Control of Electron Motion in a Molecular Ion: Dynamical Creation of a Permanent Electric Dipole

The dynamics of a diatomic one-dimensional homonuclear molecule driven by a two-laser field is investigated beyond the usual fixed nuclei approximation. The dynamics of the nuclei is treated by means of Newton equations of motion; the full quantum description is used for the single active electron. The first laser pulse (pump) excites vibrations of the nuclei, while the second very short pulse (probe) has the role of confining the electron around one of the nuclei. We show how to use the radiation scattered in these conditions by the molecule to achieve real-time control of the molecular dynamics.

REAL-TIME MONITORING OF LASER-DRIVEN MOLECULES

HARMONIC PROFILE IN MOLECULAR ION IN THE PRESENCE OF A LASER RADIATION FIELD

Nanorings driven by a laser field

We present the dynamics of an electron constrained over an 1D ring with radius of 0.142 nm driven by a laser field. The temporal evolution of the system is evaluated by a semi-analytical solution of the full quantum time dependent Schr¨odinger equation. In our calculation the gap energy between the ground and the first excited state of the nanoring is three times the photon energy laser (0.63 eV) and the laser intensity is 4·1014 W/cm2 . Our analysis is performed by considering different polarization states of the incident laser. Our attention is mainly focused on the study of the High Harmonic Generation (HHG), the energy and the angular momentum absorbed by the driven system. We observe 1…

The influence of the quantum nature of nuclei in high harmonic generation from H+2-like molecular ions

We study the full quantum dynamics of a simple molecular ion driven by an intense laser field. In particular we show that the quantum nature of the nuclear dynamics affects the emitted high harmonic generation (HHG) spectra, strongly reshaping the plateau region. In fact, it is evident that the characteristic flat trend is transformed into a descending trend, with the lower harmonics being two orders of magnitude more intense than the higher harmonics. We show that this effect is more pronounced in the lighter isotopic species of H2+ molecular ions and we also demonstrate that in this case the contribution to HHG from the antibonding electronic energetic surface is of the same order of magn…

The table top high frequency lasing device

Atomic and molecular systems, subjected to intense laser pulse, emit typical High-Order Armonic Generation (HHG) spectra. This work aims to investigate the possibility to obtain a laser device by HHG. At this end, we analyzed the emission spectra by a molecular ion driven by a linearly polarized laser field. The temporal behaviour is obtained using the Morlet wavelets transform of emission. The results show that, after filtration of the electromagnetic radiation emitted, it is possible to select a frequency which seems to have almost constant intensity and phase. This characteristic makes possible that HHG from a molecule can be used as high frequency laser fields.

Probing the Dynamics of a Molecular Ion with Laser Pulses

The dynamics of a H2+ molecular ion driven by two laser pulses separated by a time lag is studied beyond the Born-Oppenheimer approximation. The first, short, pulse prepares the molecule in some quantum state, which is probed by the second pulse. Under suitable conditions, the molecule emits a spectrum of redshifted high-order harmonics. The value of the redshift is proportional to the harmonic order and can be used as a measure of the speed of the atoms of the molecule.

Simulazione numerica di una molecola H2 in campi laser intensi

Full Quantum Treatment of an H2+ Molecule in Presence of a Laser to Study the Nuclear Motion

High-Order Harmonic Generation from Molecules: Classical versus Quantum Effects

The dynamics of the electron in a homonuclear driven molecular ion

Abstract The radiation diffused by a one-dimensional homonuclear molecular ion driven by a laser field is studied as a function of the time. When the photon energy is resonant with the energy gap between the ground and the first excited state, the electronic probability density is seen to undergo slow and deep oscillations between the two nuclei. Synchronous to such oscillations, deep modulations of the emitted power are observed. The period of oscillation is of the order of 10 optical cycles. Detection of the variation in the intensity of the emitted electromagnetic spectrum therefore brings information on the position of the electron in the molecule.

High harmonics generation from structured nanorings

In this work we study the radiation diffused by a fictitious structured nanoring driven by an intense laser field. In our model we consider an electron moving through a cosine-shape potential. The results show that the ring, under particular conditions, emits a wide spectrum of harmonics.

