Vibrational Wavepacket Dynamics Research Articles

Determination of wave packet dynamics by femtosecond time-resolved pump-dump-probe and four-wave mixing techniques

Femtosecond time-resolved four-wave mixing (FWM) spectroscopy is performed in order to investigate molecular dynamics in iodine molecules in the gas phase. Depending on both the timing of the laser pulses and on the applied FWM technique different dynamics are observed in the FWM transient signals. By using the time-evolution diagrams the varying contribution of ground and excited state dynamics can be explained conclusively. Further, a femtosecond three-color pump-dump-probe scheme in combination with a time-of-flight mass selective detection unit has been applied to study vibrational wave packet dynamics in the electronic ground state of cold K 2 molecules. A spectral analysis of the time domain signal reveals two different wave packet contributions: hot wave packets from a stimulated Raman process and cold ones from stimulated emission pumping.

Femtosecond transient-grating techniques: Population and coherence dynamics involving ground and excited states

Time-resolved transient grating techniques (TG) arising from four-wave mixing (FWM) processes are explored for the study of molecular dynamics in gas-phase systems ranging from single atoms to large polyatomic molecules. For atomic species such as Ar and Xe, each TG signal shows only a peak at zero time delay when all three incident pulses are overlapped temporally. For diatomic O2 and N2 and linear triatomic CS2 molecules, the TG signals exhibit ground state rotational wave packet recurrences that can be analyzed to obtain accurate rotational constants for these molecules. With heavier systems such as HgI2, ground state vibrational and rotational wave packet dynamics are observed. Resonant excitation allows us to select between measurements that monitor wave packet dynamics, i.e., populations in the ground or excited states or coherences between the two electronic states. To illustrate these two cases we chose the X→B transition in I2. TG measurements yield dynamic information characteristic of vibrational and rotational wave packets from the ground and excited states. Reverse transient grating (RTG) experiments monitor the time evolution of an electronic coherence between the ground and excited states which includes vibrational and rotational information as well. Early time TG signal for the polyatomic samples CH2Cl2, CH2Br2, benzene, and toluene exhibit a coherence coupling feature at time zero followed by rotational dephasing. Differences in the amplitude of these two components are related to the contributions from the isotropic and anisotropic components of the molecular polarizability. A theoretical formalism is developed and used successfully to interpret and simulate the experimental transients. The measurements in this study provide gas-phase rotational and vibrational dephasing information that is contrasted, in the case of CS2, with liquid-phase measurements. This comparison provides a time scale for intramolecular dynamics, intermolecular collisions, and solvation dynamics.

Femtosecond energy- and angle-resolved photoelectron spectra

We present energy- and angle-resolved photoelectron spectra for femtosecond pump–probe ionization of wavepackets in the 1 Σ u + double-minimum state for aligned Na 2. These results illustrate that a robust description of the underlying photoionization amplitudes can significantly enhance the utility of photoelectron spectroscopy as a probe of wavepacket motion and of the evolution of electronic structure, particularly in cases of avoided crossings and motion over large distances. The angular dependence of these photoelectron spectra provide insightful fingerprints of vibrational wavepacket dynamics and can be a useful real-time probe of molecular rotation.

Femtosecond pump-probe and four-wave mixing spectroscopies applied to simple molecules

A femtosecond three color pump/dump-probe scheme in combination with a time-of-flight (TOF) mass selective detection unit has been applied to study vibrational wave packet dynamics in the electronic ground state of cold K 2 molecules. A spectral analysis of the time domain signal reveals two different wave packet contributions: one from a stimulated Raman process and one from stimulated emission pumping. Also femtosecond time-resolved degenerate four-wave mixing (DFWM) spectroscopy is performed in order to investigate molecular dynamics in iodine molecules in the gas phase. Depending on the timing of the laser pulses different dynamics are reflected in the DFWM transient signal. By the use of time-evolution diagrams, the varying contribution of ground and excited state dynamics can be explained conclusively.

