Atomic Ionization In Super Strong Laser Fields

ABSTRACT

This work studies the phenomena which occur in atomic physics when the electric field of the applied laser radiation becomes comparable with the Coulomb field strength seen by an electron in the ground state of atomic hydrogen. This field is reached at an radiance of approximately 3    10¹⁶  W cm⁻².  The normal perturbation photon-by-photon based picture of the interaction of individual electrons with the field is replaced by a tunneling picture    in which, in a time of the order of, or less than one optical cycle, atomic wave packets are generated which escape the confining Coulomb potential. These wave packets are strongly influenced by the laser, ‘quiver’ and may be accelerated back to the parent ion in a re collision processing

TABLE OF CONTENTS

COVER PAGE

TITLE PAGE

APPROVAL PAGE

DEDICATION

ACKNOWLEDGEMENT

ABSTRACT

CHAPTER ONE

• INTRODUCTION
• BACKGROUND OF THE PROJECT
• OBJECTIVE OF THE PROJECT
• SCOPE OF THE PROJECT
• PROJECT ORGANIZATION

CHAPTER TWO

LITERATURE REVIEW

• OVERVIEW OF IONIZATION
• REVIEW OF COLTRIMS – A CLOUD CHAMBER FOR ATOMIC PHYSICS

CHAPTER THREE

METHODOLOGY

• SINGLE IONIZATION AND THE TWO-STEP MODEL
• MECHANISMS OF DOUBLE IONIZATION
• RECOIL ION MOMENTA
• ELECTRON ENERGIES
• CORRELATED ELECTRON MOMENTA

CHAPTER FOUR

• RESULT

CHAPTER FIVE

• CONCLUSION
• RECOMMENDATION
• REFERENCES

CHAPTER ONE

1.0                                                                INTRODUCTION

1.1                                                  BACKGROUND OF THE STUDY

Ionization of atoms by strong laser fields plays an important role in today´s ultrafast laser laboratories. It is at the basis of important techniques such as high-harmonic generation, which allows the generation of attosecond (1 as = 10^-18 s) laser pulses, and furthermore allows the development of tomographic methods that make it possible to observe ultrafast electronic and atomic movements on the attosecond to few femtosecond (1 fs = 10^-15 s) timescale. Theoretical methods for describing strong laser field ionization were already developed a few decades ago. They are commonly based on the so-called “strong-field approximation” (SFA), which argues that after ionization the motion of the ionized electrons is largely determined by the electric field of the ionizing laser, and hardly by the Coulomb force that the electron and the ion left behind exert on each other.

For several decades the strong-field approximation has served scientists well and has allowed them to understand many observations that were experimentally made in connection with the strong field laser ionization. That is to say, until now. In a remarkable paper last year, scientists from the US and Germany reported the observation of a new phenomenon in strong-field laser ionization, namely a very pronounced peak at low energies in the photoelectron kinetic energy distribution, that contained as many as 50% of the emitted photoelectrons. Remarkably, its physical origin could not be identified.

In the new paper, the Rostock, Heidelberg and MBI scientists argue that it is the failure to include the Coulomb attraction between the departing electron and the ion left behind that is at the root of the low energy feature. They developed a novel theoretical description of strong-field ionization process, which in its initial stages mimics the traditional SFA approach, but then switches to calculating trajectories that the electrons follow in the combined Coulomb + laser field. This approach convincingly reproduces the low energy feature, and shows that it is caused by electrons that are pushed back-and-forth by the oscillatory laser field. In this process the electrons are brought into close proximity to the ion, which strongly disturbs the electron orbit, leading to a situation where the electron can just barely escape the attraction of the ion.

1.2                                                            AIM OF THE STUDY

The main aim of this work is to study the mechanism of atomic ionization in super strong laser fields.

1.3                                                     OBJECTIVES OF THE STUDY

At the end of this work student involved shall be able study and understand the theory of atomic ionization, and review progress in understanding how this quiver motion can be coherently controlled. We discuss ionization dynamics and review mechanisms by which atoms may be stabilized in very strong fields. Finally, we discuss relativistic effects which occur at very high-intensities.