Control of the high harmonic generation spectra by changing the molecule-laser field relative orientation

The time dependent Schrodinger equation of a homonuclear diatomic molecule in the presence of a linearly polarized laser field is numerically solved by means of a split-operator parallel code. The calculations are carried out by assuming a single active electron model with fixed nuclei; a simplified two-dimensional model of the system is used. The highly nonlinear response of the electron wave function to the laser electric field stimulates the molecule to emit electromagnetic radiation consisting of a wide plateau of odd harmonics of the laser field. It is shown that the emitted spectrum can be finely controlled by changing the angle between the laser electric field and the molecular axis;…

Evidence of Nuclear Motion in Hydrogen-like Molecules by Means of High Harmonic Generation

High frequency lasing device by HHG

High frequency lasing device by HHG

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…

Study of the Effects of Nuclear Motion on High Harmonic Generation in Simple Molecules

High-order harmonic generation via bound-bound transitions in an elliptically polarized laser field

We use a simplified five-level system to investigate the high-order harmonic generation (HHG) spectrum emitted by an atom driven by a linearly or elliptically polarized laser field. For this model, the Schrödinger equation is exactly analytically reduced to the system of ordinary differential equations, which is solved numerically. Studying the intensity and polarization of the emitted radiation, we find that under high laser ellipticity the harmonic emission is suppressed. However, the harmonic intensity typically depends nonmonotonously on the laser ellipticity. Such anomalous behavior is very pronounced for the resonant harmonic. We offer an explanation of this behavior based on the incr…

Nuclear Molecular Dynamics Investigated by Using High Order Harmonic Generation Spectra

In this paper we show how it is possible to investigate the nuclear dynamics of simple molecular ions and molecules by looking at the high-order harmonic generation spectra they emit in the presence of a laser field. In particular we investigate two different effects: the presence of sidebands in the emitted spectra around the usual odd harmonics and an isotopic effect which affects the height of the plateau lines. We further study the advantages and the limitations of the semiclassical approach.

Harmonic Spectra in H2⁺ in the Presence of a Laser Field

HHG by a 3D-H2+ molecular ion

Study of the effects of nuclear motion on High Harmonic Generation in simple molecules

Sidebands of Harmonic Spectra in H2+ Molecule in the Presence of a Laser

Dynamics of H2 molecule driven by an ultra-short laser field

We describe, using a semiclassical approach, the molecular dynamics of a one-dimensional H2 molecule interacting with a laser, beyond the Born–Oppenheimer approximation. We observe and discuss different molecular behaviors, such as ionization and dissociation.

The Study of Nuclear Motion in D2+ Molecular Ion by Using the Harmonic Spectra

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.

Pulse-duration dependence of the isotopic effect in simple molecular ions driven by strong laser fields

In this paper we discuss isotopic effects in simple molecular ions subjected to strong laser fields. We show that the intensity of the emitted spectra strongly depends upon both the nuclear mass of the molecular ions and the laser pulse duration. In particular, for short pulse duration [up to 8 optical cycles (o.c.)], we confirm the trend described in the most studied case in which the high-order harmonic generation is more efficient for heavier isotopes; in contrast, an interesting physical phenomenon is predicted for pulses longer than 16 o.c. characterized by an inverse effect in which lighter molecular species are responsible for higher-order harmonic emission.

Evidence of Nuclear Motion in H2 Molecule through High Horder Harmonic Generation

High-order harmonic generation via bound-bound transitions in elliptically polarized laser field

We use a 5-level system to investigate the HHG spectrum emitted by an atom driven by a linearly or elliptically polarized laser field. For this model the Schrodinger equation is numerically solved and we study the dipendence of the spectra, harmonic intensity and polarization of emitted radiation on the laser field ellipticity. Studying the intensity of the emitted radiation we find that un alsoder high laser ellipticity the harmonic emission is greatly reduced; the analysis of results shows that the harmonic intensity and the emitted radiation depend on the laser ellipticity.

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.

