coherent control of chemical reactions. ii · 2004-02-18 · coherent control of chemical...
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Coherent control of chemical reactions. II
Jennifer L. Herek FOM-Institute for Atomic and Molecular Physics [AMOLF]
Amsterdam, The Netherlandshttp://[email protected]
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Control of chemical reactions
General goal: Maximize yield of desired products and suppress formation of unwanted byproducts
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Lasers “Bond-selective” chemistry?
Can coherent light be used for selective bond activation and cleavage?
The concept:• Choose the light frequency to be in resonance
with the vibrational frequency of the bond to be broken
• Resonant activation of the proper vibrational mode leads to selective dissociation
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Bond-selective chemistry in H + HOD
OD
OH
OD
OH
OD
OH
H2 + ODH + HOD(ν)
HD + OH
F. Crim, J. Chem. Phys. (1990) 92:6333
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Excite one bond… …but soon, the entire molecule is vibrating.
Excite one bond… …but soon, the entire molecule is vibrating.
The problem: IVR
• Vibrational motion is coupled to many atoms within the molecule
• Intramolecular vibrational redistribution (IVR) leads to a loss of selective excitation and “heating” of the molecule
• Works only for small, prototype molecules
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Coherent controlInterfering for the good of a chemical reaction
The difference:
• Exploits a broad range of quantum interference effects
• Many different feasible schemesFrequency domainTime domain
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How is it possible that light can control a reaction?
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Pulse timing controlAB + C
AC + BABC
Reactant Product
Reaction coordinateC
B
A
C
B
A
pump
C
B
A
C
B
A
dump
excitedstate
Pote
ntia
l Ene
rgy
groundstate
Tannor, D. J., Kosloff, R. & Rice, S. A. Chem. Phys. 85, 5805-5820 (1986)
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• Femtosecond probing of reactions
• Femtosecond control from the transition state region
• Reaction channels
• Population control
• Channel switching
• Magnitude of depletion
• Control vs. probe
Control of dissociation pathways in NaI
Herek, J. L., Materny, A. & Zewail, A. H. Chem. Phys. Lett. 228, 15-21 (1994)
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Multiple-path interference control
Excite the desired product channel via two different pathways:
Path 1Path 2
Ground state
Target state
Probability (P) of forming a product:P = P1 + P2 + P12 Interference term
depends on phase of optical fields
Brumer, P. & Shapiro, M. Chem. Phys. Lett. 126, 541-546 (1986)
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Tuning the phase difference
Rice, S. A., Nature 409, 422-426 (2001)
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STIRAPSTImulated Raman Adiabatic Passage
reactant
product
intermediate
Stokespump
1 >
2 >
3 >
• “Counterintuitive” pulse sequence: Stokes, then Pump• Stokes pulse creates coherent superposition of two initially
unpopulated states
• No population transfer to intermediate state; direct transfer to product
Gaubatz, U., Rudecki, P., Becker, M. Schiemann, S., Külz, M. & Bergmann, K. Chem. Phys. Lett. 149, 463 (1988)
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STIRAP applied to SO2 molecules
Stokes laser on
Stokes laser off
coupling schemeenhancement
Counterintuitive pulse sequence: signature of STIRAP
transfer efficiency vs. pulse delay
Halfmann, T. & Bergmann, K. J. Chem. Phys. 104, 7068-7072 (1996)
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Combining these concepts:For a given target distribution of photoproducts and the quantum mechanical equations of motion, what electric field is required to guide the temporal evolution of the system appropriately?
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OCT: Optimal Control TheoryElectric field design
Hamiltonianrequired!
A. Peirce, M. Dahleh & H. Rabitz, Phys. Rev. A, 37, 4950 (1988)
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OCT methodology• Forward/backward propagations of wavepackets Ψ(t) or
density matrices ρ(t) from initial to final states and vice versa
• Optimization algorithm selects best fields ε(ti)
Inherent difficulties with OCT...• Need potential energy surfaces!