1.4                                            SCOPE OF THE STUDY

Since more particles are involved, the number of observables and the challenge to the experimental as well as to the theoretical techniques increases. Early studies measured the rate of multiply charged ions as a function of laser intensity. The work reviewed here employs mainly COLTRIMS (Cold Target Recoil Ion Momentum Spectroscopy) [9] to detect not only the charge state but also the momentum vector of the ion and of one of the electrons in coincidence. Today such highly differential measurements are standard in the fields of ion-atom, electron-atom and high energy single photon-atom collision studies.

1.5                                             PROJECT ORGANISATION

The work is organized as follows: chapter one discuses the introductory part of the work,   chapter two presents the literature review of the study,  chapter three describes the methods applied,  chapter four discusses the results of the work, chapter five summarizes the research outcomes and the recommendations.

CHAPTER TWO

2.0                                                           LITERATURE REVIEW

2.1                                                     OVERVIEW OF IONIZATION

Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected (Glenn F, 2000).

Everyday examples of gas ionization are such as within a fluorescent lamp or other electrical discharge lamps. It is also used in radiation detectors such as the Geiger-Müller counter or the ionization chamber. The ionization process is widely used in a variety of equipment in fundamental science such as in mass spectrometry and in industry like in radiation therapy (Glenn F, 2000).

Production of ions

Avalanche effect between two electrodes. The original ionization event liberates one electron, and each subsequent collision liberates a further electron, so two electrons emerge from each collision: the ionizing electron and the liberated electron. Negatively charged ions are produced when a free electron collides with an atom and is subsequently trapped inside the electric potential barrier, releasing any excess energy. The process is known as electron capture ionization.

Positively charged ions are produced by transferring an amount of energy to a bound electron in a collision with charged particles (e.g. ions, electrons or positrons) or with photons. The threshold amount of the required energy is known as ionization potential. The study of such collisions is of fundamental importance with regard to the few-body problem, which is one of the major unsolved problems in physics. Kinematically complete experiments,[Schulz, Michael, 2003] i.e. experiments in which the complete momentum vector of all collision fragments (the scattered projectile, the recoiling target-ion, and the ejected electron) are determined, have contributed to major advances in the theoretical understanding of the few-body problem in recent years.

Adiabatic ionization is a form of ionization in which an electron is removed from or added to an atom or molecule in its lowest energy state to form an ion in its lowest energy state.[2]

The Townsend discharge is a good example of the creation of positive ions and free electrons due to ion impact. It is a cascade reaction involving electrons in a region with a sufficiently high electric field in a gaseous medium that can be ionized, such as air. Following an original ionization event, due to such as ionizing radiation, the positive ion drifts towards the cathode, while the free electron drifts towards the anode of the device. If the electric field is strong enough, the free electron gains sufficient energy to liberate a further electron when it next collides with another molecule. The two free electrons then travel towards the anode and gain sufficient energy from the electric field to cause impact ionization when the next collisions occur; and so on. This is effectively a chain reaction of electron generation, and is dependent on the free electrons gaining sufficient energy between collisions to sustain the avalanche according to (Glenn F, 2000).

Ionization efficiency is the ratio of the number of ions formed to the number of electrons or photons used.[4][5]

Ionization energy of atoms

The trend in the ionization energy of atoms is often used to demonstrate the periodic behavior of atoms with respect to the atomic number, as summarized by ordering atoms in Mendeleev’s table. This is a valuable tool for establishing and understanding the ordering of electrons in atomic orbitals without going into the details of wave functions or the ionization process. The periodic abrupt decrease in ionization potential after rare gas atoms, for instance, indicates the emergence of a new shell in alkali metals. In addition, the local maximums in the ionization energy plot, moving from left to right in a row, are indicative of s, p, d, and f sub-shells.

