The bound state in the spectrum of the Lee–Friedrichs Hamiltonian

Abstract The spectrum of the Lee–Friedrichs Hamiltonian, describing a two-level system embedded in a continuum, is considered. An appropriate discretization of the field modes is performed before taking the continuum limit. It is shown that the existence of an eigenstate with negative energy (bound state) is related to the nonanalyticity of the Friedrichs spectral representation. This negative energy state is a dressed state and its physical properties are studied in some significant cases.

Piecewise static Hamiltonian for an atom in strong laser field

We show that it is possible to use a piecewise constant Hamiltonian to describe the main features of the dynamics of an atom interacting with a laser field. In particular we show that using this approximation we are able to give a good description of the ionization signal, of the HHG spectra and of the attosecond pulses generated by the radiating electron. Finally, we give an explicit formula to evaluate the ionization rate in the time dependent laser field. This formula, which is a generalization of the Landau formula for the ionization rate of an atom in a static electric field, fairly well reproduces the numerical ionization rates for a broad range of laser frequency and intensity. The m…

Canonical transformation for single-atom resonance fluorescence: The strong-driving-field limit

High-order-harmonic generation in dimensionally reduced systems

The time-dependent wave function of a nanoring driven by a laser field is obtained by exploiting the symmetries inherent to the system and used for studying the properties of the electromagnetic radiation emitted by the nanoring as a function of the polarization state of the laser. The diffused radiation has the characteristics of high-order-harmonic generation. For a noncircularly polarized laser field an extension of the expected cutoff position is evident, indicating that nanorings are efficient sources of radiation. The polarization state of the emitted harmonics can be opportunely controlled by varying the parameters of the pump field. The profile of the absorbed angular moment shows t…

High order harmonic generation: The role of the acceleration matrix elements and of the bound and continuum transitions

The electromagnetic spectrum emitted by a one-dimensional atom driven by a strong laser field is obtained by use of the acceleration form and interpreted by means of few general properties of the matrix elements of the acceleration operator. We show that the emission occurs essentially in a region near the atomic core where the acceleration is significant and we investigate the role of the various emission channels arising from interference effects between transitions involving the bare atomic levels.

High-order harmonic generation in fullerenes using few- and multi-cycle pulses of different wavelengths

We present the results of experimental and theoretical studies of high-order harmonic generation (HHG) in plasmas containing fullerenes using pulses of different duration and wavelength. We find that the harmonic cutoff is extended in the case of few-cycle pulses (3.5 fs, 29th harmonic) compared to longer laser pulses (40 fs, 25th harmonic) at the same intensity. Our studies also include HHG in fullerenes using 1300 and 780 nm multicycle (35 and 40 fs) pulses. For 1300 nm pulses, an extension of the harmonic cutoff to the 41st order was obtained, with a decrease in conversion efficiency that is consistent with theoretical predictions based on wave packet spreading for single atoms. Theoreti…

Electrons on a spherical surface: Physical properties and hollow spherical clusters

We discuss the physical properties of a noninteracting electron gas constrained to a spherical surface. In particular we consider its chemical potentials, its ionization potential, and its electric static polarizability. All these properties are discussed analytically as functions of the number $N$ of electrons. The trends obtained with increasing $N$ are compared with those of the corresponding properties experimentally measured or theoretically evaluated for quasispherical hollow atomic and molecular clusters. Most of the properties investigated display similar trends, characterized by a prominence of shell effects. This leads to the definition of a scale-invariant distribution of magic n…

Cloud of virtual photons in the ground state of the hydrogen atom.

A spinless, nonrelativistic hydrogen atom coupled to an electromagnetic field is considered. The interaction is taken in the minimal-coupling form, and the ground state of the coupled system is obtained by straightforward perturbation theory. The form of the cloud of virtual photons surrounding the atom is studied through the quantum-mechanical average on this state of an appropriately defined coarse-grained energy-density (CGED) operator W(r\ensuremath{\rightarrow}). The properties of W(r\ensuremath{\rightarrow}) are studied in order to show that this operator can give a reliable description of the shape of the virtual photon cloud. The quantum-mechanical average of W(r\ensuremath{\rightar…

Ionization dynamics of a model molecular ion

We study the ionization dynamics of a model one-dimensional molecular ion as a function of the internuclear distance R, for different values of the laser intensity. The electron–nucleus potential is assumed to be a Poschl–Teller potential, whose parameters are chosen to have only two bare bound molecular states in the range of R considered. We describe three different theoretical approaches to study the dynamics of the system: an exact numerical, a semiperturbative and a phenomenological approach. All these approaches indicate the presence of a sharp ionization peak for a critical value of the internuclear distance, for which the energy difference between the two bound levels coincides with…

Space-time localization of the radiation emitted by an electromagnetically driven charge and the question of the position of an electron

Abstract We study the electromagnetic spectrum emitted by a free charge driven by a strong laser field in the proximity of a stationary scattering centre that acts as an accelerating third body. We show that under the most general conditions the radiation is emitted close to the scatterer and during a welldefined time interval. Thus it should be possible, at least in principle, to determine the position of the electron by observing the radiation that it is emitting.

