FEMTOSECOND LASER PHOTOELECTRON SPECTROSCOPY ON ATOMS AND SMALL MOLECULES: Prototype Studies in Quantum Control

Accelerated monotonic convergence of optimal control over quantum dynamics

The control of quantum dynamics is often concerned with finding time-dependent optimal control fields that can take a system from an initial state to a final state to attain the desired value of an observable. This paper presents a general method for formulating monotonically convergent algorithms to iteratively improve control fields. The formulation is based on a two-point boundary-value quantum control paradigm (TBQCP) expressed as a nonlinear integral equation of the first kind arising from dynamical invariant tracking control. TBQCP is shown to be related to various existing techniques, including local control theory, the Krotov method, and optimal control theory. Several accelerated monotonic convergence schemes for iteratively computing control fields are derived based on TBQCP. Numerical simulations are compared with the Krotov method showing that the new TBQCP schemes are efficient and remain monotonically convergent over a wide range of the iteration step parameters and the control pulse lengths, which is attributable to the trap-free character of the transition probability quantum dynamics control landscape.

Robust photon locking

We experimentally demonstrate a strong-field coherent control mechanism that combines the advantages of photon locking (PL) and rapid adiabatic passage (RAP). Unlike earlier implementations of PL and RAP by pulse sequences or chirped pulses, we use shaped pulses generated by phase modulation of the spectrum of a femtosecond laser pulse with a generalized phase discontinuity. The novel control scenario is characterized by a high degree of robustness achieved via adiabatic preparation of a state of maximum coherence. Subsequent phase control allows for efficient switching among different target states. We investigate both properties by photoelectron spectroscopy on potassium atoms interacting with the intense shaped light field.

Coherent manipulations of atoms using laser light

The internal structure of a particle - an atom or other quantum system in which the excitation energies are discrete - undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space statevector that provides the theoretical portrait of probability amplitudes - the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laser-pulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a three-dimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping "dark" states.

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.

Control of wave packets in Li(2) by shaping the pump and probe pulses for a state-selected pump-probe analysis of the ionization continuum

Wave packet signals in Li(2) prepared by shaped pump pulses are also detected with state-selected shaped probe pulses in the ionization continuum. The results show that the final states are discrete Rydberg states instead of continuum states. Final autoionizing states in the continuum are observed and characterized. By selecting specific resonant rovibrational electronic transitions from the superposition states prepared in the wave packets to the final autoionizing states with the pulse shaping system, the modulation depths of the wave packet signals are increased by as much as 5.20+/-0.03 times. Control of the wave packets is also realized by shaping the probe pulses to select specific resonant transitions between the states in the wave packets and the highly excited Rydberg states. The detected amplitude ratio of one specific vibrational quantum beat to one specific rotational quantum beat can be decreased by ten times.

Femtosecond time-resolved photoelectron imaging

Femtosecond time-resolved photoelectron imaging (TRPEI) is a variant of time-resolved photoelectron spectroscopy used in the study of gas-phase photoinduced dynamics. A new observable, time-dependent photoionization-differential cross section provides useful information on wave-packet motions, electronic dephasing, and photoionization dynamics. This review describes fundamental issues and the most recent works involving TRPEI.

Elucidation of Control Mechanisms Discovered during Adaptive Manipulation of [Ru(dpb)3](PF6)2 Emission in the Solution Phase

To design methodologies that will allow researchers to directly correlate the results of adaptive control experiments with physiochemical control pathways in arbitrary complex molecular systems it is imperative that prototype systems are developed and that exigent control pathways are understood. We have been interested in the results of adaptive control experiments in our laboratory involving the maximization of a ratio of two experimental observables: (1) the thermalized emission from the solution-phase coordination complex [Ru(dpb)3](PF6)2 and (2) the second harmonic signal (a purely intensity-dependent phenomenon) of the shaped laser fields. Using a rational pulse shaping strategy, we have made a measurement of the ratio spectrum (in essence the two-photon absorption cross section) for the molecule [Ru(dpb)3](PF6)2 in a room temperature solution of acetonitrile. This spectrum is highly varied across the accessible two-photon power spectrum of our broad-band laser pulses and demonstrates the existence of a control pathway wherein a shaped laser field can manipulate excited-state population (with respect to SHG) by conforming to the second-order spectral response of the molecule in solution. We show that our adaptive control algorithm is capable of taking advantage of these control pathways using simulated adaptive control experiments. Finally, we measure second-harmonic spectra of shaped laser fields discovered during an adaptive control experiment and show that these agree with simulation. These results suggest that our adaptive control experiment can be understood in the context of the elucidated spectral control pathway.

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.

Coherent polyatomic dynamics studied by femtosecond time-resolved photoelectron spectroscopy: Dissociation of vibrationally excited CS2 in the 6s and 4d Rydberg states

The dissociation dynamics of the 6s and 4d Rydberg states of carbon disulfide (CS(2)*) are studied by time-resolved photoelectron spectroscopy. The CS(2) is excited by two photons of 267 nm (pump) to the 6s and 4d Rydberg states and probed by ionization with either 800 or 400 nm. The experiments can distinguish and successfully track the time dynamics of both spin [1/2] (upper) and [3/2] (lower) cores of the excited Rydberg states, which are split by 60 meV, by measuring the outgoing electron kinetic energies. Multiple mode vibrational wave packets are created within the Rydberg states and observed through recurrence interferences in the final ion state. Fourier transformation of the temporal response directly reveals the coherent population of several electronic states and vibrational modes. The composition of the wave packet is varied experimentally by tuning the excitation frequency to particular resonances between 264 and 270 nm. The work presented here shows that the decay time of the spin components exhibits sensitivity to the electronic and vibrational states accessed in the pump step. Population of the bending mode results in an excited state lifetime of as little as 530 fs, as compared to a several picosecond lifetime observed for the electronic origin bands. Experiments that probe the neutral state dynamics with 400 nm reveal a possible vibrationally mediated evolution of the wave packet to a different Franck-Condon window as a consequence of Renner-Teller splitting. Upon bending, symmetry lowering from D(infinityh) to C(2v) enables ionization to the CS(2) (+) (B (2)Pi(u)) final state. The dissociation dynamics observed are highly mode specific, as revealed by the frequency and temporal domain analysis of the photoelectron spectra.