pulse.

[For unaligned samples [For unaligned samples <cos(<cos())22> = 0.33]> = 0.33]

4 5 6 7 8 9 10 11 120

1

2

3

10

12

14

16

18

0

5

10

15

20

25

31.0

31.5

32.0

(2,0)u

(2,1)

B u+

I2

I+2

R (a.u.)

I2+ 2 p

oten

tial e

nerg

y (e

V)

X g,3/2

(1,1)

(2,0)g

I2+2

X g+

A u,3/2

I 2, I+ 2 p

oten

tial e

nerg

y (e

V)

Not to scale

Pum

p

Prob

e

Laser SystemLaser System• Ti:Sapphire 800 nm Oscillator with a Ti:Sapphire 800 nm Oscillator with a

Multipass AmplifierMultipass Amplifier• 750 750 J pulses @ 1 KHzJ pulses @ 1 KHz• Transform Limited, 30 fs pulsesTransform Limited, 30 fs pulses• TOPAS Optical Parametric Amplifer:TOPAS Optical Parametric Amplifer:

490nm – 2000nm490nm – 2000nm

Ion Time-of-Flight Ion Time-of-Flight SpectrometerSpectrometer

Laser

Drift Tube MCPConical Anode

Parabolic Mirror

AMP

DiscriminatorTDCPC

Nitrogen TOF SpectrumNitrogen TOF Spectrum

0 1000 2000 3000 4000 5000 60000

10000

20000

30000

40000

50000

60000

N4+

N3+N2+

N1+

Cou

nts/

(sho

t tor

r ns)

Time-of-flight [ns]2500 2600 2700 2800 2900 3000

0

10000

20000

30000

40000

50000

Zero

K.E

. TO

F

N3+ TOF Signal N3+ + N2+

N3+ + N1+

Cou

nts/

(sho

t tor

r ns)

Time-of-flight [ns]

Wavepacket motion in the B-state of I2 gives <R>(t)

Vib

ratio

nal p

erio

d (f

s)

X-B coupling wavelength (nm)

Ionization vs. RIonization vs. R We know <R(t)> from the motion on the B state.We know <R(t)> from the motion on the B state. Can convert from time to R(t).Can convert from time to R(t).

B-state wavepacket B-state wavepacket simulationsimulation

Wavelength check:Wavelength check:

-200 0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0 (a)

Ioni

zatio

n pr

obab

ility

[arb

. uni

ts]

Pump-probe delay [fs]

500nm 513nm

5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.00.0

0.2

0.4

0.6

0.8

1.0

Ioni

zatio

n pr

obab

ility

[arb

. uni

ts]

R [a.u.]

500nm 513nm

(b)

IpRc = 3.01

Shorter wavelength: larger outer turning point longer vibrational period

Really want to study the Really want to study the ground state!ground state!

Can we return the wavepacket to the X-state?Can we return the wavepacket to the X-state? Yes, with a pump-dump scheme:Yes, with a pump-dump scheme:

4 5 6 7 8 9 100

1

2

3

9

10

11

12

13

Dum

p

(a)

Prob

e

Pum

p

I2+: X 2g,3/2

I2:B 3u+ (g

2u4g

3u1)

I2: X 1g+ (g

24g

4)

I 2, I2+ P

oten

tial e

nerg

y [e

V]

R [a.u.]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.000.020.040.06

(2,1

) Sig

nal

3600

3650

3700

3750

3800

3850

3900

Delay [ps]

TOF

[ns]

(2,1)

(2,1)

(2,0)

Depletion of B-state into X-state

0.0 0.5 1.0 1.5 2.0 2.53600

3650

3700

3750

3800

3850

3900

Delay [ps]

TOF

[ns]

Returning wavefunction in Returning wavefunction in X-stateX-state

(2,0)

(2,1)

0 2 4 6 8 10 12 14 16 18 20 22 243600

3650

3700

3750

3800

3850

3900

Frequency [ps-1]

TOF

[ns]

X-state v=0"Lochfrass"

