The Physics of Charge-Asymmetric Molecular States

Why I never let go of my Ph.D. thesis research!

Rhodes Scholars SymposiumUniversity of Illinois, ChicagoMarch 28, 2012

Supported by:National Science FoundationResearch Corporation

The story …

The review …

Major result: Inner-shell ionizationCommon assumption – only the least bound

electron is ionized by tunneling in a strong field and the resulting ion is left in the ground state.

Our (Gibson, Rhodes, et al.) result showed inner-shell ionization and, consequently, excitation of the ion by the strong laser field. In fact, excitation led to fluorescence of a previously unobserved state of N2

2+.

Results met with some resistance!

I continued to pursue this question in different ways as a postdoc and a professor.

Postdoc work at Bell Labs

Could ionize the 1πu and 2σg electrons, as well.

Dissociation Channels:Dissociation Channels: NN2 2 N N22

1+1+ NN222+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 (15.1

eV)eV)

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

eV)eV)

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

eV)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+

60 70 80 90 100 110 120 1300.000

0.005

0.010

0.015

0.020

0.025

0.030

130 140 150 160 170 180 190 2000.000

0.002

0.004

0.006

0.008

0.010

N V

: 2s

- 2

p

N I:

2s2 2p

3 - 2

s2 2p2 (1

D)3

s

N I:

2s2 2p

3 - 2

s2 2p2 (3

P)3s

N I:

2s2 2p

3 - 2

s2p4

N I

I: 2

s2 (1S)

2p2 -

2s(

2S)2

p3

N I

II:

2s2 (1

S)2p

- 2

s2p2

N I

II:

2s2p

2 - 2

p3 [25

.2 e

V]

N I

V:

2s(2

S)2p

- 2

p2

N II

: 2s2 (1

S)2p

2 - 2

s(2S

)2p3

N II

I: 2

s2p2 -

2p3

N I

II:

2s2 (1

S)2p

- 2

s2p2

N II

: 2s2 (1

S)2p

2 - 2

s2 2p(

2P°)

3s

N I

II:

2s2 (1

S)2p

- 2

s2p2

N II

: 2s2 (1

S)2p

2 - 2

s2 2p(

2P°)

3s

N II

: 2s2 (1

S)2p

2 - 2

s(2S

)2p3

VUV Fluorescence Spectrum of N2

Inte

nsity

[a.

u.]

UnidentifiedMolecular Lines?

Uni

dent

ifie

d

N I:

2s2 2p

3 - 2

s2 2p2 (3

P)3s

N I

V:

2s(2

S)2p

- 2

p2 [23

.4 e

V]

Uni

dent

ifie

d

N I:

2s2 2p

3 - 2

s2 2p2 (3

P)3s

Uni

dent

ifie

d

Wavelength [nm]

0.1 1 10 100

10-4

10-3

10-2

10-1

Pressure (mTorr)

Sign

al (

arb)

Slope = 0.97Slope = 1.71

NitrogenSi

gnal

(ar

b)

0 25 50 75 1000

1

2 Impulse response 400 nm 115 nm 115 nm fit

Cou

nts/

1K S

hot

Time (ns)

0

1

2

0.0

0.1

0 25 50 75 1000.00

0.05

0.10

N III: 2s2(1S)2p - 2s2p2

Direct excitation

VUV Impulse response

Cou

nts/

1K S

hot

N I: 2s22p3 - 2s22p2(3P)3sPlasma excitation

N I: 2s22p3 - 2s2p4 Plasma excitation

Time (ns)60 70 80 90 100 110 120 1300.000

0.005

0.010

0.015

0.020

0.025

0.030

130 140 150 160 170 180 190 2000.000

0.002

0.004

0.006

0.008

0.010

N V

: 2s

- 2

p

N I:

2s2 2p

3 - 2

s2 2p2 (1

D)3

s

N I:

2s2 2p

3 - 2

s2 2p2 (3

P)3s

N I:

2s2 2p

3 - 2

s2p4

N I

I: 2

s2 (1S)

2p2 -

2s(

2S)2

p3

N I

II:

2s2 (1

S)2p

- 2

s2p2

N I

II:

2s2p

2 - 2

p3 [25

.2 e

V]

N I

V:

2s(2

S)2p

- 2

p2

N II

: 2s2 (1

S)2p

2 - 2

s(2S

)2p3

N II

I: 2

s2p2 -

2p3

N I

II:

2s2 (1

S)2p

- 2

s2p2

N II

: 2s2 (1

S)2p

2 - 2

s2 2p(

2P°)

3s

N I

II:

2s2 (1

S)2p

- 2

s2p2

N II

: 2s2 (1

S)2p

2 - 2

s2 2p(

2P°)

3s

N II

: 2s2 (1

S)2p

2 - 2

s(2S

)2p3

VUV Fluorescence Spectrum of N2

Inte

nsity

[a.

u.]

UnidentifiedMolecular Lines?

Uni

dent

ifie

d

N I:

2s2 2p

3 - 2

s2 2p2 (3

P)3s

N I

V:

2s(2

S)2p

- 2

p2 [23

.4 e

V]

Uni

dent

ifie

d

N I:

2s2 2p

3 - 2

s2 2p2 (3

P)3s

Uni

dent

ifie

d

Wavelength [nm]

123.6 123.8 124.0 124.2 124.4 124.6 124.8 125.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

124.31nmN V: 2s - 2p(124.28nm)

123.90nmN V: 2s - 2p(123.88nm )

124.38nm

N I: 2s22p3 - 2s22p2(1D)3s (124.32nm)C

ount

s/sh

ot/m

torr

Wavelength [nm]

High pressure/Late time Low pressure/Early time

Step size = 0.025nm

Conclusions from VUV SpectraCoffee and Gibson, PRA 69 (2004)

• Nitrogen shows many fluorescence lines generated from direct strong field excitation.