Rarely known over all range of nuclear separations necessary to describe a reaction
• Search space too large to be scanned completely
• Predicted fields difficult to reproduce accurately enough under laboratory conditions
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Experimental approach“Teaching lasers to control molecules”
Learningalgorithm
Detector
Molecule
modified E(t)
pump E(t)
probe
result
Laser,pulse shaper
Objective
HamiltonianNOT required!
R. S. Judson & H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992)
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The molecular view• A molecule knows its own Hamiltonian
• Given ε(t), a molecule solves rapidly!ih = HΨ∂Ψ∂t
•No prior knowledge of PESs needed
•Broadly applicable (not limited to molecular systems)•Automated pulse compression•Control of 2-photon transitions in atoms•Shaping of Rydberg wavepackets•Optimization of high-harmonic generation•Control of ultrafast semiconductor nonlinearities•Laser cooling
•Laboratory conditions accounted for automatically
Advantages
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Advantage of fs lasers
Ground state
Target state
Broadband!
• allows for manipulation of many pathways to provide control over complex dynamics
• allows different control mechanisms: phase, timing, etc.
pump dumppump dumppumppump dump
Path 1Path 2
Path 1Path 2
Stokespump
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Experimental realizationFeedback-driven adaptive femtosecond pulse shaping
H. Rabitz, R. de Vivie-Riedle, M. Motzkus & K.-L. Kompa, Science 288: 824-828 (2000)
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Femtosecond pulse shaping
A pulse is defined by its intensity and phase in either the time or frequency domain.
( ) ( ) ( )i tE t I t e φ−= ( ) ( ) ( )iE S e ϕ ωω ω −=%
( ) ( ) ( )out inE t h t E t=fs pulses too fast
Modulation in time domain:
( ) ( ) ( )out inE H Eω ω ω=% %Modulation in frequency space:frequency disperse the pulse in space and createa spatially varying transmission and phase delay
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Shaped pulse = “optical melody”
A musical score is a plot of frequency vs. time:fr
eque
ncy
time
Transform-limited pulse:chord
Shaped pulse:melody
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“Ordinary” femtosecond laser pulses
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“Shaped” femtosecond laser pulses
The temporal shape of the laser pulse can be changed by varying the phases between its frequency components
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Acoustic analogy
-1 0 1-1
1
Ampl
itude
[A.U
.]
Time [s ]200 300 4000
1
Inte
nsity
[A.U
.]
Frequency [Hz]
2 frequencies
-1 0 1-1
1
Ampl
itude
[A.U
.]
Time [s ]200 300 4000
1
Inte
nsity
[A.U
.]
Frequency [Hz]
4 frequencies
-1 0 1-1
1
Ampl
itude
[A.U
.]
Time [s ]200 300 4000
1
Inte
nsity
[A.U
.]
Frequency [Hz]
16 frequencies
-1 0 1-1
1Am
plitu
de [A
.U.]
Time [s ]200 300 4000
1
Inte
nsity
[A.U
.]
Frequency [Hz]
Many frequencies
K.A. Nelson and J.C. Vaughan, MIT
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Linear phase modulation
I(ω)φ(ω)
I(ω)
φ(ω)
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“V” & quadratic phase modulation
I(ω)
φ(ω)
I(ω) φ(ω)
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Cubic or periodic phase modulation
I(ω)
φ(ω)
I(ω)
φ(ω)
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Methods of pulse shaping
Liquid-crystal Acousto-optic Deformable mirror
Individually-addressed pixels can vary phase or amplitude
Movable elements allow smooth phase variationModulated rf field
creates an amplitude-and phase-dependent grating
A. M. Weiner, Rev. Sci. Inst. 71, 1929 (2000)
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Liquid crystal spatial light modulator
Dual stack—phase & amplitude control
State-of-the-art:2 x 640 elements = 1280 adjustable parameters!!
G. Gerber
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Dual stack LC-SLM
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Shaped pulses with LC-SLMs
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The learning loop
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Evolutionary algorithms
Survival of the fittest
o oo o
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Metaphors of biological evolution
• A breeding population, in which those individuals (pulses) that are more “fit” have a higher probability of spawning offspring and passing their genetic information to succeeding generations.
