Excitation of multilevel Rydberg states (atoms and diatomic molecules) is studied under an intense time-periodic perturbation that is instantaneously turned on and off. For a one-quantum excitation from a lower lying state, general expressions for the Laplace images of the population amplitudes of Rydberg states are obtained with regard to their decay characteristics. It is shown that the problem considered is reduced to the determination of the positions and widths of the energy levels of a quantum system in the field of monochromatic laser radiation of the same frequency and intensity as that in a pulse mode. To determine these quantities, an integral formulation is proposed for the eigenvalue problem for energies that is relatively simply solved with regard to the effect of the ionic core and its complex vibration-rotation structure on diatomic molecules. The specific features of the excitation of Rydberg states and the behavior of Rydberg wave packets are studied depending on the intensity and duration of laser radiation. A quantum phenomenon of rotational orientation of electron-excited diatomic molecules is considered.
Excitation of multilevel Rydberg states (atoms and diatomic molecules) is studied under an intense time-periodic perturbation that is instantaneously turned on and off. For a one-quantum excitation from a lower lying state, general expressions for the Laplace images of the population amplitudes of Rydberg states are obtained with regard to their decay characteristics. It is shown that the problem considered is reduced to the determination of the positions and widths of the energy levels of a quantum system in the field of monochromatic laser radiation of the same frequency and intensity as that in a pulse mode. To determine these quantities, an integral formulation is proposed for the eigenvalue problem for energies that is relatively simply solved with regard to the effect of the ionic core and its complex vibration-rotation structure on diatomic molecules. The specific features of the excitation of Rydberg states and the behavior of Rydberg wave packets are studied depending on the intensity and duration of laser radiation. A quantum phenomenon of rotational orientation of electron-excited diatomic molecules is considered.
We develop a theory describing laser excitation of a Rydberg series by an intense laser field. Our theory is based on the fact that the radiative coupling is restricted to a region around the atomic nucleus (the reaction zone) which is small in comparison with the extent of the excited Rydberg states. The physical processes inside the reaction zone are characterized by a few parameters which are slowly varying functions of energy across the Rydberg threshold. This finite range of the radiative coupling allows us to apply methods from quantum-defect theory and to treat the laser interaction with the Rydberg series and the adjoining electron continuum as a whole. Within this approach we derive analytical expressions for transition probabilities as a function of time in either a dressed-state representation which is appropriate as long as only a few Rydberg states are excited or a multiple-scattering expansion which is particularly suited for a description of the excitation process close to threshold. The physical picture emerging in this limit is one of a radial electronic wave packet which is generated within the reaction zone and moves in the Coulomb potential of the ionic core. Every time it returns to the inner turning point of its orbit, i.e., to the reaction zone, it is either deexcited back to the initial atomic state or is scattered by the ionic core.
This thesis is a theoretical study of the behavior of electrons in atoms and molecules subjected to external electromagnetic fields. Three electronic systems have been central in this work, the atomic and quasimolecular Rydberg states and the carbon allotrope graphene. The exaggerated properties of the highly excited Rydberg atoms, such as long lifetime, large spatial extension and low binding energy make them excellent candidates for both theoretical and experimental considerations. The analytical solutions of the hydrogen atom in quantum mechanics provide a good description for most Rydberg atoms. This is exploited in the work presented in this thesis and the accompanying papers, where we show results of numerical computations on interacting Rydberg atoms, with and without the presence of radiating fields, as well as dynamic Rydberg wave packets influenced by a train of femtosecond laser pulses. In the final part of the thesis the optical process of high-order harmonic generation in an extended molecular structure, represented by graphene, is considered. Rydberg atoms have a large dipole moment due to the large average electronic radius in the atom, which leads to a very strong dipole-dipole coupling between interacting particles in a gas of cold Rydberg atoms. This interaction, which is dependent on the internuclear separation between the atoms, induces a shift in the energy levels, which again prohibits the excitation of more than one atom in the gas, an effect commonly known as the Rydberg blockade. A correlated behavior is observed for the intrashell transitions in mutually excited Rydberg atoms. The microwave field driven dynamics is significantly supressed for internuclear distances below a given conditional radius which scales linearly with the principal quantum number n. Such an entangled electronic behavior may open for the realization of quantum gates applied in quantum informatics. The long-range interaction of Rydberg atoms is dominated by the dipole-dipole terms. Nevertheless, the investigation of two interacting Rydberg atoms, without the influence of electromagnetic radiation, has shown that the lower order multipolar terms play a vital role in the energy shifts as well as for the electronic probability distributions. We found that the energy curves, when including all multipole orders, correspond to both repulsive and attractive states with a stronger repulsion than attraction. We also propose a laser assisted approach for stabilization of Rydberg gases by controlled transitions between such attractive and repulsive energy states. Single-electron ionization of a dynamic Rydberg wave packet confined within a single energy level has been investigated. The ionization probability of an intrashell Rydberg wave packet depends strongly on the degree of polarization. For a wave packet driven repeatedly between the circular (least polarized) state and the linear (most polarized) state by a rotating microwave field and subjected to a train of femtosecond laser pulses, the ionization probability will depend crucially on the laser repetition rate and number of pulses. The angular-resolved ionization probability and energy distribution in the continuum are also influenced by these parameters. The last part of the thesis is devoted to the study of high-order harmonic generation (HHG) in graphene. In the simple man’s model HHG can be described by an electron that is ionized and driven in an external field, after which it returns to the parent atom and recombines, emitting a high-energy photon with frequency that is a multiple of the incident laser frequency. We show that the harmonic spectra obtained from the interaction with linearly as well as circularly polarized femtosecond lasers yield harmonics up the classical limit for extended molecules. In contrast to diatomic molecules, the stable grid structure of graphene ensures that the harmonic generation cutoff remains constant with increasing signal power as the graphene diameter extends beyond the classical limit. Additionally, for circularly polarized lasers harmonics exceeding the classical predictions have been observed.
