RYDBERG WAVEPACKETS IN MOLECULES: From Observation to Control

Wave packet dynamics and control in excited states of molecular nitrogen

Wave packet interferometry with vacuum ultraviolet light has been used to probe a complex region of the electronic spectrum of molecular nitrogen, N2. Wave packets of Rydberg and valence states were excited by using double pulses of vacuum ultraviolet (VUV), free-electron-laser (FEL) light. These wave packets were composed of contributions from multiple electronic states with a moderate principal quantum number (n ∼ 4-9) and a range of vibrational and rotational quantum numbers. The phase relationship of the two FEL pulses varied in time, but as demonstrated previously, a shot-by-shot analysis allows the spectra to be sorted according to the phase between the two pulses. The wave packets were probed by angle-resolved photoionization using an infrared pulse with a variable delay after the pair of excitation pulses. The photoelectron branching fractions and angular distributions display oscillations that depend on both the time delays and the relative phases of the VUV pulses. The combination of frequency, time delay, and phase selection provides significant control over the ionization process and ultimately improves the ability to analyze and assign complex molecular spectra.

Probing Rydberg-Rydberg interactions in N2 by ultrafast EUV-NIR photoelectron spectroscopy

The ultrafast dynamics of molecular nitrogen (N₂) just below the ionization threshold has been investigated by time-resolved photoelectron spectroscopy using a single harmonic centered at hν = 15.38 eV. The evolution of the Rydberg wavepacket launched by the ultrashort EUV pulse is probed by a time-delayed femtosecond NIR laser pulse. The observed photoelectron spectra show two series of vibrational peaks to the ground X²Σg+ state and the first excited A²Πu state of N2+. Among these, two photoelectron peaks with the vibrational quantum numbers v_X+ = 4 and v_A+ = 1 exhibit clear anti-phase oscillation with a period of 300 fs, showing that two Rydberg states converging to the X²Σg+ and A²Πu ionic states interact with each other, thus causing periodic switching in the population of the ion core states.

Single-order laser high harmonics in XUV for ultrafast photoelectron spectroscopy of molecular wavepacket dynamics

We present applications of extreme ultraviolet (XUV) single-order laser harmonics to gas-phase ultrafast photoelectron spectroscopy. Ultrashort XUV pulses at 80 nm are obtained as the 5th order harmonics of the fundamental laser at 400 nm by using Xe or Kr as the nonlinear medium and separated from other harmonic orders by using an indium foil. The single-order laser harmonics is applied for real-time probing of vibrational wavepacket dynamics of I₂ molecules in the bound and dissociating low-lying electronic states and electronic-vibrational wavepacket dynamics of highly excited Rydberg N₂ molecules.

Visualizing the coupling between red and blue stark states using photoionization microscopy

In nonhydrogenic atoms in a dc electric field, the finite size of the ionic core introduces a coupling between quasibound Stark states that leads to avoided crossings between states that would otherwise cross. Near an avoided crossing, the interacting states may have decay amplitudes that cancel each other, decoupling one of the states from the ionization continuum. This well-known interference narrowing effect, observed as a strongly electric field-dependent decrease in the ionization rate, was previously observed in several atoms. Here we use photoionization microscopy to visualize interference narrowing in helium atoms, thereby explicitly revealing the mechanism by which Stark states decay. The interference narrowing allows measurements of the nodal patterns of red Stark states, which are otherwise not observable due to their intrinsic short lifetime.

Correlated diskoid-like electronic states

We study highly excited diskoid-like electronic states formed in the vicinity of charged and strongly polarizable diskotic nanostructures, such as circular graphene flakes. First, we study the nature of such extended states in a simple two-electron model. The two electrons are attached to a point-like nucleus with a charge 2+, where the material electron is forced to move within a 2D disk area centered at the nucleus, while the extended electron is free to move in 3D. Pronounced and complex correlations are revealed in the diskoid-like states. We also develop semiclassical one-electron models of such diskotic systems and explain how the one-electron and many-electron solutions are related.

