Understanding Strong Field Closed Loop Learning Control

Experiments

PRACQSYS August 2006

Motivation and Outline

• Want to understand strong field learning control(closed loop)

• Single atom vs collective dynamics

• From atoms to molecules- controlling fragmentation

+=

The ‘Coherent’ Control Toolbox

Optical field control

Feedback andlearning algorithms

• S t r i c k l a n d a n d M o u r o u O p t . C o m m . 5 6 , 2 1 9 ( 1 9 8 5 )• S t r i c k l a n d a n d M o u r o u O p t . C o m m . 5 6 , 2 1 9 ( 1 9 8 5 )

Amplified ultrafast lasers

Output:= 3*10-14sEnergy = 10-3JIcontrol(1018W/m2)>> Isun(6*107W/m2)

Control E()~1000 ‘knobs’

Strong Field Population Inversion

o

o

EStark shift: 2)(tE

• Coupling strengthand energy shifts are of the same order of magnitude -> low efficiency•Absorption -> Emission

WithoutStark shift

WithStark shift

Na energy levels

|3s>

|4s>

|3p>

589 nm

1141 nm

777nm

P|4

s>

R. R. Jones PRL 74, 1091 (1995)

Experimental Setup

Pinhole

PMT

589 nm

Lens

Na

0'0 8.0 II

Sodium vaporT ~ 3500 C

Lasert = 30 fs0 = 772 nm - 784

Pulse shaper

G.A.

PMT

Cross correlation

Na energy levels

|3s>

|4s>

|3p>589 nm

1141 nm777nm

Feeding back on Stimulated vs Spontaneous emission

Spontaneous Emission Stimulated Emission

Improvement over unshaped ~ 3 Improvement over unshaped ~ 103

Understanding Single Atom Dynamics I

0=784 nm

0=772 nm

0=777 nm

I(t) and (t) ---

All solutions give substantial improvement over an unshaped pulse – but only for strong fields!

C. Trallero-Herrero et al Phys. Rev. Lett. 96 063603 (2006)

Understanding Single Atom Dynamics II

2

Need to maximize:

…but with constraints.

P4s(t),(t) shapedP4s(t), (t) unshapedI(t)

Understanding Increase in Stimulated Emission Yield

•Solve coupled Schroedinger and Maxwell Equations

•Time and Frequency domainMeasurements of StimulatedEmission

D. Flickinger et. al. Applied Optics 45 6187 (2006)

Modeling Collective Behavior Na energy levels

|3s> (Q11)

|4s> (Q22)

|3p> (Q33)589 nm = 2

1141 nm = 1

777nm

After laser field

M. Spanner & P. Brumer PRA 70 023809 (2006)

Simulation Results

Time [ps]

Inte

nsit

y [a

rb]

Measurement of the Stimulated Emission

Experiment Theory

Superfluorescence (Yoked)

cdp T

• Delayed pulse – not a parametric process

• t<1(~0.5) – almost perfectly coherent

• - not ASE

Cross correlation of Stimulated Emission

M. S. Malcuit et. al. PRL 59 1189 (1987)

Stimulated Emission vs |4s|2

Experiment Theory

Note threshold at 2/3

• Control is through optimizing single atom

inversion to get over SF threshold

• Stimulated emission is superfluorescence

– locking of dipole phases in ensemble

Molecular Experimental Apparatus

Control in Trifluoroacetone

Unshaped Pulse

Shaped Pulse

CF3+

CH3+

R. J. Levis, G. M. Menkir, and H. Rabitz, Science 292, 709 (2001).

D. Cardoza, M. Baertschy, T. Weinacht, J. Chem Phys. 123, 074315 (2005).

Control goal = CF3+/CH3

+

CH3COCF3

A

B

Optimal solution and Pump-Probe Measurement

))(cos( 0 tttAtE

Time (fs)

Inte

nsi

ty

Phase

(radia

ns)τ

τ =170 fs

Laser cooperates with Molecular dynamics

All other fragments flat

CF3+ yield vs pump-probe delay

A~170 fsB~85 fs

Ab initio structure & wave packet calculations help reveal mechanism

CH3COCF3+

CF3 + CH3CO+

Control Model

1

1. Ionization (launch)

2. Wave packet evolution

3. Enhanced ionization

C-CF3 bond length [Å]

C-C-O angle [degrees]

Ene

rgy[

eV]

J. Chem. Phys. 123 074315 (2005)

Wave packet takes 145-175 fs to reach EI point. Pump-

Probe peak is ~170 fs1

2

3

Predictions for ‘Family Members’

CH3COCCl3

CH3COCD3

CH3COCF3

Fragmentation of Family Members

CH3COCD3

CH3COCCl3CH3COCF3

Results for CH3COCCl3 and CH3COCD3

Control Pulse Shape Pump-probe

Chemical Physics Letters 411, 311 (2005)

i

ii Hx

i

ii kx cos

General techniques for interpreting control: What are the

right knobs?

Transforming from ‘bad’ to ‘good’ bases

21

21

0,

TTthen

xAxAif

FA

Gx

eEtE

tEFFitness

ijij

nn

n

i

Can a given lineartransformation, T1,diagonalize entire search space?

x1 x2

For linear transformations, PCA – J. Phys. B 37 L399 (2004)

Hessian Analysis Comparison 2

2122

2121, xxxxxxF BrCHBr 2/

Physically Motivated Basis Transformation in CH3COCF3

nn

n kx cos nn

nHx Journal of Chemical Physics, 122, 124306 (2005)

Hessian Analysis Shows Basis Change Works

nn

n kx cos

nn

nHx

Conclusions & Future Directions

• Demonstrated closed loop coherent control over strong field dynamics

• Both quantitative and qualitative understanding of both stimulated emission and single atom dynamics

• Understand control in a molecular family – ‘photonic reagents’

Acknowledgements

David CardozaCarlos Trallero

Sarah NicholsDaniel FlickingerBrendan KellerBrett Pearson

Jay Brown

Collaborators:Mark Baertschy (CU Denver)

Jayson Cohen (Focus, U Michigan)Michael Spanner (Toronto)Herschel Rabitz (Princeton)

Funding: NSF, ACS-PRF,DURIP & Research Corp