X-state v= 33!Returning wavepacket

Single ionization: ISingle ionization: I22++

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7FF

T Si

gnal

Frequency [ps-1]

Diatomic molecules in Diatomic molecules in strong fields:strong fields:

NN2 2 N N221+1+ NN22

2+2+ N N1+1+ + N + N1+1+

NN22

3+3+ N N1+1+ + N + N2+2+

NN22

4+4+ N N2+2+ + N + N2+2+

NN225+5+ N N3+3+ + N + N2+2+

NN22

6+6+ N N3+3+ + N + N3+3+

NN227+7+ N N4+4+ + N + N3+3+

NN2+2+ + N + N0+0+ (15.1 eV) (15.1 eV)

NN3+3+ + N + N1+1+ (17.8 eV) (17.8 eV)

NN4+4+ + N + N2+2+ (30.1 eV) (30.1 eV)

1400 1450 1500 15500

25

50

75

100

1251050 1075 1100 1125 1150 11750

3

6

9

12

15

(4,2)

(2,4)(2,4)

(2,3)

(2,3)(2,2)(2,2)

(2,1)(2,1)

N2+ Correlation with Early N4+

Correlation with Late N4+

Cou

nts/

(1k

shot

s)

Time of Flight [ns]

(4,3)(4,3)

(4,2)

N4+ Correlation with Early N2+

Correlation with Late N2+

Why is the observation of Why is the observation of Charge-Asymmtric Charge-Asymmtric

Dissociation so important?Dissociation so important? It represents direction excitation of states with It represents direction excitation of states with

energies in the VUV spectral region. (Up to 30eV in energies in the VUV spectral region. (Up to 30eV in NN22

6+6+).). Excitation involves many photons.Excitation involves many photons. Have seen everything up to IHave seen everything up to I22

12+12+ I I5+5+ + I + I7+7+.. Optimizing excitation process may lead to amplifiers Optimizing excitation process may lead to amplifiers

in the VUV as inversions are likely occurring.in the VUV as inversions are likely occurring. May be a new high-harmonic source.May be a new high-harmonic source. CAD is a ubiquitous and robust process:CAD is a ubiquitous and robust process:

There must be something generic about the There must be something generic about the structure of homonuclear diatomic molecules. structure of homonuclear diatomic molecules.

What is so special about What is so special about (even) charged diatomic (even) charged diatomic

molecules?molecules? Ground state Ground state is a far off-is a far off-resonant resonant covalent covalent state.state.

Above this is a Above this is a pair of pair of strongly strongly coupled ionic coupled ionic states.states.

Only a weak Only a weak coupling coupling between between them.them.

3-Level Model System3-Level Model System

This system can be solved exactly for the n-photon Rabi frequency!

0.114 0.116 0.118 0.120 0.122 0.124 0.126

0.0

0.2

0.4

0.6

0.8

1.0

11-p

hoto

nze

ro fi

eld

6-ph

oton

zero

fiel

d

Popu

latio

n

Photon Energy [a.u.]

Ground Ionic-u Ionic-g Covalent-u Covalent-g Ionization

Three-level systems:

“V”:

“”:

Now the “”:

Diatomic DicationsDiatomic Dications How are asymmetric states populated? Is it How are asymmetric states populated? Is it

through multiphoton transitions in the through multiphoton transitions in the --system?system?

(2,0) must have binding. In fact, it is an (2,0) must have binding. In fact, it is an excimer-like system, bound in upper state, excimer-like system, bound in upper state, unbound in lower state. Can we trap population unbound in lower state. Can we trap population in this state?in this state?

Can we make a multiphoton pumped excimer Can we make a multiphoton pumped excimer laser?laser?

We have evidence for bound population.We have evidence for bound population. Evidence for 3-Evidence for 3- excitation – but is it due to the excitation – but is it due to the

structure??? structure???

Need spectroscopic Need spectroscopic informationinformation

Namely, there should be (2,0)Namely, there should be (2,0)gg and (2,0) and (2,0)uu.. TOF spectroscopy not sensitive enough to TOF spectroscopy not sensitive enough to

distinguish them.distinguish them.

