Quantum dynamics of solid Ne upon photo-excitation of a NO impurity: a Gaussian wave packet approach

A high-dimensional quantum wave packet approach based on Gaussian wave packets in Cartesian coordinates is presented. In this method, the high-dimensional wave packet is expressed as a product of time-dependent complex Gaussian functions, which describe the motion of individual atoms. It is applied to the ultrafast geometrical rearrangement dynamics of NO doped cryogenic Ne matrices after femtosecond laser pulse excitation. The static deformation of the solid due to the impurity as well as the dynamical response after femtosecond excitation are analyzed and compared to reduced dimensionality studies. The advantages and limitations of this method are analyzed in the perspective of future applications to other quantum solids.

Vibrational relaxation and dephasing of Rb2 attached to helium nanodroplets

The vibrational wave-packet dynamics of diatomic rubidium molecules (Rb(2)) in triplet states formed on the surface of superfluid helium nanodroplets is investigated both experimentally and theoretically. Detailed comparison of experimental femtosecond pump-probe spectra with dissipative quantum dynamics simulations reveals that vibrational relaxation is the main source of dephasing. The rate constant for vibrational relaxation in the first excited triplet state 1(3)Σ(g)+ is found to be constant γ ≈ 0.5 ns(-1) for the lowest vibrational levels v ≲ 15 and to increase sharply when exciting to higher energies.

Tracing, amplifying, and steering chromophore-bath coherences by ultrashort pulse trains

With a train of 5 phase controlled ultrashort pulses, we enhance a coherent vibronic transition to exceed a dominant incoherent background. The interference in the chromophore generates a spectral comb which is adjusted to a progression of internal Br2 vibrations coupled to phonons of the surrounding Ar lattice. It steers the mode-specific phase evolution of the system. The trains are generated by straightforward programing of the spectral comb in a pulse shaper unit. Excitations involving several hundred degrees of freedom remain coherent on a picosecond time scale.

Valence transitions of Br2 in Ar matrices: interaction with the lattice and predissociation

Fluorescence spectra from v(')=0 of the B, A and A(') states of Br(2)Ar are presented for excitation wavelengths from 630 to 540 nm with high resolution, to evaluate isotopic splittings in emission and absorption. The observed progression of sharp zero phonon lines (ZPLs) from v(')=2 to v(')=19 in B excitation is used to derive spectroscopic constants. The ZPL broadening and the growing phonon sideband (PSB) contributions indicate an increase of matrix influence on the X-B transition with rising v('). Contributions of the PSB are parameterized with the Huang-Rhys coupling constant S, where S=1 near the potential minimum reflects the electron-phonon coupling and S=4 close to Franck-Condon maximum originates from vibrational coupling. The PSB spectral composition correlates with the matrix phonon density of states, and the ZPL broadens and shifts with temperature. Two crossings with repulsive states (between v(')=4-5 and v(')=7-9) leading to matrix induced predissociation and a third tentative one between v(')=14 and 15 are indicated by ZPL broadening, population flow, and spectral shifts. The crossing energies are close to gas phase and matrix calculations. The stepwise flow of intensity from B via repulsive states to A(') and, similarly, from the A continuum to A(') is discussed. Emission quantum efficiency of the B state decreases from near unity at v(')=0 to less than 10(-3) at v(')=19. Broadening of ZPL near crossings yields predissociation times of 5 and 2.5 ps corresponding to probabilities of 5% and 10% per round-trip for the two lowest crossings, respectively.

Nonlinear wave-packet interferometry and molecular state reconstruction in a vibrating and rotating diatomic molecule

We formulate two-color nonlinear wave-packet interferometry (WPI) for application to a diatomic molecule in the gas phase and show that this form of heterodyne-detected multidimensional electronic spectroscopy will permit the reconstruction of photoinduced rovibrational wave packets from experimental data. Using two phase-locked pulse pairs, each resonant with a different electronic transition, nonlinear WPI detects the quadrilinear interference contributions to the population of an excited electronic state. Combining measurements taken with different phase-locking angles isolates various quadrilinear interference terms. One such term gives the complex overlap between a propagated one-pulse target wave packet and a variable three-pulse reference wave packet. The two-dimensional interferogram in the time domain specifies the complex-valued overlap of the given target state with a collection of variable reference states. An inversion procedure based on singular-value decomposition enables reconstruction of the target wave packet from the interferogram without prior detailed characterization of the nuclear Hamiltonian under which the target propagates. With numerically calculated nonlinear WPI signals subject to Gaussian noise, we demonstrate the reconstruction of a rovibrational wave packet launched from the A state and propagated in the E state of Li2.