Properties of the radiation Emitted by a Laser driven quantum Ring

We present the electromagnetic emission from one electron confined in a quantum ring driven by an intense laser field. We consider both a plain ring and one structured by six potential wells that produce a static tangential force. Through a suitable one-dimensional model we numerically solve the associated Schroedinger equation obtaining the correspondent time evolution of the wave-function. We show that the emission is formed by a wide plateau that can be both quasi-continuum or resolved in discrete lines. We study the dependence of the emitted spectra from the polarization status of the external laser field and in particular we concentrate on the intensity of the emitted lines and of thei…

High harmonic generation from structured nanorings

Tertiary relict laurophyll vegetation in the Madonie mountains (Sicily)

Laurel woodlands in the Madonie mountains (Sicily) are characterized by the presence of Laurus nobilis, Rhamnus lojaconoi and Vitis vinifera subsp. sylvestris. The results of a phytosociological study are presented, and a new endemic association, Rhamno lojaconoi–Lauretum nobilis, is described. Present Mediterranean laurel communities are the result of an adaptive response by Tertiary laurel forest to the peculiar microclimatic conditions that characterize the refugia where they persist. These refugia have been recently considered as a priority habitat under the Directive 92/43/EEC, and their plant communities are very vulnerable. Protection measures of the studied laurel populations are ne…

Laser Assisted Atomic Ionization by a Short XUV Pulse

We report on numerical results of energy spectra of photoelectrons emitted by irradiating an hydrogen atom with a relatively weak single attosecond XUV pulse in the presence of a two-color IR laser pulse. The densities of probabilities have been obtained by treating the interaction of the atom with the XUV radiation at the first order of the time-dependent perturbation theory and describing the emitted electron through the Coulomb-Volkov wavefunction. The results of the calculations agree with the ones found by numerically solving the time-dependent Schrödinger equation. Specifically, we use an algorithm that implements an high recision variant of the Cranck Nicolson integration method and …

Modello numerico tridimensionale di uno ione H2+ in campi laser intensi

Laser driven structured quantum rings

In this work we study harmonic emission from structured quantum rings (SQRs). In SQRs, electrons trapped in two-dimensional structures are further confined by an external potential composed of N scattering centers arranged on a circle. We build a suitable one-dimensional model Hamiltonian describing this class of systems and analytically solve the associated Schödinger equation. We find that the solution can be expressed in terms of Mathieu functions and focus on the specific case of N = 6. By exactly solving the time-dependent Schödinger equation, we then show how the harmonic response to linearly polarized lasers strongly depends on the ring physical parameters. The results illustrate how…

Classical chaos and harmonic generation in laser driven nanorings

A quantum ring driven by an intense laser field emits light in the form of high-harmonic radiation resulting from the strong acceleration experienced by the active electrons forced to move on a curved trajectory. The spectrum of the emitted light is rich and strongly dependent on the parameters of the problem. In order to investigate the physical origin of such variability, we focus on the seemingly simple problem of a laser-driven charge constrained to a ring from a classical standpoint. As it turns out, the dynamics of such a classical electron is governed by a nonlinear equation which results into a chaotic motion - by nature depending on the initial conditions in an unpredictable way. O…

Signature of Nuclear Motion in H2 by Menas of High Harmonic Generation

The influence of the quantum nature of nuclei in high harmonic generation from H$_2^+$-like molecular ions

We study the full quantum dynamics of a simple molecular ion driven by an intense laser field. In particular we show that the quantum nature of the nuclear dynamics affects the emitted high harmonic generation (HHG) spectra, strongly reshaping the plateau region. In fact, it is evident that the characteristic flat trend is transformed into a descending trend, with the lower harmonics being two orders of magnitude more intense than the higher harmonics. We show that this effect is more pronounced in the lighter isotopic species of H$_2^+$ molecular ions and we also demonstrate that in this case the contribution to HHG from the antibonding electronic energetic surface is of the same order of …

Polarization of high harmonic generated spectra in ion

We study the polarization of the harmonics generated by a homonuclear diatomic molecule in the presence of an intense, linearly polarized laser field. The polarization parameters of the emitted radiation are investigated as function of the angle $\theta$ between the laser electric field and the molecular axis. The calculations are carried out by assuming a single active electron model with fixed nuclei; a two-dimensional model of the system is used. We find a different dependence of the parameters of the harmonics vs $\theta$ in the first or second half of the emitted spectrum. In particular, the differences are accentuated for $0^\circ < \theta < 50^\circ$, while for higher angles, until t…

Bremsstrahlung from a repulsive potential: attosecond pulse generation

The collision of an electron against a repulsive potential in the presence of a laser field is investigated. It is found that a sufficiently strong laser field forces the electron to remain in the neighbourhood of the repulsive potential causing bremsstrahlung. By appropriately filtering the emitted signal, an electron in the presence of a repulsive potential is capable of generating attosecond pulses.

