Theoretical models for above threshold ionization in atomic hydrogen springerlink. The procedure is based on a raleighschrodinger perturbative expansion of the timeindependent nonhermitian floquet hamiltonian. Nonperturbative theory of abovethreshold ionization. Angular distribution and circular dichroism in the twocolour. Polarization control in twocolor abovethreshold ionization of atomic helium. We show that when the laser field is sufficiently intense the usual perturbation theory is not valid. Intensityresolved above threshold ionization of xenon with short laser pulses n. The problem of the threshold law for electronatom impact ionization is reconsidered as an extrapolation of inelastic cross sections through the ionization threshold.
In this regime, the optical field is no longer a small perturbation on the atomic potential. The hydrogen atom in combined electric and magnetic fields with arbitrary mutual orientations j. Qualitative strong eld ionization models v v v rempi resonanceenhanced multiphoton ionization multiphoton ionization nonresonant multiphoton ionization ati abovethreshold ionization a. Monte carlo calculation of the abovethreshold ionization. A critical feature of the technique is a middle step that breaks the problem into solvable and perturbation parts. Abovethreshold ionization near the 3p4d f autoionizing. Atoms and molecules in intense laser fields 1 berlin, 07. Bound electron nonlinearity beyond the ionization threshold. Energy sharing and asymmetry parameters for photo double. Anisotropy parameters in twocolor twophoton abovethreshold. Dynamics of the abovethreshold ionization of atoms in an.
Twophoton double ionization of he and h purdue physics. Results and discussion to evaluate the integrals of mtlv and j. Polarization control in twocolor abovethreshold ionization. Abovethreshold ionization of mg by linearly and circularly. A variational theory for high rydberg stark ionization. These limitations are not very restrictive for attosecond metrology based on abovethreshold ionization. The resulting electrically charged atom or molecule is called an ion. If we already know all eigenstates of h0, can we get eigenstates of h1 approximately. Semiclassical matrix elements, essentialstates models and. Above threshold ionization ati is the name given to the absorption by an atomic electron of more photons than are required for ionization.
In the photoelectron spectrum, lines associated with direct ionization and above threshold ionization show. Abovethreshold ionization by fewcycle pulses d b milosevi. Asymmetry parameters of the angular distribution were determined and compared to theoretical predictions based on the strong field approximation and perturbation theory, respectively. Dynamics of multiphoton ionization in a femtosecond laser.
Abovethreshold ionization ati, a wellstudied process by now 1,2, is a process in which atoms exposed to an intense laser. Perturbation theory and the semiclassieal approach. Ishikawa,3 klaus schiessl, 4emil persson,4 and joachim burgdorfer. Atlow intensity, where perturbation theory applies. We present intensityresolved abovethreshold ionization ati spectra of xenon using an intensity scanning. Study of attosecond delays using perturbation diagrams and. Photoelectron angular distributions and cross section. Classicalquantum correspondence for abovethreshold.
Timeindependent perturbation theory introduction as discussed in lecture notes 14, relatively few problems in quantum mechanics are exactly solvable. Circularly polarized xuv pulses from the free electron laser fermi have been spatially and temporally overlapped with circularly polarized optical pulses in the interaction region with an atomic helium jet. Angular distribution and circular dichroism in the two. Twocolor multiphoton ionization of atomic helium was investigated by combining extreme ultraviolet xuv radiation from the free electron laser in hamburg with an intense synchronized optical laser. Pdf abovethreshold ionization kazimierz rzazewski academia. Interference structure of abovethreshold ionization.
The method is based on the sturmian expansion of the transition matrix elements and the analytical continuation of the divergent part of the sturmian transition matrix elements in the case of above threshold ionization with one excess photon. These quantities are related to recent ati experiments, and. We first rotate the integration contour into the upper right quadrants of the complex plane, that is, we replace r by s e where os s %co and o eld ionization models v v v rempi resonanceenhanced multiphoton ionization multiphoton ionization. An analytical theory of the reflection and transmission of light from nonlinear optical interfaces is described. In the theoretical study of abovethreshold ionization ati, one of the major. A highorder perturbation theory is presented for efficient and accurate computation of multiphoton and abovethreshold ionization cross sections of atoms and molecules in weak to medium strength laser fields. Regarding theory, it is known that the phases of the complex transition amplitudes. F approximates the experimentally important stark ionization threshold for rydberg states and typifies critical fields encountered in mathematical. We examine hydrogen atom stark energies calculated with nonlinear variational theory using square. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules. Classicalquantum correspondence for abovethreshold ionization. Ati was discovered in 1979 and is now expected to be a universal phenomenon observable in all atomic species.
