Semiclassical Dirac Theory of Tunnel Ionization (original) (raw)
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The electron dynamics in the classically forbidden region during relativistic tunnel-ionization is investigated. The classical forbidden region in the relativistic regime is identified by defining a gauge invariant total energy operator. Introducing position dependent energy levels inside the tunneling barrier, we demonstrate that the relativistic tunnel-ionization can be well described by a one-dimensional intuitive picture. This picture predicts that, in contrast to the well-known nonrelativistic regime, the ionized electron wave packet arises with a momentum shift along the laser's propagation direction. This is compatible with results from a strong field approximation calculation where the binding potential is assumed to be zero-ranged. Further, the tunneling time delay, stemming from Wigner's definition, is investigated for model configurations of tunneling and compared with results obtained from the exact propagator. By adapting Wigner's time delay definition to the ionization process, the tunneling time is investigated in the deep-tunneling and in the near-threshold-tunneling regimes. It is shown that while in the deep-tunneling regime signatures of the tunneling time delay are not measurable at remote distance, it is detectable, however, in the latter regime.
2015
A recurrent scheme for finding the quasiclassical solution of the onedimensional equation obtained after the separation of variables in the Schrödinger equation in parabolic coordinates is derived. The method of quasiclassical localized states is developed for the Dirac equation with an arbitrary axially symmetric potential of barrier type which does not allow complete separation of the variables. By means of the proposed quasiclassical methods the non-relativistic and relativistic wavefunctions for hydrogenlike (H-like) atoms in an external uniform electrostatic field of intensity F are constructed in the classically forbidden and allowed regions. The general analytical expressions of the leading term of the asymptotic behaviour (at small F) of the ionization rate of an H-like atom in the uniform electrostatic field are obtained for the non-relativistic and relativistic cases.
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We discuss the possibility of non-exponential tunneling ionization of atoms irradiated by intense laser field. This effect can occur at times which are greater than the lifetime of a system under consideration. The mechanism for non-exponential depletion of an initial quasistationary state is the cutting of the energy spectrum of final continuous states at long times. We first consider the known examples of cold emission of electrons from metal, tunneling alpha-decay of atomic nuclei, spontaneous decay in two-level systems, and the single-photon atomic ionization by a weak electromagnetic field. The new physical situation discussed is tunneling ionization of atoms by a strong low-frequency electromagnetic field. In this case the decay obeys ~t 1/ power-law dependence on the (long) interaction times.
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We investigate tunneling ionization of a model helium atom in a strong circularly polarized short laser pulse using the classical backpropagation method and compare ten different tunneling criteria on the same footing, aiming for a consistent classical picture of the tunneling dynamics. These tunneling criteria are categorized into velocity-based, position-based, and energy-based criteria according to different notions of a tunnel exit. We find that velocity-based criteria give consistent tunneling exit characteristics with nonadiabatic effects fully included. Other criteria are either inconsistent or only able to include nonadiabatic effects partially. Furthermore, we construct a simple tunneling rate formula, identify a term in the rate responsible for the nonadiabatic effects, and demonstrate the importance of this term.
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Physical Review A
The electron nondipole dynamics in tunneling ionization in an elliptically polarized laser field is investigated theoretically using a relativistic Coulomb-corrected strong field approximation (SFA) based on the eikonal approximation of the Klein-Gordon equation. We calculate attoclock angle-resolved light-front momentum distributions at different ellipticities of the laser field in quasistatic and nonadiabatic regimes and analyze them with an improved Simpleman model. The nondipole correlations between longitudinal and transverse momentum components are examined. Deviations of the photoelectron momentum distribution calculated via SFA with respect to the available experimental results as well as with the improved Simpleman model are discussed and interpreted in terms of nonadiabatic as well as Coulomb effects in the continuum and under-the-barrier. The favorable prospects of an experimental observation are discussed.
Spin effects in relativistic ionization with highly charged ions in super-strong laser fields
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Subcycle nonadiabatic strong-field tunneling ionization
Physical Review A, 2016
We present a subcycle nonadiabatic strong-field tunneling theory and derive the position of tunnel exit, the transverse and longitudinal momentum distributions at the tunnel exit, and the ionization rate in an instantaneous laser field. These tunneling coordinates are shown to nonadiabatically couple with each other in an instantaneous laser field when the electron tunnels through the barrier. We have further incorporated the nonadiabatic tunneling theory with the quantum-trajectory Monte Carlo approach to investigate the nonadiabatic effect on the photoelectron angular distributions. The simulated photoelectron angular distributions with the nonadiabatic corrections have been validated by comparison with the ab initio results through numerically solving the time-dependent Schrödinger equation. The nonadiabatic coordinates at the tunnel exit play important roles in both the direct ionization and rescattering process. The nonadiabatic tunneling theory provides an intuitive understanding on subcycle dynamics of tunneling ionization.
