2D Femtosecond Spectroscopy - Walter Scott, Jr. College of ...
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1 2D Femtosecond Spectroscopy Jesse Wilson Ph.D. Qualifying Exam Advisor: Prof. Randy A. Bartels SDG
Transcript of 2D Femtosecond Spectroscopy - Walter Scott, Jr. College of ...
1
2D Femtosecond
Spectroscopy
Jesse Wilson Ph.D. Qualifying Exam
Advisor: Prof. Randy A. Bartels
SDG
2
Motivation
Who needs another dimension?
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Broadening Mechanisms
Palese, et al. J. Phys. Chem. 1994.
Homogeneous Inhomogeneous
1D Raman
2D Raman
4
(ii)
(i)
Mode Coupling
*Okumura, et al. J. Chem. Phys. (1999)
Complex molecules
Raman-active dipoles
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Mode Coupling (1D Raman)
*Okumura, et al. J. Chem. Phys. (1999)
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2D Raman Spectrum
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2D Raman Spectrum (Fundamentals)
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2D Raman Spectrum (Coupling)
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Another example
*Zhang, et al. J. Chem. Phys. (1999)
Linear Uncoupled
Coupled
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2D IR Spectra Contain Structural
Information
Acetyleproline-NH2 in chloroform.
*Hochstrasser, et al. Bull. Chem. Soc. Jpn. (2002)
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2D IR Spectra Contain Structural
Information
Magnitude
*Hochstrasser, et al. Bull. Chem. Soc. Jpn. (2002)
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2D IR Spectra Contain Structural
Information
Real part
*Hochstrasser, et al. Bull. Chem. Soc. Jpn. (2002)
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2D IR Spectrum Features
*Hochstrasser, et al. Bull. Chem. Soc. Jpn. (2002)
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2D IR Spectrum: Broadening
*Hochstrasser, et al. Bull. Chem. Soc. Jpn. (2002)
Homogeneous/inhomogeneous width
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2D IR Spectrum: Anharmonicity
*Hochstrasser, et al. Bull. Chem. Soc. Jpn. (2002)
Vibrational anharmonicity
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2D IR Spectrum: Mode Coupling
*Hochstrasser, et al. Bull. Chem. Soc. Jpn. (2002)
Mode coupling
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2D Spectroscopy Advantages
Discern homogeneous, inhomogeneous lines
Mode coupling
Vibrational anharmonicity
Structural information
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Papers Reviewed
Steffen, Fourkas, and Duppen.
“Time resolved four-and six-wave mixing
in liquids. I. Theory.”
Journal of Chemical Physics (1996).
Blank, Kaufman, and Fleming.
“Fifth-order two-dimensional Raman
spectra of CS2 are dominated by third-
order cascades.”
Journal of Chemical Physics (1999).
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Steffen, et al. (Part I. Theory)
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Steffen, et al (Part II. Experiment)
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Blank, et al.
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Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
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1D Methods
…and their shortcomings
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Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
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Time-resolved ISRS
t = 0
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Time-resolved ISRS: Pumping
t = 0
pump
Stokes
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Time-resolved ISRS: Ultrafast
t = 0
pump
wwpumpwstokes
E(w)
•Ultrafast pulse spectrum
•Short pulses: pulse << vib
•Impulsive excitation
Stokes
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Time-resolved ISRS: Coherence
t
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Time-resolved ISRS: Probing
t =
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1D Experimental SetupLaser
Oscill
ato
r
Detector
pump
probe
signal
sample
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Liquid Intermolecular
Modes
Homogeneous or Inhomogeneous?
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Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
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CS2
Instantaneous response
Diffusive tail
Steffen and Duppen. J. Chem. Phys. (1997)
Librations
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H2O
Palese, et al. J. Phys. Chem. 1994.
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Broadening
Homogeneous: g(w) rapidly fluctuates
Inhomogeneous: g(w) changes slowly
w
ww )cos()()( tgtR)cos()( ttR w
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Inhomogeneous Model
2
20
2
)(
)(
ww
ww
eg
= degree of inhomogeneity
)()3( tR
0
)3(
inh
)3(
inh ),()()( tRgdtR www
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Model fit to data
Steffen and Duppen. J. Chem. Phys. (1997)
Experiment
Homogeneous limit
= 1.00 rad/ps
= 2.53 rad/ps
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2D Provides Discrimination
*Palese et al. J. Phys. Chem. 1994.