Monte carlo calculation of the above threshold ionization of atomic hydrogen c s han and joseph c i yaung department of electrophysics, national chiao tung university, hsinchu, taiwan, republic of china received 30 march 1990 abstract. Pdf the abovethreshold ionization spectrum in a strong linearly. Abstract for the hydrogen atom in combined magnetic and electric elds we inves. Analytic formulas for abovethreshold ionization or detachment plateau spectra, m. Berry1 1department of chemistry and the james franck institute, the university of chicago, chicago, illinois 60637, usa. An ati spectrum consists of a series of peaks, equally separated by the photon energy, in a photoelectron energy spectrum pes. Anisotropy parameters and cross section ratios of twocolor twophoton above threshold ionization sidebands from argon are measured using photoelectron velocity map imaging with the selected th or 15th highorder harmonics in a perturbative 800 nm dressing field. Timeresolved photoelectron angular distributions and. Osa multiphoton absorption above ionization threshold by. For low nir intensities, the ratio of the partial waves in the twophoton ionization process and their relative phase could be deduced. Timeindependent perturbation theory is used when one wishes to nd energy eigenstates and the corresponding energy levels for a system for which the hamiltonian h. Highorder abovethreshold ionization of hydrogen in. It is known that the multiphoton yield at low intensities is proportional to the probability, since 0534142.
Introduction development of highpower lasers has led to the discovery of a whole range of. The trial function for each state has a characteristic critical field f above which the variational energy is complex. Anisotropy parameters in twocolor twophoton abovethreshold ionization steven hutchinson department of physics and astronomy, university college london, gower street, london wc1e 6bt, united kingdom michael a. While extensive absolute measurements of have been done in neutral atomic and molecular gases below the ionization threshold 810, the nonlinear response above the ionization threshold is. Timedependent perturbation theory so far, we have focused on quantum mechanics of systems described by hamiltonians that are timeindependent. For optical photons this discrepancy need not be significant. Perturbation theory and selection rules for ati 339 11. Abovethreshold ionization of atomic hydrogen 617 3. With the discovery of abovethreshold ionization ati by agostini et al. Theoretical models for abovethreshold ionization in atomic hydrogen springerlink. We solve the model dynamics exactly, and several interesting quantities, including the initialstate decay rate and photoelectron spectrum, are calculated. If mp is calculated to lowestorder perturbation theory so that. The validity of the perturbation theory lies on the adiabatic assumption, which assumes the eigenenergies and eigenstates of the hamiltonian are smooth functions of parameters such that their values in the vicinity region can be calculated in power series like taylor expansion of the parameters. Calculated vertical ionization potentials, electron af.
We present an atomic model to study above threshold ionization ati. Telnov and shihi chu department of chemistry, university of kansas, and kansas center for advanced scienti. Resonant abovethreshold ionization peaks at quantized intensities. Highorder perturbation expansion of nonhermitian floquet theory for multiphoton and abovethreshold ionization processes dmitry a. Monte carlo calculation of the abovethreshold ionization of. The eigenstates of the hamiltonian should not be very different from the eigenstates of h0.
We present results for up to 20photon ionization of h1s and d1s by 1064 nm circularly, linearly, or elliptically polarized radiation. This paper adresses the problem of abovethreshold ionization ati of hydrogen interacting with an intense xray electromagnetic field. In such cases, time dependence of wavefunction developed through. It is found that the threshold intensity decreases rapidly with the order of perturbation and the result may not correctly describe the. We study the classicalquantum correspondence and build a bridge between the abovethreshold ionization and the tunneling theory. We have used the greens function method in the feshbach formalism and an l2 close coupling method, with.
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. Timeresolved anisotropy parameters and crosssection ratios of the positive and negative sidebands from twocolour twophoton above threshold ionization of helium atoms are measured using photoelectron velocity map imaging with the selected 19th highorder harmonic at 29. The loss of perturbation theory as a viable quantummechanical calculational procedure corresponds to a. We describe a very efficient basisset method for calculating cross sections for highorder above threshold ionization of a hydrogenic atom in perturbation theory. Abovethreshold ionization near the 3p4d f autoionizing state. The plateau in abovethreshold ionization iopscience. Twophoton abovethreshold ionization cross sections and angular distributions have been calculated for mg in the region between the 3p and 4s ionization thresholds.