A paradigm of fullerene

We study the dynamics of an electron constrained over the surface of a rigid sphere, with geometrical parameters similar to those of the C60 fullerene, embedded in a low intensity linearly polarized laser field. The model is shown to emit odd harmonics of the laser even at very low field intensity. For more intense laser fields, the spectrum presents odd harmonics and hyper-Raman lines shaped in a broad plateau. The spectrum of the model is compared to that theoretically obtained by other authors for more realistic models of C60. It is concluded that the model can be used as a paradigm for mesoscopic molecules in the fullerene family, particularly in practical applications where it is conve…

Evidence of Nuclear Motion in H2-like Molecule by Means of High Order Harmonic Generation

The dynamics of hydrogen-like molecules is investigated beyond the usual fixed nuclei approximation. The nuclear motion introduces in the familiar spectrum of emitted radiation additional regular lines whose separation is essentially given by the vibrational frequency of nuclear motion. A wavelet analysis of the emitted spectrum shows that the intensity of the harmonic lines is modulated with the same period of the nuclear motion; this suggests the possibility of the real-time control of the nuclear dynamics.

High Order Harmonics from a Molecule: Evidence of the Nuclear Motion

The electromagnetic spectrum emitted by a molecule driven by a laser presents harmonics and satellite lines whose separation is equal to the oscillation frequency of the nuclei. Full quantum and semiclassical calculations are presented.

Confinement and high-order harmonic generation by a repulsive potential

The dynamics of an electron wave packet in the presence of laser radiation and of a one-dimensional repulsive soft-core potential is investigated. For different laser intensities and for different initial positions of the electron wave packet, these results are compared with those for an attractive potential. The repulsive potential is capable of confining the electron quite efficiently under appropriate conditions. In these conditions, the electron is shown to emit a high harmonic spectrum similar to that emitted by the more conventional attractive potential. It is thus argued that recombination into an atomic bound state as required by the three step model is not essential for the emissio…

Spectrum emitted by a trapped electron

We study the behaviour of a homonuclear molecule driven by an intense laser field. Newton's laws are used to describe the dynamics of nuclei while the quantal approach is reserved to the study of the electron. It is observed that the nuclei can oscillate or dissociate according to the degree of ionization of the molecule. In case of low ionization rate it is shown that great amount of information can be obtained by using the simplified approaches of fixed nuclei and of two-state approximation. Under suitable conditions the electron wave function spends a long time localized around one nucleus. The harmonic generation of the molecule is studied and seen to contain even harmonics.

The electron wavefunction in laser-assisted bremsstrahlung

The active region for emission of radiation by an electron driven by a strong laser field in the proximity of a stationary scattering centre is localized in space and time. It is argued that the extension of this region can be controlled by changing the velocity of the electron, and that information on this extension is contained in the duration and in the spectrum of the emitted radiation pulse.

Reply to “Comment on ‘Limits of the measurability of the local quantum electromagnetic field amplitude’ ”

Direct theoretical evidence of nuclear motion in H+2by means of high harmonic generation

The numerical solution of the time-dependent Schro ̈dinger equation for vibrating hydrogen molecular ions in many-cycle laser pulses shows that high- order harmonic generation is sensitive to laser-induced molecular vibrations. In particular, the odd harmonic lines in the emitted spectra are surrounded by additional regular peaks whose spacing is given by the vibrational frequency of the nuclei motion. Analytical theory relates these satellite peaks to the molecular vibrations in terms of an approximated effective potentials. These results are not affected by the dimensionality of the system.

Even harmonics from laser driven homonuclear molecules

The dynamics of a homonuclear diatomic molecule driven by a laser pulse is obtained beyond the fixed nuclei approximation. Laser parameters can be adjusted to confine the electron over one of the two nuclei for a relatively long time or not. A time-resolved analysis of the electromagnetic spectrum emitted by the molecule presents the usual odd harmonics far from confinement and even harmonics during the confinement periods. A physical interpretation of the results is given.

Rescattering and vibrations in homonuclear diatomic molecules in a strong electromagnetic field

Abstract The electron of a H 2 + driven by a strong electromagnetic field induces molecular vibrations. Numerical and analytical results show that the molecule behaves as a parametric oscillator and can be treated as a kicked oscillator. The results are discussed from the point of view of the electron's periodic dressing and undressing processes.