• Genetic makeup of the offspring is a mixture (characterized by a crossover rate) of the genetic makeup of the parents.
• Genetic material is occasionally altered by mutation, thereby generating offspring that can be more or less “fit” than they would have been otherwise.
• Cloning is possible.
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Evolutionary operators
Multiple-point crossover
Single-point crossover
Double-point crossover
Intermediary recombination
Recombination
Mutation
Cloning
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Evolutionary algorithm example
First Generation
Parameter 1
1.The first generation evenly samples the parameter space. From this we select the parents for the next generation.
2.The second generation is concentrated around the first set of parents, and from this we select the next set of parents.
3.Successive generations converge on the optimal solution.
Second Generation
Para
met
er 2
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The learning curve
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The learning loop
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Examples of closed-loop experiments
• Fluorescence spectrum manipulation (Wilson 1997)
• Molecular fragmentation selectivity (Gerber 1998, Levis 2001, Woste 2003)
• Atomic excitation tailoring (Bucksbaum 1999)
• High-harmonic X-ray tailoring (Murnane & Kapteyn 2000)
• Ultrafast optical switching (Keller 2000)
• Molecular rearrangement selectivity (Levis &Rabitz 2001)
• Chemical discrimination in mixtures (Gerber 2001)
• Distortion-free transmission through optical fibers (Omenetto 2001)
• Vibrational excitation tailoring in polymers (Motzkus 2002)
• Decoherence management (Walmsley 2002)
• Energy transfer in photosynthesis (Herek & Motzkus 2002)
So far, more than 40 systems successfully controlled
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Changing the pulse shape changes the product ratio
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Simultaneous but selective absorption of two different molecules using shaped femtosecond pulses:
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Control of energy flow in light harvesting
The LH2 light harvesting antenna from Rps. acidophila
0 -2
B8 0 0
B8 5 0
400 450 500 550 600 650 700 750 800 850 900 950Wave length, nm
CarotenoidS2
BChlQy
BChlQx
0 -1 0 -0
B8 0 0 / B8 5 00 -2
B8 0 0
B8 5 0
400 450 500 550 600 650 700 750 800 850 900 950Wave length, nm
CarotenoidS2
BChlQy
BChlQx
0 -1 0 -0
B8 0 0 / B8 5 0
Energy transfer
Energyloss
DonorCar
AcceptorBChl
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Two competing channels:internal conversion vs. energy transfer
Can we control the IC/ET branching ratio?
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Experimental setup
Car BChl
Sn
S2
S1
S0
Qy
g
ETIC
excλ510 nm
prλ580 nm
prλ880 nm
Excitation Probe Rotatingsample
Feed-backImproved
shape
whitelightgen.
shaperΦ λ, )A((λ)
ETIC
nc-OPA
=510nm=30fs
λ∆τ0
IF
Evolutionary algorithm
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“Blind” optimization (64 parameters)Target: maximize ratio of IC/ET signals
0 5 10 15 20 25 30 35
1,0
1,1
1,2
1,3
1,4
Car/B
Chl r
atio
(rel
ativ
e to
TL)
Generation
TL
IC/E
T ra
tio (r
elat
ive
to T
L) “best” individual result
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What is the pulse shape?Unshaped pulse Shaped pulse
1500 fs
IC ETIC ET
40 fs
Time
490
530
Wav
elen
gth,
nm
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Reducing the complexity: restricted optimization
Sinusoidal phase mask in FREQUENCY DOMAIN:
φ(pix) = a*sin(b*pix + c)
Only 3 parameters:a: modulation depth b: frequencyc: phase offset
a
2π/b
c
pix(λ)
Time, ps
a: length of pulse trainb: inter-pulse separationc: carrier phase pattern
Result in TIME DOMAIN: pulse train
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Restricted optimization (3 parameters)Target: maximize ratio of IC/ET signals
0 5 10 15 20 25 30 350,6
0,8
1,0
1,2
1,4
1,6
1,8
∆∆O
D (re
lativ
e to
TL)