Vibrational wave packet dynamics in NaK: The A [formula omitted] state

A combined experimental and theoretical study of the vibrational wave packet dynamics for the NaK molecule in the A 1 Σ + state is presented. The experiment utilises a 790 nm one-colour femtosecond pump-probe scheme with detection of a previously not reported dissociation pathway of the 3 1 Π + state, leading to the Na(3p)+K(4s) product channel. The dissociation is suggested to proceed via either collisionally mediated processes or a molecular cascading process via the 4 1 Σ + state, which crosses several states correlating to the Na(3p)+K(4s) limit. Time-dependent quantum mechanical calculations are used for studying the dynamics in detail. Simulations are performed both for 790 nm and for 766 nm, to relate also to earlier studies. The previous interpretations of the probe processes are revised. Inclusion of vibrational and rotational temperature effects are shown to be crucial for explaining the shape of the signal and the vibrational period, and leads to excellent agreement with the experiments.

A Theoretical Study of the Dynamics of Vibrational Wave Packets in the 1g State Of Xe2

We present a theoretical description of the dynamics of vibrational wave packets in the 1g state of Xe2. As an illustration, a simulation of a picosecond pump excitation-probe ionization laser experiment is carried out. The initial wavepacket is calculated using an explicit modelling of the short-pulse excitation process and propagated for up to 160 picoseconds. Evidence of fractional and full revivals of the wavepacket has been found and analyzed. The time delayed ionization signal is simulated using first order perturbation theory and shows clear oscillations corresponding to the temporal development of the wavepacket.

Femtosecond time-resolved observation of above-threshold ionization inNa2

Femtosecond pump-probe techniques are applied to the measurement of above-threshold ionization (ATI) electrons to observe the influence of vibrational wave-packet dynamics on molecular above threshold ionization in real time. When ionized by a single laser pulse structural changes in the ATI electron spectra map the changes of the vibrational wave-packet evolution in the resonant intermediate electronic states as a function of laser intensity. Molecular vibrational motion in the coherently coupled electronic states dominates the electron energy distribution rather than the energy splitting induced by Rabi oscillations.

Molecules in intense femtosecond laser fields

The interaction of small molecules (Na2, Na3) and larger molecules (C60, C70 and Fe(CO)5) with intense femtosecond laser fields is investigated experimentally. The experiments are performed by combining molecular beam and femtosecond pump-probe techniques with ion- and photoelectron detection. The recently developed femtosecond time resolved photoelectron spectroscopy is used to observe molecular dynamics over a wide range of internuclear distances. A main focus of the paper regarding small molecules is the change of the dynamics of molecular multiphoton ionization from the low laser intensity regime, where perturbation theory still can be applied, to the high laser intensity regime, where the electronic states participating in the multiphoton ionization processes are coupled coherently in Rabi-type processes. In this laser intensity regime, the influence of vibrational wavepacket dynamics on molecular above threshold ionization is also observed. Experiments on larger molecules are performed in a laser intensity regime where the generally accepted description of molecular multiphoton excitation has to be changed and recently proposed mechanisms due to the high field strenghts are discussed to explain the observations.

Femtosecond laser spectroscopy on the vibrational wave packet dynamics of the A 1Σ+ state of NaK

The vibrational wave packet dynamics of a heteronuclear diatomic alkali molecule in an excited state, the A 1 Σ + state of gaseous NaK, has been measured for the first time. At λ pump = 790 nm, a wave packet oscillation period of 442 fs and dephasing within 10 ps has been observed. This dynamics has been analysed by calculation of Franck-Condon factors and difference potentials. It is from this seen that initially the pump pulse prepares a wave packet at the inner turning point of the A-state. The wave packet then evolves in time and is probed at the outer turning point by a transition to the E-state with subsequent fluorescence detection.

Vibrational wave packets in the C 1Πu state of Cs2: Two color pump–probe experiments

Two color, pump–probe laser experiments on the ∼100 fs time scale have been applied to examining the dynamics of vibrational wave packets in the C 1Πu state of Cs2. Wave packets consisting of more than 20 C state vibrational levels are produced with an initial pulse having a central wavelength between ∼620 and 680 nm. The temporal history of the wave packet is inferred from the time and energy-integrated photoelectron signal produced when the excited state is photoionized by a time-delayed pulse centered at 605, 610, 615, 617, or 620 nm. Because of the difference in equilibrium internuclear separations for the Cs2(C) and Cs+2(X) states (ΔRe≊0.75 Å), wave packets are readily observed (signal-to-noise ratio ≳10) without the need to resort to mass selection techniques. Frequency analysis of the wave packet data shows a dominant (fundamental) component that decreases from 29 to ∼28.3 cm−1 as the pump wavelength is tuned from 627 to 641 nm. Other spectral modes at ∼23.5 and ∼34 cm−1 and a weaker term at twice the fundamental frequency are also observed and quantum mechanical calculations of the wavepacket motion are in accord with the experimental results.