Homogeneous
Inhomogeneous
Intermediate
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2D Simulations
Homogeneous Inhomogeneous
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Four Wave Mixing
Theory
Third-order, or one-dimensional theory…
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Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
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3rd Order Response
)()()()](~),(~[
)()()(),,,(
32211221
32211321
ttttHtttti
ttttttttttR
)()()(),,,(ddd)( 321321
)3(
321
)3( tEtEtEttttRttttP
Raman
Hyper-polarizability (THG…)
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Simplified 3rd Order Response
)()()()](~),(~[
)()()(),,,(
32211221
32211321
ttttHtttti
ttttttttttR
)]0(~),(~[2
)()( 111
iR
132
1 0
tt
t
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Harmonic Oscillator
Unperturbed Hamiltonian:
Raising, lowering operators:
Displacement operator
)(21
0 aaH BO w
)(2
aam
qw
1~ a 1~ a
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Polarizability Depends on q
2
21)( qqq
)(2
aam
qw
)2(2
)(2
22 aaaaaam
aam
qww
One-level transitions
Two-level transitions
Zero-level transition
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3rd order HO Response
ww
ww
)2sin()()12(2
)sin(2
)()(
122
2
2
1
2
1
11
)3(
Pm
m
R
Hyperpolarizability
2
1
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Double-Sided Feynman
Diagrams
Illustrating density matrix evolution
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Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
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Optical Polarization
)(Tr)( tVtP
)( rrqV
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1101
1000
Density Matrix
Population densities
Coherencesbra
ket
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Liouville Equation
HHi
HHi
Hi
t
,
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Perturbation Expansion
)()()()( )2()1()0( tttt
E2E 43 EE
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Time evolution
*Mukamel, Principles of Nonlinear Optical Spectroscopy
]]]]),0([),([[),([),()( 0111
)(
VtVttVtrEi
t nn
n
n
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Initial State
aaVV ),0(]),0([ 0
11
00
aa
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Commutator
baV )0(
11
00
aa
,12,10,11
,02,01,00
)0( abaaV
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Commutator
)0()0(),0(]),0([ 0 VaaaaVaaVV
baV )0(
baabV ]),0([ 0
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Double-sided Feynman Diagrams
*Yee and Gustafson, Optics Communications (1977)
a
t
a a a
b a
0t
a b
baabVaaaaVaaVV )0()0(),0(]),0([ 0
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Second order commutator
]]),0([),([ 01 VtV aaVtV ),0(),( 1
caabtV ),( 1
)()()()( 1111 tVcacatVtVababtV
bacbcbac
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Liouville Space Paths
aa ba
ac bc
ca
ab
]]),0([),([ 01 VtV
)()()()( 1111 tVcacatVtVababtV
bacbcbac
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Second Order Diagrams
a a
t
0t
c
1tt
b
a
a a
b
a
c
ca
a a
b
b
c
a
a a
a b
ca
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Third order (1 of 8)
a at
0t
c
2tt
d
b
b
1tt
d
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Polarization
a
at
0t
c
2tt
d
b
b
1tt
d
)(Tr)( tVtP
a
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Polarization
a
at
0t
b
2tt
d
b
b
1tt
d
3tt c
a
b
a
)(Tr)( tVtP
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Time-resolved ISRS
a
at
0t
b
2tt
d
b
b
1tt
d
3tt c
a
b
a
01 t 32 tt
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Time-resolved ISRS
a
at
0t
b
t
a
a
a a
01 t 32 tt
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Time-resolved ISRS
a
at
0t
b
t
a
a
a a
a
a b
a
b b
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Coherence
a
at
0t
b
t
a
a
a a
a
a b
a
b b
Cohere
nce
w
ab
ba
i
EEi
e
e
/)(
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Time-resolved ISRS
a
0t
0t
1
t
0
0
0 0
012
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Time-resolved ISRS
a
0t
0t
1
t
0
0
0 1
012
01
w
10
01 /)(2
EE
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Time-resolved ISRS
t
0t
t
10
w
10
01 /)(2
EE
0
0 1
0
1 1
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Time-resolved ISRS
a
0t
0t
1
t
0
0
0 1
1001
www
10sin1010 ii
ee0
0 1
0
1 1
75
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2D Methods
Tanimura and Mukamel (1993)
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Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
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2D Femtosecond Spectroscopy
t = 0
1 2
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2D Femtosecond Spectroscopy:
Impulsive pumping
t = 0
1 2
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2D Femtosecond Spectroscopy:
Coherence propagation
t 1
1 2
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2D Femtosecond Spectroscopy:
Rephasing pulse
t = 1
1 2
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2D Femtosecond Spectroscopy:
Second coherence propagating
t 2
1 2
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2D Femtosecond Spectroscopy:
Probing
t = 2
1 2
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2D Experimental SetupLaser
Oscill
ato
r
Detector
1
signal
sample
2
2
1
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Example: CS2
*Astinov, et al. Chemical Physics Letters (2000).