Under-the-barrier electron-ion interaction during tunnel ionization
Report submitted in partial fulfilment of the requirements of the degree of MRes of Imperial College London 1 arXiv:1307.7329v2 [quant-ph] Abstract We consider tunnel ionization of an atom or molecule in a strong field within an analytical treatment of the R-matrix method, in which an imaginary boundary is set up inside the classically forbidden region that acts as a source of ionized electrons. These electrons are then propagated in the semiclassical approximation, and relying on a numerical solution of the inner region, which is accessible using quantum chemical techniques, we describe the subsequent evolution of the ionized electron and the ionic core.
Relativistic quantum theory of high harmonic generation on atoms/ions by strong laser fields
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High-order harmonic generation (HHG) by hydrogenlike atoms/ions in the uniform periodic electric field, formed by the two linearly polarized counterpropagating laser beams of relativistic intensities, is studied. The relativistic quantum theory of HHG in such fields, at which the impeding factor of relativistic magnetic drift of a strong wave can be eliminated, is presented arising from the Dirac equation. Specifically, a scheme of HHG in underdense plasma with the copropagating ultraintense laser and fast ion beams is proposed.
Physical Review A, 2006
Electron-momentum distributions for above-threshold ionization of argon in a few-cycle, linearly polarized laser pulse are investigated. Spectral features characteristic of multiphoton as well as tunneling ionization coexist over a range of the Keldysh parameter ␥ in the transition regime ␥ ϳ 1. Surprisingly, the simple strong-field approximation ͑SFA͒ is capable of reproducing the key features of the two-dimensional momentum distributions found in the full solution of the time-dependent Schrödinger equation, despite the fact that SFA is known to severely underestimate the total ionization probability.
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Physica Scripta, 2011
The dynamics of highly charged ions in a strong laser field are investigated by solving the two-dimensional time-dependent Dirac equation. Relativistic effects are discussed for the hydrogen-like ions with nuclear charges of Z = 4, 24 and 79 by considering the changes in the electron trajectory and coherent emission spectrum with changes in the frequency and intensity of the laser field. With increasing Z , the relative field strength between the ionic core and laser fields changes and this results in different characteristics of the dynamical electronic trajectory as well as the corresponding emission spectrum. For an infrared laser field of strength E = 8.0 au, the tunneling ionization can hardly be seen for the hydrogen-like ions of Z = 24 and only the resonant multiphoton emission spectra below the ionization threshold are predicted. The above threshold harmonics need more intense laser fields or a higher photon energy.
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The direct multiphoton ionization (MPI) of hydrogenlike ions by intense, linearly polarized, ultrashort infrared laser pulses is investigated within the framework of the strong field approximation (SFA) for laser peak intensities and angular frequencies where relativistic effects are important. We obtain an expression for the differential MPI probability using the Dirac equation and demonstrate that, for the particular case of light ions, the Dirac spin-unresolved MPI probabilities agree with those obtained using the Klein-Gordon equation as well as the relativistic Schrödinger equation. As an example, the interaction of hydrogenlike neon ions with an intense fourcycle Ti:sapphire laser pulse is considered. We show that, in contrast to the nonrelativistic regime, for ultrashort pulses in the relativistic regime, interference effects do not play a role in determining the main features of the energy-resolved photoelectron spectrum. Moreover, we find that the angle-integrated photoelectron spectrum can be obtained using the well-known nonrelativistic SFA formula, properly adjusted to account for the electron drift along the laser propagation direction.
Physical Review A, 2013
We develop a relativistic Coulomb-corrected strong field approximation (SFA) for the investigation of spin effects at above-threshold ionization in relativistically strong laser fields with highly charged hydrogen-like ions. The Coulomb-corrected SFA is based on the relativistic eikonal-Volkov wave function describing the ionized electron laser-driven continuum dynamics disturbed by the Coulomb field of the ionic core. The SFA in different partitions of the total Hamiltonian is considered. The formalism is applied for direct ionization of a hydrogen-like system in a strong linearly polarized laser field. The differential and total ionization rates are calculated analytically. The relativistic analogue of the Perelomov-Popov-Terent'ev ionization rate is retrieved within the SFA technique. The physical relevance of the SFA in different partitions is discussed.
Relativistic Nondipole Effects in Strong-Field Atomic Ionization at Moderate Intensities
Physical Review Letters, 2019
We present a detailed experimental and theoretical study on the relativistic non-dipole effects in strong-field atomic ionisation by near-infrared linearly-polarised few-cycle laser pulses in the intensity range 10 14-10 15 W/cm 2. We record high-resolution photoelectron momentum distributions of argon using a reaction microscope and compare our measurements with a truly ab-initio fully relativistic 3D model based on the time-dependent Dirac equation. We observe counter-intuitive peak shifts of the transverse electron momentum distribution in the direction opposite to that of laser propagation as a function of laser intensity and demonstrate an excellent agreement between experimental results and theoretical predictions.
Atoms in strong optical fields: Evolution from multiphoton to tunnel ionization
Physical Review Letters, 1993
Electron energy spectra from ionization of the noble gases by 617-nm, 100-fs intense laser pulses show that the periodical double structure of narrow Stark-induced resonances and above-threshold ionization disappears gradually from xenon to helium. This implies that shifts and widths become of the order of the atomic-orbital frequencies, as expected at the onset of the tunneling regime.
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