• In all cases, the excitation involves one or two 2s holes.

• Some upper states consist of multiply excited states. One is at 25 eV above the ground state. N2+: 2s2p2 – 2p3.

• Direct lines identified from N4+ - a state not seen in ion TOF data, until recently.

Theory of Multiphoton Coupling in Molecules [PRL 89 263001, PRA 67 043401]

• Atoms do not show signs of multiphoton excitation when exposed to strong laser fields: at intensities high enough to drive multiphoton transitions, the ac Stark shift detunes the laser and ionization sets in.

• So, what is so special about ionized diatomic molecules?

• They have an excited state structure that is highly susceptible to multiphoton coupling.

2 electrons in a double well.

Ground state is a far off-resonant covalent state.

Above this is a pair of strongly coupled ionic states.

Only a weak coupling between them.

3-Level Model System

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

N-photon Rabi Frequency:

2-level frequency from Duvall (or Shirley), et al.:

In the 3-level system, multiphoton coupling depends on R23 while the AC Stark shift depends on R12. In the 2-level system, both effects come from the same coupling.

Perfect Floquet Ladder of States:

The pair of ionic states are strongly modulated by the laser field and create a complete Floquet ladder of states – with no ac Stark shift!

The ground state couples to this through a 1-photon process which only produces a small Stark shift.

Example: Population transfer in a model system: A2

4+.

0.114 0.116 0.118 0.120 0.122 0.124 0.1260.0

0.2

0.4

0.6

0.8

1.0

6-p

hoto

nze

ro f

ield

Popu

latio

n

Photon Energy [a.u.]

Ground Ionic-u Ionic-g

Ionization

0.114 0.116 0.118 0.120 0.122 0.124 0.1260.0

0.2

0.4

0.6

0.8

1.0

11-p

hot

onze

ro f

ield

6-p

hoto

nze

ro f

ield

Popu

latio

n

Photon Energy [a.u.]

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

Again, a Floquet Ladder of States:

The pair of strongly coupled ionic states is so effective, it can assist a high-order multiphoton transition to a regular covalent state!

Verified through a 5-level calculation. Transition requires R23 to be large.

3

2

1

0

-1

-2

-3

2

3

1

4

5

Can even get adiabatic Can even get adiabatic transfer on a 10-photon transfer on a 10-photon

transition!transition!

0.15 0.20 0.25 0.300.0

0.2

0.4

0.6

0.8

1.0

dE/dt = 6/Tn

2

Popu

latio

n

Field Strength [a.u.]

Pump-probe experiments in I2

Iodine potential curves

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 scalePu

mp

Prob

e

Many time-resolved pump-probe experiments are possible. Right now, we are specifically interested in the I2+ + I0+ states.

The (2,0) and (1,1) curves form an excimer-type system in the dication!(2,0) is strictly bound while the (1,1) is at best quasi-bound.

Wanted to see if we could populate the (2,0) states.

Populating the (2,0) state:

Simulation: trapped population in the (2,0) potential well

The (2,0) potential curve measured from the A state of I2

+ in our previous work:

pump-probe delay=180 fs

PRA 73, 023418 (2006)

..31.6,..48.1,60

))(exp(1)(1

02

uaRuameVD

VRRDRV

ee

ee

Asymmetric channels can show spatial asymmetry in a 12 field An asymmetric channel like (2,0) An asymmetric channel like (2,0)

actually consists of two states with actually consists of two states with gerade and ungerade symmetry. gerade and ungerade symmetry. Then one can form:Then one can form:(2,0)(2,0)RR ~ (2,0) ~ (2,0)gg + (2,0) + (2,0)uu

(2,0)(2,0)LL ~ (2,0) ~ (2,0)gg - (2,0) - (2,0)uu

where R and L refer to the 2where R and L refer to the 2++ ion ion going to the right or the left.going to the right or the left.

Of course, the (2,0)Of course, the (2,0)gg and (2,0) and (2,0)uu states states must be populated coherently.must be populated coherently.

I2+ TOF Region with 1ω2ω fields

0 50 100 150 200 2503650

3700

3750

3800

3850

Pump-probe delay [fs]

Tim

e-of

-Fli

ght [

ns]

Experimental results

0 20 40 60 80 100 120 140 160 180 2000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45A

mpl

itud

e of

Rig

ht/L

eft A

sym

met

ry

Time Delay [fs]

Fast (2,0) Slow (2,0)

1-D 2-electron model1-D 2-electron model

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

A2

2+

Pot

enti

al e

nerg

y [a

u]

Internuclear Separation [au]

From the asymmetry measurements, we can show that the ionization projects the molecules into the field-induced states.

This has not really been considered before and suggests a new form of strong-field control.

Strong laser fields do a lot more than just ionize the least bound electron and leave the ion in its ground state.

Diatomic molecules have a structure that is highly susceptible to strong field excitation.

High levels of excitation are seen through the dissociation channels and direct fluorescence from the excited molecule.

Ionization occurs within the electronic structure induced by the strong laser field.

Conclusions