The hydrogen atom in combined electric and magnetic fields. We study the classicalquantum correspondence and build a bridge between the above threshold ionization and the tunneling theory. Diffraction at a time grating in abovethreshold ionization. Perturbationtheory analysis of ionization by a chirped fewcycle attosecond pulse. The process known as abovethreshold ionization ati 1, in which the atom absorbs more photons than.
Pdf resonant abovethreshold ionization peaks at quantized. Ethynyl was generated using a microwave discharge flow tube. The resulting theory has been called quantumorbit theory 710. Ionization or ionisation, 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. Multiphoton and abovethreshold detachment computed for a. For onephoton ionization as a function of the nuclear.
The general theory is applied to some simple twodimensional nonlinear waveguide configurations. Abovethreshold ionization near the 3p4d 1fo autoionizing state in magnesium a. Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. The intensities of both the sidebands and the singlephoton ionization. This book presents and describes a series of unusual and striking strongfield phenomena concerning atoms and free electrons. Theoretical models for abovethreshold ionization in atomic. It follows that standard lowestorder perturbation theory is not well adapted to the description of the situation at hand.
Lowestorder perturbation theory lopt low laser intensities. Multiphoton and abovethreshold detachment computed for a model negative ion and compared with perturbation theory authors. Abovethreshold ionization of hydrogen and hydrogenlike. This type of shaped pulses is likely to impact all phenomena stemming from electron recollision processes induced by strong laser fields such as above threshold ionization, high harmonic. Twodimensional harmonic oscilator 3 timedependent perturbation theory 4 literature igor luka cevi c perturbation theory. A new data analysis technique determines accurate anisotropy parameters of the photoelectron angular distributions for. Absolutephase effects detected by a correlation technique 212 3. Highorder perturbation expansion of nonhermitian floquet. Robicheaux department of physics, auburn university, auburn, alabama, usa received 8 february 2011.
In atomic, molecular, and optical physics, above threshold ionization ati, is a multiphoton effect where an atom is ionized with more than the energetically required number of photons. On a certain generalization of the keldyshfaisalreiss model arxiv. Study of attosecond delays using perturbation diagrams and exterior complex scaling 3 in nite order in terms of coulomb interactions, the interactions with the elds must be restricted to lowestorder perturbation theory in our approach. We find that in all gases studied, the nearly linear relationship between the bound electronic response and intensity observed at lower intensities 8, 9 extends to intensities where up to a few percent of atoms or molecules are ionized, a region significantly beyond the limits of perturbation theory 11. The townsend discharge is a good example of the creation of positive ions and free electrons due to ion impact. The intensity dependence of total versus differential ionization, rates in laserinduced abovethreshold ionization is also discussed. Channelclosing effects in highorder abovethreshold. I, spectra resulting from lowest order perturbation theory to those obtained within a nonperturbative model. The keldyshfaisalreiss kfr theory 14 describes nonresonant multiphoton processes such as above threshold detachment of ions and above threshold ionization of atoms in.
Lysaght irish centre for high end computing, tower building, trinity technology and enterprise campus, grand canal quay, dublin 2. We presenl a systematic study on the above threshold ionization of the hydrogen. Light polarization and angular distributions 359 ionization 334 10. Anisotropy parameters in twocolor twophoton above threshold ionization steven hutchinson department of physics and astronomy, university college london, gower street, london wc1e 6bt, united kingdom michael a. Intensityresolved abovethreshold ionization of xenon. A new qed perturbation theory is developed, in which the coupling between an electron and the second quantized laser mode is. Within the framework of perturbation theory, the method of analytical continuation of transition matrix elements is proposed. This can be expected for example at very high photon energies, where one. Intensityresolved abovethreshold ionization of xenon with. Photoelectron properties of dna and rna bases from many. In the first approach, we calculate generalized differential and total cross sections based on secondorder perturbation theory for the electron interaction with a monochromatic plane wave, with the a 2 and a. Dynamics of the abovethreshold ionization of atoms in an intense field. These limitations are not very restrictive for attosecond metrology based on above threshold ionization.
Within the past few years, the phenomenon called abovethreshold ionization ati has been observed 193, in which the spectrum of the photoe1ectrons from atomic ionization exhibits a series of peaks corresponding to the absorption of more than the minimum number of photons required for ionization. We present an atomic model to study abovethreshold ionization ati. Perturbation theory analysis of attosecond photoionization. Theoretical models for abovethreshold ionization in. Above threshold ionization ati is the production of higherenergy electrons that have absorbed additional photons over the minimum number no required for ionization agostini et al 1979, kruit et a1 1981, petite et a1 1984. Resonant above threshold ionization peaks at quantized intensities. A highorder perturbation theory is presented for ef.
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