coherent nonlinear spectroscopy - ihee labtime.kaist.ac.kr/lec/pchem2/topic1.pdf · coherent...
TRANSCRIPT
Coherent Nonlinear Spectroscopy:
From Femtosecond Dynamics to Control Annu.rev.phys.chem., 52, 639
Marcos dantus
ⅠIntroduction
1. History of breaking time resolution limit
mid 1950 ; microsecond time resolution. First pump-probe work (porter)
1960s ; nano or picosecond time resolution
1985 ; zwail probe the ultrafast dynamics of isolated molecules with subpicosecond time resolution
1987 publishing the first time-resolved observation of transition states in a chemical reaction
2. relation between linear and nonlinear spectroscopy
① linear spectroscopy; emission and 1-photon absorption – output properties is linear input properties
② nonlinear spectroscopy; using the coherent interaction between sample and one or more of the laser pulse – output
properties is not linear input properties
3. “The goal of for active laser control is to devise electromagnetic fields”
① frequency resolved scheme (coherent control)
Utilizing the quantum interference between different rxn channel
Ex) chirped pulse enhancement of multiphoton ionization, optimal control
② time resolved scheme
‘the time dependent motion of wavepacket created by ultrafast laser pulses manipulates the outcome
of reaction’
Ex) Pump-probe, pump-dump, four wave mixing..
4. Schematic diagram of some techniques
Ⅱ Bound-free transitions ; concerted-elimination rxn
1-1. Concerted rxn ; multiple fundamental change (bond, formation, charge transfer)
Classification depends on the sensitivity of the chosen method to detect the ‘short-lived intermediates’
→rxn is rapid compared with the detection method
1-2. in the condensed phase
solvent provides ‘cage’
→ products are closed to each other
→ difficult to determine if a rxn proceeds by a concerted mechanism
1-3. Example case ; I2 elimination from CH2I2 (for more info ; j.chem.phys., 109, 4415)
① I/I* elimination channel is major one at 248.351 nm
② two photon absorption of 267 nm ; initiation of I2 elimination channel
③ at 310, 342, 369 nm (pump-probe spectroscopy)
→ I-C-I symmetric stretch, antisymmetric stretch, bending
④ PES(potential energy surface)
CH2I2
⑤ experimental result
I2(D’) ; more probable (rotation anisotropy is almost zero) → synchronous concerted
I2(f) ; less probable (anisotropy dependent) → asynchronous concerted
pump(312nm ; three photon excitation and molecular iodine dissociation)
+ probe (624nm ; I2 excitation from D’ to f )
⑥ kinetic model for the dissociation of CH2I2
Based on assumption of only two contributions of signal
⑦ What is the character of PES correlated with product??
If this process is direct, fast and pseudo-diatomic problem, then Eavail is almost same with Ekin. IVR (time is
longer than one vibration freq) isn’t observable.
L ; distance for bond breaking
τ; experimental dissociation time
then, if L1 = L2, Eavail = Ekin
comparison MeI2, BuI2 (equal rxn enthalpy)
Experimental τ2/τ1 = 1.85
τ2/τ1 estimated from eq = 1.85
→assumption is valid → ‘repulsive potential’
2. Chirped pulse enhanced multi-photon ionization
① chirped pulse
A pulse in which the wavelength changes during the duration of the pulse.
Intensity spectrum of a negatively chirped pulse
blue red
‘CPA(chirped pulse amplification)’
Positive group velocity dispersion
red blue
negative group velocity dispersion
②control of yield
This phenomena follows ‘Wave-packet following’ mechanism
As the wave-packet moves, the transition energy becomes time
dependent and a chirp that follows this dependence, while not necessarily
exactly on resonance, will be more effective in transferring population to
the higher state.
③ Another mechanism
- time delay resonance mechanism ; when considering negatively
chirped pulse, initially prepared wave-packet on B state, propagates until
it reaches a region of the PES, where it can be resonantly excited to the C
state by the trailing high frequency component.
- sequential resonance effect
This mechanism is suitable for spectroscopic property.
