Coherent Nonlinear Spectroscopy: From Femtosecond Dynamics to Control

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 ; I 2 elimination from CH 2 I 2 (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 I 2 elimination channel 3 at 310, 342, 369 nm (pump-probe spectroscopy) I-C-I symmetric stretch, antisymmetric stretch, bending 4 PES(potential energy surface) CH 2 I 2 5 experimental result I 2 (D ) ; more probable (rotation anisotropy is almost zero) synchronous concerted I 2 (f) ; less probable (anisotropy dependent) asynchronous concerted pump(312nm ; three photon excitation and molecular iodine dissociation)

+ probe (624nm ; I 2 excitation from D to f ) 6 kinetic model for the dissociation of CH 2 I 2 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 E avail is almost same with E kin. IVR (time is longer than one vibration freq) isn t observable. L ; distance for bond breaking τ; experimental dissociation time then, if L 1 = L 2, E avail = E kin comparison MeI 2, BuI 2 (equal rxn enthalpy) Experimental τ 2 /τ 1 = 1.85 τ 2 /τ 1 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 D 1u 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 7 1 S 0 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)

ω i =4πBj (rotational freq) j max 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 k 2 =2k 1 - 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 ρ ee, ρ gg ;population of each vibrational level ρ ee, ρ gg ; 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 Vibrational coherence Population 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 τ ab 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 τ ab =610 fs ; resulting in a significant ground state population (d) Double-sided Feynman diagram 6. Example 1sient grating, Rverese transirnt grating Gas phase I 2 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 (3/2τ e τ e =2πω e ) the dynamics show 307 fs oscillations, reflecting only an excited-state contribution. When τab is 614 fs (2τ e ), the dynamics show 160 fs oscillations, (ground) In the PE I configuration, when τ ab is 460 fs, the dynamics reflect an excited-state contribution with 307 fs oscillations ; no ground-state contribution is observed in this transient. When τ ab 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 τ ab =τ ba =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, Ψ (1) b is at the outer turning point of the excitedstate 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 τ ba =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 τ 13 is in phase with the excited-state dynamics, τ 13 =2πn/ω e (mode suppression is on), the amplitude of the excited-state vibrations was greatly reduced. When τ 13 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. vibrational coherence. Mode suppression is useful in liquid phase studies because when mode suppression is on, R3 contributes a large signal that overwhelms the excited-state