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Six-wave Mixing Theory
Steffen, Fourkas, and Duppen
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Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
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Fifth-order Response
0
21
2
1
2
21
)5(
2
0
1
)5( )()(),(dd)()( tEtERtEtP
)0(~,)(~),(~
4
)()0(~),(~
2
)()0(~),(~
4
)()(),(
1212
21
11
2121
)5(
i
i
i
R
6WM
Raman / 2nd hyper-Raman
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Conditions
Nonlinear polarizability (NP)
Anharmonic coupling (AN)
ij
ji
qjii
i
qi
qqqq
00
2
02
1)()(
ijk
kjiijk
i
ii qqqqqV )3(2)2(
6
1
2
1)(
Coupling of ortho modesOrdinary Raman
Tokmakoff, et al. Chem Phys. (1998)
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Harmonic Oscillator
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Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
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Phenomenological Damping
Weak systembath coupling
ww i
*2/)(
State lifetime Decoherence
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Full 3rd Order Damped Response
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Full 5th Order Damped Response
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State-independent Damping
State decay
One quantum coherences
Two quantum coherences
1
1
*
1,
2
2
*
2,
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Damped 3rd Order Response
decoherence rates
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Damped 5th Order Response
Undamped
Damped
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Brownian Oscillator Bath
System / Bath linear coupling
Tanimura and Mukamel’s approach
Equivalent to phenomenological model when:
damping is state dependent!
21
221
1
100
Coupled Bath Dephasing
First excited state decayOne-quantum dephasing
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Level-dependent dephasing leads to a
new term in R(5)
102
Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
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Inhomogeneous Damping
),,()(d),(
),()(d)(
21
)5(
0
21
(5)
inh
1
)3(
0
1
(3)
inh
www
www
RgR
RgR
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One term is invariant to g(w
105
Rephasing Pathways
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Initial State
1t 1
107
Pump Interaction
1t
0t
1 0
1
w10ie01
108
Rephasing Pulse
1t
0t
1 0
1
1 2
w10ie01
1t
21 w12ie
109
Probe Pulse
1t
0t
1
21 t
0
1
2 2
1 2
w10ie01
1t
21 w12ie
110
Phase Cancellation
1t
0t
1
21 t
0
1
2 2
1 2
w10ie01
1t
21 w12ie
)()( 21102110212110 wwwww
iiee
111
112
Third-order Cascades
Blank, Kaufman, and Fleming
113
Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
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CS2 Predicted 2D Response
115
CS2 Predicted 2D Response
116
What was measured:
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Sequential Cascades
t = 0
chromophore a
chromophore b
2 4
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Sequential Cascades
t = 0
chromophore a
chromophore b
2 4
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Sequential Cascades
t 2
chromophore a
chromophore b
2 4
120
Sequential Cascades
t = 2
chromophore a
chromophore b
2 4
121
Sequential Cascades
t 2 + 4
chromophore a
chromophore b
2 4
122
Sequential Cascades
t = 2 + 4
chromophore a
chromophore b
2 4
123
Sequential response
124
Eliminating Sequential Cascades
Theory Measured
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Parallel Cascades
t = 0
chromophore a
chromophore b
2 4
126
Parallel Cascades
t = 0
chromophore a
chromophore b
2 4
127
Parallel Cascades
t 2
chromophore a
chromophore b
2 4
128
Parallel Cascades
t = 2
chromophore a
chromophore b
2 4
129
Parallel Cascades
t 2+4
chromophore a
chromophore b
2 4
130
Parallel Cascades
t = 2+4
chromophore a
chromophore b
2 4
131
Parallel Response
132
Measured Parallel Response
Simulated Measured
133
134
Eliminating Cascades
135
Roadmap
1) One-dimensional Raman methods
a) Motion in Liquids
b) Third order response theory
c) Liouville space paths and Feynman diagrams
2) Two-dimensional Raman methods
a) Fifth order response theory
b) Homogeneous damping effects
c) Inhomogeneous damping and rephasing
d) Third order Cascades
e) Solutions to the problem of cascades
136
Diffractive Optics
Astinov, et al. Opt. Lett. (2000)
137
Diffractive Optic Results
Cascade
Astinov, et al. Opt. Lett. (2000)
138
More Accurate Phase Matching
sinc(Dkl/2) assumes
collinear propagation
Constant spatial overlap
Account for z-
dependent spatial
overlap:
Blank, et al. J. Chem. Phys. (2000)
139
Reduced Interaction Length
LEekL
REn
LiE kLi
s
s
D D
signal
2/
42
)5(5
signal2
sinc),( w
2
cascade
2/
2/
42
)3(
cas
5
int
int
cas
cas2
cascade
2sinc
2sinc
),(
LEeLk
eLk
REnn
iLE
Lkib
Lkia
b
a
D
D
D
D
ww
140
Heterodyne Detection
141
Heterodyne Detection Results
Astinov, et al. Chem. Phys Lett. (2000)
142
143
Conclusions
Steffen et al’s theory did not account for
parallel cascades
Blank, et al. found parallel cascades
dominate the signal
Eliminating parallel cascades reveals desired
signal
144
Thanks
145
Roadmap
1. One-dimensional Raman methods
1. Motion in Liquids
2. Third order response theory
3. Illustrating 3rd order response with Feynman
diagrams
2. Two-dimensional Raman methods
1. Fifth order response theory
2. Homogeneous damping effects
3. Inhomogeneous damping and rephasing
4. Third order Cascades
5. Solutions to the problem of cascades
146
147
2D Resonant IR (Part I)
148
2D Resonant IR (Part II)