Semi-classical description of ionization

Classical physics and the Bohr model of the atom can qualitatively explain photoionization and collision-mediated ionization. In these cases, during the ionization process, the energy of the electron exceeds the energy difference of the potential barrier it is trying to pass. The semi-classical description, however, cannot describe tunnel ionization since the process involves the passage of electron through a classically forbidden potential barrier.

Quantum mechanical description of ionization

The interaction of atoms and molecules with sufficiently strong laser pulses leads to the ionization to singly or multiply charged ions. The ionization rate, i.e. the ionization probability in unit time, can only be calculated using quantum mechanics. In general, the analytic solutions are not available, and the approximations required for manageable numerical calculations do not provide accurate enough results. However, when the laser intensity is sufficiently high, the detailed structure of the atom or molecule can be ignored and analytic solution for the ionization rate is possible.

Tunnel ionization

Tunnel ionization is ionization due to quantum tunneling. In classical ionization, an electron must have enough energy to make it over the potential barrier, but quantum tunneling allows the electron simply to go through the potential barrier instead of going all the way over it because of the wave nature of the electron. The probability of an electron’s tunneling through the barrier drops off exponentially with the width of the potential barrier. Therefore, an electron with a higher energy can make it further up the potential barrier, leaving a much thinner barrier to tunnel through and, thus, a greater chance to do so. In practice, tunnel ionization is observable when the atom or molecule is interacting with near-infrared strong laser pulses. This process can be understood as a process by which a bounded electron, through the absorption of more than one photon from the laser field, is ionized. This picture is generally known as multiphoton ionization (MPI).

Keldysh[ Keldysh, L. V, 1965] modeled the MPI process as a transition of the electron from the ground state of the atom to the Volkov states.[ Perelomov, 1966] In this model the perturbation of the ground state by the laser field is neglected and the details of atomic structure in determining the ionization probability are not taken into account. The major difficulty with Keldysh’s model was its neglect of the effects of Coulomb interaction on the final state of the electron. As it is observed from figure, the Coulomb field is not very small in magnitude compared to the potential of the laser at larger distances from the nucleus. This is in contrast to the approximation made by neglecting the potential of the laser at regions near the nucleus. Perelomov et al.[ Larochelle, S, 1998 and Perelomov A. M 1967] included the Coulomb interaction at larger internuclear distances. Their model (which we call PPT model) was derived for short range potential and includes the effect of the long range Coulomb interaction through the first order correction in the quasi-classical action. Larochelle et al.[Ammosov M. V, 1986] have compared the theoretically predicted ion versus intensity curves of rare gas atoms interacting with a Ti:Sapphire laser with experimental measurement.

Multiphoton ionization of inner-valence electrons and fragmentation of polyatomic molecules

The ionization of inner valance electrons are responsible for the fragmentation of polyatomic molecules in strong laser fields. According to a qualitative model [Mehdi Sharifi, 2008] the dissociation of the molecules occurs through a three-step mechanism:

• MPI of electrons from the inner orbitals of the molecule which results in a molecular ion in ro-vibrational levels of an excited electronic state;
• Rapid radiationless transition to the high-lying ro-vibrational levels of a lower electronic state; and
• Subsequent dissociation of the ion to different fragments through various fragmentation channels.

The short pulse induced molecular fragmentation may be used as an ion source for high performance mass spectroscopy. The selectivity provided by a short pulse based source is superior to that expected when using the conventional electron ionization based sources, in particular when the identification of optical isomers is required.[Talebpour, 2000]

Kramers-Henneberger frame and ionization phase effects

Studying the strong field ionization of the atom in so called Kramers-Henneberger (K-H) frame[ Mathur D, 2013] leads to the conclusion that the ionization efficiency strongly depends on the temporal details of the ionizing pulse but not necessarily on the field strength and the total energy of the ionizing pulse pumped into the atom.[ Mathur D, 2013] The Kramers-Henneberger frame is the non-intertial frame moving with the free electron under the influence of the harmonic laser pulse.