Two-electron systems in strong laser fields

In this paper we investigate the single and double ionization signals of ${\text{H}}_{2}$ molecules, with fixed and moving nuclei, as a function of laser intensity, for two different values of laser wavelength ($\ensuremath{\lambda}=390\text{ }\text{nm}$ and $\ensuremath{\lambda}=780\text{ }\text{nm}$), using an approach for evaluating the ionization signals which allows the investigation of relatively long-lasting pulses. The He system is first investigated to benchmark our calculation against already known results. We confirm the evidence of nonsequentiality in the ionization processes of all the systems investigated. Furthermore, we show that the nuclei motion enhances the double ionizat…

Ionization and Dissociation Dynamic of H2 Molecule Driven by a Laser Field

We study the single and double ionization yields and the dissociation dynamics of a onedimensional two-electron molecule exposed to an intense laser pulse. The double ionization yields are systematically investigated for both fixed and moveable nuclei. At low intensities the ionization curves have a power law shape, followed by a knee profile for higher intensities. A temporal correlation between the nuclear motion and the electron ionization shows that the nuclear motion deeply affects the ionization yield.

Three-Dimensional Numerical Model of an H2+ Ion in Intense Laser Fields

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.

Quantum ring: HHG spectrum control

Atoms, molecules , clusters and other systems driven by a strong laser field of frequency \omega_L can emit a spectrum of laser harmonics. The high harmonics generation (HHG) phenomen is strongly affected by the symmetries of the system. It is well known that systems with rotational symmetries emit only odd harmonics. Numerous researcher make mainly attention to the possibilities to set different initial conditions in order to control the spectrum. Recently, the study of nanotechnology is hot-topics and in particular the study of very symmetric systems such as fullerene, nanoring and structured nanoring (nanoring with identical and symmetric scattering centers). Therefore, it is natural and…

Polarization of high harmonic generated spectra in H+2ion

AbstractWe study the polarization of the harmonics generated by a homonuclear diatomic molecule in the presence of an intense, linearly polarized laser field. The polarization parameters of the emitted radiation are investigated as a function of the angle between the laser electric field and the molecular axis. The calculations are carried out by assuming a single active electron model with fixed nuclei; a two-dimensional model of the system is used. We find a different dependence of the parameters of the harmonics vs in the first or second half of the emitted spectrum. In particular, the differences are accentuated for , while for higher angles, until the perpendicular orientation, almost …

Efficient attosecond pulse generation from HHG spectra

H2 Molecule Driven by a Laser Field

We study the single and double ionization yields and the dissociation dynamics of a one-dimensional two-electron molecule exposed to a laser pulse of intensity IL in the range 1013 − 1015 W/cm2 and photon energy hω¯L =3.18 eV. The calculations are carried out in the case of both fixed and movable nuclei. At low IL the ionization curves have a power law shape In that is interrupted by a knee at higher intensity.

Tertiary relict laurophyll vegetation in the Madonie mountains (Sicily)

:Laurel woodlands in the Madonie mountains (Sicily) are characterized by the presence of Laurus nobilis, Rhamnus lojaconoi and Vitis vinifera subsp. sylvestris. The results of a phytosociological study are presented, and a new endemic association, Rhamno lojaconoi–Lauretum nobilis, is described. Present Mediterranean laurel communities are the result of an adaptive response by Tertiary laurel forest to the peculiar microclimatic conditions that characterize the refugia where they persist. These refugia have been recently considered as a priority habitat under the Directive 92/43/EEC, and their plant communities are very vulnerable. Protection measures of the studied laurel populations are n…