However, coherent 1However, coherent 122 fields provide an fields provide an interesting spectroscopic tool.interesting spectroscopic tool.

What are What are 1122

fields?fields?0 50 100 150 200 250 300

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 50 100 150 200 250 300-1.5

-1.0

-0.5

0.0

0.5

1.0

1.50 50 100 150 200 250 300

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Phase = /2

Phase = /4

Spat

ial d

irect

ion

Phase = 0

Time

If you add a fundamental laser frequency and its second harmonic, you can break spatial symmetry.

Molecular dissociationMolecular dissociation ChargeCharge-asymmetric dissociation is -asymmetric dissociation is

generally generally spatiallyspatially symmetric (with a symmetric (with a single frequency pulse).single frequency pulse).I.e., for II.e., for I2+2+ + I, the I + I, the I2+2+ goes to the left as goes to the left as much as to the right.much as to the right.

However, with a spatially-asymmetric However, with a spatially-asymmetric laser field can break the spatial laser field can break the spatial symmetry of the dissociation.symmetry of the dissociation.

Molecular dissociation,Molecular dissociation,with a 1with a 122 field field

Phase = 0

Phase = /2

Eigenstates vs. Eigenstates vs. ObservablesObservables

Observable: IObservable: I2+2+ + I + I (2,0) or (0,2) (left (2,0) or (0,2) (left or right)or right)

Eigenstates:Eigenstates: (2,0)(2,0)gg ~ (2,0) + (0,2) ~ (2,0) + (0,2)(2,0)(2,0)uu ~ (2,0) – (0,2) ~ (2,0) – (0,2)

Eigenstates Eigenstates mustmust dissociate spatially dissociate spatially symmetric.symmetric.

Therefore, a spatial asymmetry requires a coherent superposition of g and u states, which is only possible in a spatially asymmetric field.

Simple tunneling modelSimple tunneling model g and u states g and u states

strongly coupled – strongly coupled – diagonalize in a dc diagonalize in a dc field.field.

Assuming ionization Assuming ionization into the lowest into the lowest lying (down field) lying (down field) level.level.

Project back onto Project back onto field-free states and field-free states and calculate spatial calculate spatial asymmetry.asymmetry.

0 1 2 3 4 5 6 7 8 9 10-4.0

-3.5

-3.0

-2.5

-2.0

(2,0)up field

(2,0)down field

(1,1)g

(2,0)g

(2,0)u

A22+

Pote

ntia

l ene

rgy

[a.u

.]

R [a.u.]

Spatial asymmetry as a Spatial asymmetry as a function of Rfunction of R

We can measure the spatial asymmetry of the (2,0) We can measure the spatial asymmetry of the (2,0) dissociation channel by populating the B-state of Idissociation channel by populating the B-state of I22..

What do we learn from What do we learn from 1122 fields? fields?

In strong-field ionization, it appears that the In strong-field ionization, it appears that the field induced states are populated directly field induced states are populated directly through tunneling ionization.through tunneling ionization.

It is not the case that ionization populates It is not the case that ionization populates the ground state and the asymmetric states the ground state and the asymmetric states are then populated through the are then populated through the -system. -system. (Very difficult to reproduce the spatial (Very difficult to reproduce the spatial asymmetry dependence.)asymmetry dependence.)

Really must consider the field-induced Really must consider the field-induced molecular structure to understand strong-molecular structure to understand strong-field ionization.field ionization.

Also, raises interesting questions about Also, raises interesting questions about decoherence and dephasing.decoherence and dephasing.

ConclusionsConclusions Strong fields offer unprecedented Strong fields offer unprecedented

control over t, R, and control over t, R, and .. We also have considerable control We also have considerable control

over nuclear wavepackets.over nuclear wavepackets. Can measure strong field processes Can measure strong field processes

as a function of these variables.as a function of these variables. Can investigate the structure of Can investigate the structure of

unusual (highly ionized) molecules.unusual (highly ionized) molecules.