Generation0 5 10 15 20 25 30 35
1,0
1,2
1,4
1,6
1,8
2,0
2,2
2,4
Car/B
Chl r
atio
(rel
ativ
e to
TL)
Generation
ratio Car
BChl
TL
TL
IC/E
T ra
tio (r
elat
ive
to T
L)
IC
ET
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-1
0
1
Pul
se e
nvel
ope
and
Elec
tric
field
-1
0
1
Pha
se (r
ad)
0 5000 10000 15000 20000
Time, a.u.0 5 10 15 20 25 30
-1
0
1
Pixel number
Effect of the phaseShifting the offset parameter (c) changes the phase pattern of the excitation pulse
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Optimized vs. π-shifted-optimized pulsesPhase offset of optimal mask pattern shifted by half a period
-1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0
02468
Time, ps-1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0
02468
phas
e (r
ad)
Time, ps
I(t)
optimized pulses π-shifted-optimized pulses
Result: No change in pulse envelope, energy or spectrumDifferent phase pattern between subpulses
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Energy flow depends on the carrier phase
Evidence of coherent control
Ο π 2π 3π0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
IC
ET
Flow
(rel
ativ
e to
π p
hase
shi
fted)
Shift of optimized phase parameter
Nature 417, 533 (2002)
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Histogram of successive optimizations
Spectroscopy by coherent control
0 50 100 150 200 250 300
5155 cm-1
num
ber o
f res
ults
4
3
2
1
0
active mode, cm-1
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The carotenoid loss channel
Promoting modes for carotenoid internal conversion:
CC stretch~1100, 1500 cm-1
symmetric (ag)
CCC bend~120-180 cm-1
asymmetric (bu)
S (1A )0 g -
S (1B )2 u +
S (2A )1 g -
tuning ~ a g
ener
gy
coupling ~ b u
Resonant coupling to bending mode promotes internal conversion via conical intersection(stretch)
(bend)
0 100 200 300 400
∆A
(a.u
.)
Time Delay (fs)
800 1000 1200 1400 1600 1800
1155
1508
Frequency (cm-1)
Time delay (fs)0 100 200 300 400
11501508
Frequency (cm-1)
G. Cerullo, Politechnico di Milano
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What is the control mechanism?
• Couple to specific molecular motion(155 cm-1 bending mode)
• Manipulate quantum interferences (coherent control)
Vibrational mode matching
Coherent Impulsive Raman Scattering
BChl
S2
S 1
S0
hotS0shap
ed p
ump
Φ(ω) ω
02πCar
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Reducing the complexity: Model systems
LH2
• Biological complexes (wild-type, mutants)function
• Biomimetic molecular assembliesreactivity
caroteno-porphyrin dyad
• Isolated moleculesmotion
porphryincarotenoid
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A new spectroscopic tool for reducing biological complexity
Blind optimizations:Identify functionally important motion
Restricted parameter space:Test simple pulse shapes correlated to• shapes of potential energy surfaces• specific vibrational modes
Control knobs:
∆t
• Wavelength• Spectral amplitude• Temporal envelope• Phase• Polarization
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Challenges and opportunitiesInversion: Can we extract microscopic information of the molecular system by analysis of the optimized laser field?
• Parametrization. Test/catalogue the effects of simple pulse shapes
Finessed quantum mechanical manipulations may provide a unique source of data on intramolecular forces
Develop coherent control “rules of thumb”
• Analyze relevant electric field shapes to obtain information about the temporal evolution of the system
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Recent review articles:Walmsley, I. & Rabitz, H. Quantum physics under control.Physics Today (Aug 2003) 43-49
Brixner T., Damrauer N. H. & Gerber G. Femtosecond quantum control. Adv. Atom. Mol. Opt. Phys. 46, 1-54 (2001)
Rice, S. Interfering for the good of a chemical reaction. Nature 409, 422-426 (2001)
Rabitz, H., deVivie-Riedle, R., Motzkus, M. & Kompa, K.-L. Whither the future of controlling quantum phenomena?Science 288, 824-828 (2000)
A fun website:http://www.physik.uni-wuerzburg.de/femto-welt/