Suppose the first transition is resonant with the low frequency part of the pulse and the
second is resonant at high frequency. In this case, positively chirped pulse is more effective in
multiphoton transition. This effect only occurs for on sign of the chirp since the electronic
level spacing are uniquely determined
Ⅲ Bound-free transitions; photoassociation rxn
1.The difficulty of studying bimolecular rxn
① Two counters are required
→The encounters occur at random time, with random configurations, and random energy
② Experimental challenge
→to devise ways to determine or restrict the initial collision condition (impact parameter, orientation, collision
energy, time of collision)
→The traditional method is using the molecular beam where the energy of rxn can be regulated
2. Unimolecular dissociation rxn ; ‘half collision’
→“microscopic reversibility” ; Unimolecular photodissociation ≈ second half of a full collision
→ first half ; collision of the fragments
→ very specific initial condition (impact parameter & reagent energy) would reproduce the observed dissociation
dynamics
→ Unimolecular dissociation is small subset of the possible bimolecular pathway
3. The yield of bimolecular rxn
→ determined by the energy of collision, relative orientation, impact parameter
→ short pulse dissociation ; well determine life time, alignment of reagent
4. Photoassociation (excimer, free-bound transition)
① dispersed fluorescence
→ Only collision pairs that are in resonance with the binding laser at 312 nm (pump)
→ Only collision pairs oriented parallel to the polarization of the pulse are photoassociated to the D1u state.
→ The D→X fluorescence is used to monitored
→ 624 nm probe pulse ; depletion of D state
→ (b) Dispersed fluorescence spectrum resulting from excitation with a 60 fs laser pulse centered at 312 nm.
The peak at 407.8 nm is an atomic line resulting from two-photon excitation to the 71S0 state.
→ (c) Fluorescence spectrum resulting from the excitation of mercury vapor at 266 nm with a nanosecond laser
pulse. The D→X emission is blue-shifted compared to the emission produced by 312 nm excitation because
of the difference in excitation energy.
② Femtosecond transients
→ Femtosecond transients from the photoassociation of mercury at 312 nm. The heavy (thin) line corresponds to
parallel (perpendicular) polarization of the bind and probe pulses relative to each other.
→ the data is clearly anisotropic, indicating alignment of the photoassociated collision pairs.
→ Rotational anisotropy r(t) obtained from the experimental data. The heavy line is the best fit to the
Experimental
→ Rotational population of the photoassociated product, obtained from the fit to the rotational anisotropy.
③ rotational anisotropy
(exp) (theo)
→ ωi=4πBj (rotational freq) jmax ≈30 fwhm Δj ≈90
④ control of impact parameter
→ Frank-Condon factors dictate that transition probability is greatest when the laser wavelength is with energy
difference between ground and excited state
→ As a result, energy gap depends on the distance reactants
→ The wavelength of the binding pulse can thus be used to select a range of reactive impact parameter
→ relative collision E
V1(R′) ; potential energy of the ground state
R′ ; internuclear distance at which the laser is resonant
In order for photoassociation to occur, the relative collision energy of an atom pair with a given impact parameter b
should satisfy this condition
differential photoassociation cross section dóPA/db
P(b) is the opacity function.
-Figure 6 at 350 nm, only those collision pairs with very small impact parameters are photoassociated.
- As the binding laser is tuned to shorter wavelengths, the position of highest photoassociation probability shifts to
larger
-The opacity function reaches a limiting value P(b)=1 at high excitation energies, when V1(R′) approaches zero.
-Jh=μVb, where V is the relative velocity of the atoms when they are photoassociated.
Ⅳ Bound-bound molecular transition; vibrational dynamics and coherence
1. Transient grating
① three pulses has an identical pulse envelope ans frequency
components
② spatial modulation – constructive & destructive interference
③ the molecule in the interaction region experience varying
electric field intensities “according to their position”
④ The formation of the grating does not require that the two
crossing beams coincide in time as long as the coherence is
maintained in the sample
Grating ; any regularly spaced collection of essentially identical, parallel, elongated elements, but can consist of two
sets, in which case the second set is usually perpendicular to the first. When the two sets are perpendicular, this is
also known as grid
2. Phase matching
To ensure that a proper phase relationship between the interacting waves is maintained along the propagation
Direction
In phase-sensitive nonlinear process (freq doubling, sum & difference freq generation, four wave mixing) require
phase matching to be efficient
Ex) frequency doubling
“without chromatic dispersion k2=2k1”
- dispersion ; freq or mode dependence of the phase velocity in a medium
- phase velocity ; the velocity with which phase fronts propagate in a medium
- the chromatic dispersion of an optical medium is basically the freq dependence of the phase velocity
3. Density matrix
① diagonal block
ρee , ρgg ;population of each vibrational level
ρee’ , ρgg’ ; coherence of each vibrational level
② off diagonal block
(the vibronic coherence between the two electronic states)
cf) coherence ; a fixed phase relationship between the electric field values at different locations or at different
times
③ in the weak interaction limit (for vanishing multiphoton transition)
For four level system, we will include two electronic states with two vibrational levels each, |1> |2> |3> |4>
FWM signal
Population
Vibrational coherence
Each field, En, interacts linearly with the media, producing a change ρ(n) to the initial matrix
N is odd ; ρ(n) contains the changes in the probability amplitude of the electronic coupling
N is even ρ(n) represents the changes in the population and the coherence of the vibrational levels with each
electronic states
④ Density matrix calculation of nonlinear response functions
the density matrix is defined using the outer product of the state of the system |ket⟩ with its Hermitian conjugate ⟨bra|
a probability Pj to be in the state |Ψ j⟩ with ∑jPj = 1.