2.2             REVIEW OF COLTRIMS – A CLOUD CHAMBER FOR ATOMIC PHYSICS

For a long time the experimental study of electron correlation in ionization processes of atoms, molecules and solids has suffered from the technical challenge to observe more than one electron emerging from a multiple ionization event. The main problem lies in performing coincidence studies employing conventional electron spectrometers, which usually cover only a small part of the total solid angle. COLTRIMS (Cold Target Recoil Ion Momentum Spectroscopy) is an imaging technique, which solves this fundamental problem in atomic and molecular coincidence experiments. Like the cloud chamber and its modern successors in nuclear and high energy physics, it delivers complete images of the momentum vectors of all charged fragments from an atomic or molecular fragmentation process. The key feature of this technique is to provide a 4π collection solid angle for low energy electrons (up to a few hundred eV ) in combination with 4π solid angle and high resolution for the coincident imaging of the ion momenta.

As we will show below the ion momenta in most atomic reactions with photons or charged particles are of the same order of magnitude as the electron momenta. Due to their mass, however, this corresponds to ion energies in the range of µeV to meV . These energies are below thermal motion at room temperature. Thus, the atoms have to be substantially cooled before the reaction. In the experiments discussed here this is achieved by using a supersonic

gas-jet as target. More recently, atoms in magneto-optical traps have been used to further increase the resolution [13–16].

A typical setup as it was used for the experiments discussed here is shown in figure 1. The laser pulse is focused by a lens of 5cm focal length or a parabolic mirror into a supersonic gas- jet providing target atoms with very small initial momentum spread of below 0.1au (atomic units are used throughout this paper) in the direction of the laser polarization (along z- axis in figure 1). For experiments in ion-atom collisions or with synchrotron radiation the

ionization probability is very small: That’s why one aims at a target density in the range of up to 10−4mbar local pressure in the gas-jet. Accordingly, a background pressure in the chamber in the range of 10−8mbar is sufficient. In contrast for multiple ionization by femtosecond laser pulses the single ionization probability easily reaches unity. Thus, within the reaction volume defined by the laser focus of typically (10µm)2 · 100µm all atoms are ionized. Since for coincidence experiments it is essential that much less than one atom is ionized per laser shot a background pressure of less than 10−10mbar is required. The gas-jet

has to be adjusted accordingly to reach single collision conditions at the desired laser peak power. With standard supersonic gas-jets this can only be achieved by tightly skimming the atomic beam, since a lower driving pressure for the expansion would result in an increase of the internal temperature of the jet along its direction of propagation. Single ionization (see section III) allows for an efficient monitoring of the resolution as well as online controlling of single collision conditions.

The ions created in the laser focus are guided by a weak electric field towards a position sensitive channel plate detector. From the position of impact and the time-of-flight (TOF) of the ion all three components of the momentum vector and the charge state are obtained.

The electric field also guides the electrons towards a second position sensitive channel plate detector. To collect electrons with large energies transverse to the electric field a homogeneous magnetic field is superimposed parallel to the electric field. This guides the electrons on cyclotron trajectories towards the detector. Depending on their time-of-flight the electrons perform several full turns on their way to the detector. Figure 3 shows the electron TOF versus the radial distance of the position from a central trajectory with zero transverse momentum of the electron. When the TOF is an integer multiple of the cyclotron frequency the electrons hit the detector at his position, independently of their momentum transverse to the field. These TOFs represent points in phase space where the spectrometer has no resolution in the transverse direction. For all other TOFs the initial momentum can be uniquely calculated from the measured positions of impact and the TOF. Using a magnetic field of 10 Gauss 4π solid angle collection is achieved for electrons up to about 30eV . The typical detection probability of an electron is in the range of 30%-40%. Thus, even for double ionization in most cases only one electron is detected. The positions of impact and the times-of-flight are stored for each event in list mode. Thus the whole experiment can be replayed in the offline analysis. A detailed description of the integrated multi-electron-ion momentum spectrometer can be found in [18].