Collisional enhancement of Rydberg lifetimes observed in vibrational wave packet experiments

Evidence for lifetime enhancement of Rydberg states by interactions with surrounding ions is obtained from femtosecond pump–probe experiments on the vibrational wave packet dynamics of the I2(B)-state, in which either detection of I+2 ions or zero-kinetic energy (ZEKE) electrons was used. The use of the ZEKE technique leads to the appearance of new frequency components in the Fourier transform power spectra of pump–probe time delay scans, as well as the observation of enhanced peak-to-valley ratios in these scans. These observed frequency components do not correspond to any energy level spacings in the molecule; they correspond to a sum of two energy level spacings, suggesting a nonlinear detection mechanism in the ZEKE technique (i.e., interaction with ions). Additional evidence for our interpretation is presented through experiments in which additional ions were formed through nonresonant multiphoton ionization of I2 with a picosecond 266 nm laser, as well as experiments in which both the decay time of the ZEKE signal and the appearance of the pump–probe time delay scans as a function of the pulsed field time delay were studied. Theoretical wave packet calculations which support the conclusions are presented.

Dissipative vibrational dynamics in a curve–crossing system

The density matrix theory is utilized for the description of ultra fast optical properties and related vibrational wave packet dynamics of molecular systems in condensed media. As an example, optically induced vibrational wave packets in the so-called curve–crossing system are considered. Such a system goes beyond the standard treatment of optical phenomena since the vibrational wave packet moves in a double well potential and is subject to environmental influences like wave function dephasing and relaxation. The complete theoretical description has been carried out in a representation of the vibrational wave functions of the diabatic states which refer to the two coupled vibrational surfaces. Solving the corresponding density matrix equations by numerical methods allows us to incorporate the static coupling between the crossed surfaces in a nonperturbative manner. Standard projection operator technique is used to treat environmental contributions up to the second order. For the case of a bilinear coupling between the molecular system and the environment we determine the time development of an initially prepared Gaussian wave packet. Corresponding time-resolved spectra of a pump–probe configuration are also derived. The developed formalism is finally applied to the system of the coupled electronic states c′ 1Σ+u and b′ 1Σ+u of the N2 molecule.

Density matrix theory of dissipative wave packet dynamics

We demonstrate the applicability of the density matrix approach to describe dissipative effects like dephasing and relaxation on the dynamics of vibrational wave packets. As a simple example we study a single excess electron or exciton in a dimer system with a single interaction coordinate coupling to the electronic state. The other molecular vibrations constitute the dissipative environment which is assumed to be in thermal equilibrium. We compare the dissipative dynamics of two distinct initial wave packets for different effective damping rates.

Wave-packet dynamics of photodissociation of a linear triatomic molecule under intense nonstationary laser field condition

Vibrational wave-packet dynamics of photodissociation of a linear triatomic BAB-type molecule under intense nonstationary radiation field condition is theoretically studied. We clarify how the wave-packets on the ground and excited adiabatic potential surfaces are coupled with each other through the molecule—laser field interaction. The excited state wave-packet is localized with double maximum structure, and the photodissociation process is suppressed during the intense molecule-radiation field interaction. It is also clarified how oscillatory behavior in intensity signals in femtosecond transition state experiments originates from the wave-packet propagation on the two-dimensional potential surface of the excited state after termination of the pulsed laser. The final momentum distribution of the photodissociation fragments is evaluated, and the fragment formation mechanism is discussed.

Dynamics of vibrational wave packets in the C 1Π u state of Cs 2

The dynamics of vibrational wave packets in the weakly predissociated C 1Π u of Cs 2 have been examined by two color, femtosecond laser pump—probe techniques. The motion of the wave packet is detected by photoionizing the dimer with a time-delayed 620nm pulse and monitoring the time-and energy-integrated photoelectron signal with a proportional counter. Since the anharmonicity of Cs 2(C 1Π u is light (ω e/ω e x e≈700) and the ground state vibrational manifold is equilibrated at T≈500 K, wave packets consisting of the superposition of wavefunctions of more than 20 vibrational levels are formed that dephase in ≈ 18 ps.