When Pj=1 for one state and is zero, otherwise, the system is in a pure state (a state with maximum information)
and can be described by a wave function. Otherwise, we have a mixed state that may not be described by a single wave
function. Adopting a basis set (æa), we have
the elements of the density matrix are given by
Solution of time dependent density matrix of n th interaction with electric field
Each term of the interaction operator has a well-defined direction (kn or -kn). Therefore each pulse interaction contributes in
a unique way to the phase matching direction of the nonlinear signal
Kn ; excitation ket
or deexcitation bra
-Kn ; deexcitation ket
or excitaqtion bra
⑤ vibrational wave packet description
(a) the initial wavepacket Ψ(0) in υ”=2 of the ground
electronic state is excited by field, Ea, to the excited
state B
(b) The resulting excited-state wavepacket Ψ(1) is
allowed to evolve until field Eb is applied at time τab at
τ=460 fs. The wavepacket located at the outer turning
point. Therefore the frank-Condon overleap with the
optically resonant level in the ground state is negligible
(c) The wavepacket is localized at inner turning point, providing a good overlap τab=610 fs ; resulting in a
significant ground state population
(d) Double-sided Feynman diagram
6. Example
①sient grating, Rverese transirnt grating
Gas phase I2
In PE is that field Eb acts first and is then
followed by fields Ea and Ec. PE processes
involve a rephasing of the coherence that is
lost owing to inhomogeneities in the sample
The wavepacket motion in the excited state
has a much wider range of internuclear
distance. This takes the wave packet in and
out of the franck-condon region. Therefore,
electronic polarization reflects
predominantly excited state dynamics
② Virtual echo, Stimulated photon echo
In the VE I measurement, when τab is 460 fs (3/2τe τe=2πωe) the dynamics show 307 fs oscillations, reflecting only
an excited-state contribution.
When τab is 614 fs (2τe), the dynamics show 160 fs oscillations, (ground)
In the PE I configuration, when τab is 460 fs, the dynamics reflect an excited-state contribution with 307 fs
oscillations ; no ground-state contribution is observed in this transient.
When τab is 614 fs, the 307 fs oscillations still dominate(excited); however, 2 ps later,
160 fs oscillations can be seen.
The selection between ground- or excited-state dynamics is much more effcient for the virtual echo set-up. The
observation of ground state has three laser interactions acting on the ket. This leads to high selectivity between the
two states.
For VE I, the appearance of ground-state dynamics arises from a wave packet being prepared in the excited
state, then pumped to the ground state and finally probed as a function of time, thereby giving a clear and intense
ground-state signal.
For PE I ground-state dynamics shows that the first two interactions are on the bra while the third interaction
is on the ket. This action on an unperturbed ground state by the third pulse leads to loss of the selectivity. The
reason for the small
Experimental data for VE (bold line) and PE (line)
measurements with τab=τba=460 fs.
out of phase with each other
In both cases, field Ec must interact with the wave packet
formed in the excited state by field Eb.
PE I case, Ψb(1) is at the outer turning point of the excited-
state potential when τ=0fs, minimizing the transition
probability when the third pulse is applied in the Franck-
Condon region.
③ variable time delay followed by followed time delay
For τba=460 fs, the transient shows 307 fs oscillations, corresponding to excited-state dynamics. The signal is
weaker and shows only a small background.
When τba=614 fs, the transient is dominated by 307 fs oscillations. The signal is stronger and shows a larger
background. Weak 160 fs vibrations are also observed.
Fourier transforms have confirmed that the τba=614fs transient shows a contribution of the ground state. For a
time delay of sba=614 fs, the observed background arises from the process depicted by the DSFD on the right.
The use of the fixed delay as a filter for the dynamics changes the ground-state contributions to the signal
slightly but does not give the same degree of control as is observed in the VE I case.
④ Mode suppression
Suppressing the contribution of excited-state
vibrational dynamics in order to improve relaxation
rate measurements in liquids.
They observed that when τ13 is in phase with the
excited-state dynamics, τ13=2πn/ωe(mode suppression
is on), the amplitude of the excited-state vibrations
was greatly reduced.
When τ13 was out of phase (mode suppression is off ),
the excited-state vibrations were very prominent.
When mode suppression is on, both R2 and R3
(photon echo) contribute to the signal.
Mode suppression is useful in liquid phase studies
because when mode suppression is on, R3 contributes a
large signal that overwhelms the excited-state
vibrational coherence.