Dynamics of Electronic States and Spin−Flip for Photodissociation of Dihalogens in Matrices: Experiment and Semiclassical Surface-Hopping and Quantum Model Simulations for F2 and ClF in Solid Ar

Three approaches are combined to study the electronic states' dynamics in the photodissociation of F(2) and ClF in solid argon. These include (a) semiclassical surface-hopping simulations of the nonadiabatic processes involved. These simulations are carried out for the F(2) molecule in a slab of 255 argon atoms with periodic boundary conditions at the ends. The full manifold of 36 electronic states relevant to the process is included. (b) The second approach involves quantum mechanical reduced-dimensionality models for the initial processes induced by a pump laser pulse, which involve wavepacket propagation for the preoriented ClF in the frozen argon lattice and incorporate the important electronic states. The focus is on the study of quantum coherence effects. (c) The final approach is femtosecond laser pump-probe experiments for ClF in Ar. The combined results for the different systems shed light on general properties of the nonadiabatic processes involved, including the singlet to triplet and intertriplet transition dynamics. The main findings are (1) that the system remains in the initially excited-state only for a very brief, subpicosecond, time period. Thereafter, most of the population is transferred by nonadiabatic transitions to other states, with different time constants depending on the systems. (2) Another finding is that the dynamics is selective with regard to the electronic quantum numbers, including the Lambda and Omega quantum numbers, and the spin of the states. (3) The semiclassical simulations show that prior to the first "collision" of the photodissociated F atom with an Ar atom, the argon atoms can be held frozen, without affecting the process. This justifies the rigid-lattice reduced-dimensionality quantum model for a brief initial time interval. (4) Finally, degeneracies between triplets and singlets are fairly localized, but intertriplet degeneracies and near degeneracies can span an extensive range. The importance of quantum effects in photochemistry of matrix-isolated molecules is discussed in light of the results.

Decoherence control by tracking a Hamiltonian reference molecule

A molecular system in contact with a bath undergoes strong decoherence processes. We examine a control scheme to minimize dissipation, while maximally retaining coherent evolution, by relating the evolution of the molecule to that of an identical freely propagating system. We seek a driving field that maximizes the projection of the open molecular system onto the freely propagated one. The evolution in time of a molecular system consisting of two nonadiabatically coupled electronic states interacting with a bath is followed. The driving control field that overcomes the decoherence is calculated. A proposition to implement the scheme in the laboratory using feedback control is suggested.

Femtosecond quantum control of molecular dynamics in the condensed phase

We review the progress in controlling quantum dynamical processes in the condensed phase with femtosecond laser pulses. Due to its high particle density the condensed phase has both high relevance and appeal for chemical synthesis. Thus, in recent years different methods have been developed to manipulate the dynamics of condensed-phase systems by changing one or multiple laser pulse parameters. Single-parameter control is often achieved by variation of the excitation pulse's wavelength, its linear chirp or its temporal subpulse separation in case of pulse sequences. Multiparameter control schemes are more flexible and provide a much larger parameter space for an optimal solution. This is realized in adaptive femtosecond quantum control, in which the optimal solution is iteratively obtained through the combination of an experimental feedback signal and an automated learning algorithm. Several experiments are presented that illustrate the different control concepts and highlight their broad applicability. These fascinating achievements show the continuous progress on the way towards the control of complex quantum reactions in the condensed phase.

Ultrafast dynamics of halogens in rare gas solids

We perform time resolved pump-probe spectroscopy on small halogen molecules ClF, Cl2, Br2, and I2 embedded in rare gas solids (RGS). We find that dissociation, angular depolarization, and the decoherence of the molecule is strongly influenced by the cage structure. The well ordered crystalline environment facilitates the modelling of the experimental angular distribution of the molecular axis after the collision with the rare gas cage. The observation of many subsequent vibrational wave packet oscillations allows the construction of anharmonic potentials and indicate a long vibrational coherence time. We control the vibrational wave packet revivals, thereby gaining information about the vibrational decoherence. The coherence times are remarkable larger when compared to the liquid or high pressure gas phase. This fact is attributed to the highly symmetric molecular environment of the RGS. The decoherence and energy relaxation data agree well with a perturbative model for moderate vibrational excitation and follow a classical model in the strong excitation limit. Furthermore, a wave packet interferometry scheme is applied to deduce electronic coherence times. The positions of those cage atoms, excited by the molecular electronic transitions are modulated by long living coherent phonons of the RGS, which we can probe via the molecular charge transfer states.