Quantum excitation is usually regarded as a transient process occurring instantaneously, leaving the underlying physics shrouded in mystery. Recent research shows that Rydberg-state excitation with ultrashort laser pulses can be investigated and manipulated with state-of-the-art few-cycle pulses. We theoretically find that the efficiency of Rydberg state excitation can be enhanced with a short laser pulse and modulated by varying the laser intensities. We also uncover new facets of the excitation dynamics, including the launching of an electron wave packet through strong-field ionization, the re-entry of the electron into the atomic potential and the crucial step where the electron makes a U-turn, resulting in twin captures into Rydberg orbitals. By tuning the laser intensity, we show that the excitation of the Rydberg state can be coherently controlled on a sub-optical-cycle timescale. Our work paves the way toward ultrafast control and coherent manipulation of Rydberg states, thus benefiting Rydberg-state-based quantum technology.
The absolute laser phase dependence of the time-dependent populations of the molecular states, including the steady-state (long time) populations of the states, associated with the interaction of a molecule with a pulsed laser is investigated using illustrative two-level examples. One-photon transitions, including the effects of permanent dipoles, are discussed as a function of the pulse duration, intensity, and (absolute) laser phase, for selected laser frequencies. The effects of laser phase can be large, depending on the values of the pulse duration for a given frequency and intensity. The effects of permanent dipoles, relative to no permanent dipoles, are significant for large laser field strengths ε0. When the laser-molecule coupling parameter b=μ12ε0/E21⩾0.2, where μ12 and E21 are the transition dipole and energy difference between the ground and excited states, respectively, the dynamics of the pulse-molecule interaction are (strongly) phase dependent, independent of pulse duration, whereas the corresponding steady-state populations of the molecular states may or may not be phase-dependent depending on the pulse duration. Analytical rotating wave approximations for pulsed laser-molecule interactions are useful for interpreting the dynamics and the steady-state results as a function of field strength and pulse duration, including the effects of permanent dipole moments. The results reported in this paper are based on molecular parameters associated with an S0→S1 electronic transition in a dipolar molecule. However, they are presented in reduced form and therefore can be scaled to other regions of the electromagnetic spectrum. Short, intense pulses at or beyond the limits of current laser technology will often be required for the types of absolute laser phase effects of this paper to be appreciable for electronic excitations. The discussion, in the UV-VIS, also suffers from the use of a two-level model and from the requirement of field intensities that can be beyond the Keldysh limit. For other spectral regions, these absolute laser phase effects will be much more readily applicable.
The short-pulse dynamics of excitation and stimulated emission between highly excited states (15<n<60) is studied with picosecond far-infrared pulses (40--60 $\ensuremath{\mu}\mathrm{m}$) originating from a free electron laser. We measured the excitation of a Rydberg wave packet in rubidium around n=40 excited from a deeper bound $(n\ensuremath{\approx}20)$ Rydberg state by a picosecond far-infrared laser pulse. Moreover, starting from a stationary n=40 state we found that upon irradiating with a short far-infrared laser pulse, adjacent Rydberg states are populated by resonant Raman transfer via a deeper (n=20) bound state. Finally, we discuss the dynamics of wave-packet excitation at a Cooper minimum in lithium, where sign change of the excitation matrix elements causes excitation at large distances from the atomic core. Possible measurement methods for this effect are discussed and found to yield different information.
Rydberg-state excitation of atoms in strong infrared laser fields provides a new complementary aspect of the perspective of atom--strong field interactions. In this article, we perform an experimental and theoretical study on the corresponding process of diatomic molecules, N2 and O2. We show that neutral molecules can also survive strong 800-nm laser fields in high Rydberg states, while their behavior is remarkably different in comparison with their companion atoms, Ar and Xe. The Rydberg excitation of N2 generally behaves similarly to Ar, while that of O2 is more significantly suppressed than the ionization compared to Xe in a high intensity region, which can be understood in the frame of a semiclassical picture, together with their different structures of molecular orbitals. However, distinct quantum features in the Rydberg excitation processes that are apparently beyond the semiclassical picture have been identified, i.e., the less suppressed probability of O2 at low intensity and the oscillation behavior of the ratio between N2 and Ar, indicating that our understanding of the relevant physics is still far from complete.