Control of coherent excitation of neon in the extreme ultraviolet regime

Coherent excitation of a superposition of Rydberg states in neon by the 13th harmonic of an intense 804 nm pulse and the formation of a wave packet is reported. Pump-probe experiments are performed, where the 3d-manifold of the 2p6-->2p5 (2P3/2) 3d [1/2]1- and 2p6-->2p5 (2P3/2) 3d [3/2]1-transitions are excited by an extreme ultraviolet (XUV) radiation pulse, which is centered at 20.05 eV photon energy. The temporal evolution of the excited state population is probed by ionization with a time-delayed 804 nm pulse. Control of coherent transient excitation and wave packet dynamics in the XUV-regime is demonstrated, where the spectral phase of the 13th harmonic is used as a control parameter. Modulation of the phase is achieved by propagation of the XUV-pulse through neon of variable gas density. The experimental results indicate that phase-shaped high-order harmonics can be used to control fundamental coherent excitation processes in the XUV-regime.

Long-lasting molecular alignment: fact or fiction?

It has been suggested that appropriate periodic sequences of laser pulses can maintain molecular alignment for arbitrarily long times [J. Ortigoso, Phys. Rev. Lett. 93, 073001 (2004)]. These aligned states are found among the cyclic eigenstates of truncated matrix representations of the one-period time propagator U(T,0). However, long time localization of periodic driven systems depends on the nature of the spectrum of their exact propagator; if it is continuous, eigenstates of finite-basis propagators cease to be cyclic, in the long time limit, under the exact time evolution. We show that, for very weak laser intensities, the evolution operator of the system has a point spectrum for most laser frequencies, but for the laser powers needed to create aligned wave packets it is unknown if U(T,0) has a point spectrum or a singular continuous spectrum. For this regime, we obtain error bounds on the exact time evolution of rotational wave packets that allow us to determine that truncated aligned cyclic states do not lose their alignment for millions of rotational periods when they evolve under the action of the exact time propagator.

Wave-Packet and Coherent Control Dynamics

This review summarizes progress in coherent control as well as relevant recent achievements, highlighting, among several different schemes of coherent control, wave-packet interferometry (WPI). WPI is a fundamental and versatile scenario used to control a variety of quantum systems with a sequence of short laser pulses whose relative phase is finely adjusted to control the interference of electronic or nuclear wave packets (WPs). It is also useful in retrieving quantum information such as the amplitudes and phases of eigenfunctions superposed to generate a WP. Experimental and theoretical efforts to retrieve both the amplitude and phase information are recounted. This review also discusses information processing based on the eigenfunctions of atoms and molecules as one of the modern and future applications of coherent control. The ultrafast coherent control of ultracold atoms and molecules and the coherent control of complex systems are briefly discussed as future perspectives.

Coherent control of population transfer in Rydberg atoms via chirped microwave pulses

We present a comprehensive and ab initio nonperturbative investigation of the coherent population transfer among the 3D high-lying Rydberg hydrogen and alkali atomic states via linearly polarized chirped microwave pulses. The time-dependent Schrödinger equation for the dynamical evolution of Rydberg atoms is accurately and efficiently solved by means of the time-dependent generalized pseudospectral method. For atomic H, the population transfer from n = 35 to 30 with nearly 100% efficiency is achieved by means of the sequential two-photon Deltan = -1 transitions. The calculation fully utilizes all of the available orbital angular momentum l states for a given n, and the interference pattern and population evolution dynamics of individual l states are analyzed in detail. It is shown that the coherent control of the population transfer from the high n to the low n states can be accomplished by the optimization of the chirping parameters and microwave field strength. Similar analysis is performed for the Na atom, where the alkali atomic structure is described by an accurate model potential. We found that while the global population transfer pattern is qualitatively similar, there are significant differences in the dynamical response of atomic H and Na to the chirped microwave fields. Due to the degeneracy of the l states (for a given n) in unperturbed atomic H, the population transfer involves significant coupling and interference among a number of low-lying l states. For the case of Na atoms, however, the population transfer from the n to (n - 1) state is dominated by a single channel, namely, from the |n,l = 0> to the |n - 1,l = 0> state.

VIBRATIONAL AUTOIONIZATION IN POLYATOMIC MOLECULES

▪ Abstract  The vibrationally autoionizing Rydberg states of small polyatomic molecules provide a fascinating laboratory in which to study fundamental nonadiabatic processes. In this review, recent results on the vibrational mode dependence of vibrational autoionization are discussed. In general, autoionization rates depend strongly on the character of the normal mode driving the process and on the electronic character of the Rydberg electron. Although quantitative calculations based on multichannel quantum defect theory are available for some polyatomic molecules, including H3, only qualitative information exists for most molecules. This review shows how qualitative information, such as Walsh diagrams along different normal coordinates of the molecule, can provide insight into the vibrational autoionization rates.