Quenched by ice: Transient grating measurements of vibronic dynamics in bromine-doped ice

In both water and in ice, the absorption spectra of bromine are dramatically broadened and blueshifted, and all fluorescence is quenched. Time resolved, electronically resonant transient grating measurements are carried out to characterize the vibronic dynamics of the trapped molecule in its electronic B(3Pi0u) state in ice. Independent of the initial excitation energy, after the first half-period of motion, a vibrational packet is observed to oscillate near the bottom of the potential, near nu=1. The oscillations undergo a chirped decay to a terminal frequency of 169 cm(-1) on a time scale of taunu=1240 fs, to form the stationary nu=0 level. The electronic population in the B state decays in taue=1500 fs. Adiabatic following to the cage-compression coordinate is a plausible origin of the chirp. Analysis of the absorption spectrum is provided to recognize that solvent coordinates are directly excited in the process. The observed blueshift of the absorption is modeled by considering the Br2-OH2 complex. Two-dimensional simulations, that explicitly include the solvent coordinate, reproduce both the time data and the absorption spectrum. The observed sharp vibrational recursions can be explained by overdamped motion along the solvent coordinate, and wave packet focusing by fast dissipation during the first half-period of motion of the molecular coordinate.

Effective chromophore potential, dissipative trajectories, and vibrational energy relaxation: Br2 in Ar matrix

The intramolecular wave packet dynamics on the electronic B (3pi0) potential of Br2 in solid argon is induced and interrogated by femtosecond pump-probe spectroscopy. An effective potential of the chromophore in the solid is derived from the wave packet period for different excitation photon energies. Deep in the potential well, it is consistent with vibrational energies from wavelength-resolved spectra. It extends to higher energies, where the vibrational bands merge to a continuum, and even beyond the dissociation limit, thus quantifying the cage effect of the argon matrix. This advantage of pump-probe spectroscopy is related to a reduced contribution of homogeneous and inhomogeneous line broadenings. The vibrational energy relaxation rates are determined by a variation of the probe window spatial position via the probe quantum energy. A very large energy loss in the first excursion of the wave packet is observed near the dissociation limit. This strong interaction with the argon matrix is directly displayed in an experimental trajectory.

Pump-dump iterative squeezing of vibrational wave packets

The free motion of a nonstationary vibrational wave packet in an electronic potential is a source of interesting quantum properties. In this work we propose an iterative scheme that allows continuous stretching and squeezing of a wave packet in the ground or in an excited electronic state, by switching the wave function between both potentials with pi pulses at certain times. Using a simple model of displaced harmonic oscillators and delta pulses, we derive the analytical solution and the conditions for its possible implementation and optimization in different molecules and electronic states. We show that the main constraining parameter is the pulse bandwidth. Although in principle the degree of squeezing (or stretching) is not bounded, the physical resources increase quadratically with the number of iterations, while the achieved squeezing only increases linearly.

Pump–probe spectroscopy with phase-locked pulses in the condensed phase: decoherence and control of vibrational wavepackets

Electronic and vibrational coherences of Cl2 embedded in solid Ar are investigated by exciting to the B state with a phase-locked pulse pair from an unbalanced Michelson interferometer, where the chirp difference matches the B state anharmonicity. Recording the A' --> X fluorescence after relaxation is compared to probing to charge transfer states by a third pulse. The three-pulse experiment delivers more details on the decoherence processes. The signal modulation due to phase tuning up to the third vibrational round-trip time indicates that the electronic coherence in the B <-- X transition is preserved for more than 660 fs in the solid Ar environment where many body electronic interactions take place. Vibrational coherence lasts longer than 3 ps according to the observed half revival of the wavepacket. Control of the coupling between wavepacket motion and lattice oscillation is demonstrated by tuning the relative phase between the phase-locked pulses, preparing wavepackets predominantly composed of either zero-phonon lines or phonon side bands.