199 research outputs found
Existence criteria for stabilization from the scaling behaviour of ionization probabilities
We provide a systematic derivation of the scaling behaviour of various
quantities and establish in particular the scale invariance of the ionization
probability. We discuss the gauge invariance of the scaling properties and the
manner in which they can be exploited as consistency check in explicit
analytical expressions, in perturbation theory, in the Kramers-Henneberger and
Floquet approximation, in upper and lower bound estimates and fully numerical
solutions of the time dependent Schroedinger equation. The scaling invariance
leads to a differential equation which has to be satisfied by the ionization
probability and which yields an alternative criterium for the existence of
atomic bound state stabilization.Comment: 12 pages of Latex, one figur
Influence of asymmetry and nodal planes on high-harmonic generation in heteronuclear molecules
The relation between high-harmonic spectra and the geometry of the molecular
orbitals in position and momentum space is investigated. In particular we
choose two isoelectronic pairs of homonuclear and heteronuclear molecules, such
that the highest occupied molecular orbital of the former exhibit at least one
nodal plane. The imprint of such planes is a strong suppression in the harmonic
spectra, for particular alignment angles. We are able to identify two distinct
types of nodal planes. If the nodal planes are determined by the atomic
wavefunctions only, the angle for which the yield is suppressed will remain the
same for both types of molecules. In contrast, if they are determined by the
linear combination of atomic orbitals at different centers in the molecule,
there will be a shift in the angle at which the suppression occurs for the
heteronuclear molecules, with regard to their homonuclear counterpart. This
shows that, in principle, molecular imaging, which uses the homonuclear
molecule as a reference and enables one to observe the wavefunction distortions
in its heteronuclear counterpart, is possible.Comment: 14 pages, 7 figures. Figs. 3, 5 and 6 have been simplified in order
to comply with the arXiv size requirement
The quantum brachistochrone problem for non-Hermitian Hamiltonians
Recently Bender, Brody, Jones and Meister found that in the quantum brachistochrone problem the passage time needed for the evolution of certain initial states into specified final states can be made arbitrarily small, when the time-evolution operator is taken to be non-Hermitian but PT-symmetric. Here we demonstrate that such phenomena can also be obtained for non-Hermitian Hamiltonians for which PT-symmetry is completely broken, i.e. dissipative systems. We observe that the effect of a tunable passage time can be achieved by projecting between orthogonal eigenstates by means of a time-evolution operator associated with a non-Hermitian Hamiltonian. It is not essential that this Hamiltonian is PT-symmetric
Enhancement of bichromatic high-harmonic generation with a high-frequency field
Using a high-frequency field superposed to a linearly polarized bichromatic
laser field composed by a wave with frequency and a wave with
frequency , we show it is possible to enhance the intensity of a
group of high harmonics in orders of magnitude. These harmonics have
frequencies about 30% higher than the monochromatic-cutoff frequency, and,
within the three-step-model framework, correspond to a set of electron
trajectories for which tunneling ionization is strongly suppressed. Particular
features in the observed enhancement suggest that the high-frequency field
provides an additional mechanism for the electron to reach the continuum. This
interpretation is supported by a time-frequency analysis of the harmonic yield.
The additional high frequency field permits the control of this group of
harmonics leaving all other sets of harmonics practically unchanged, which is
an advantage over schemes involving only bichromatic fields.Comment: 6 pages RevTex, 5 figures (ps files), Changes in text, figures,
references and equations include
High-harmonic generation from a confined atom
The order of high harmonics emitted by an atom in an intense laser field is
limited by the so-called cutoff frequency. Solving the time-dependent
Schr\"odinger equation, we show that this frequency can be increased
considerably by a parabolic confining potential, if the confinement parameters
are suitably chosen.
Furthermore, due to confinement, the radiation intensity remains high
throughout the extended emission range. All features observed can be explained
with classical arguments.Comment: 4 pages(tex files), 4 figures(eps files); added references and
comment
Metric Operators for Quasi-Hermitian Hamiltonians and Symmetries of Equivalent Hermitian Hamiltonians
We give a simple proof of the fact that every diagonalizable operator that
has a real spectrum is quasi-Hermitian and show how the metric operators
associated with a quasi-Hermitian Hamiltonian are related to the symmetry
generators of an equivalent Hermitian Hamiltonian.Comment: 6 pages, published versio
Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
We provide a reviewlike introduction into the quantum mechanical formalism
related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting
with the time-independent framework we explain how to determine an appropriate
domain of a non-Hermitian Hamiltonian and pay particular attention to the role
played by PT-symmetry and pseudo-Hermiticity. We discuss the time-evolution of
such systems having in particular the question in mind of how to couple
consistently an electric field to pseudo-Hermitian Hamiltonians. We illustrate
the general formalism with three explicit examples: i) the generalized Swanson
Hamiltonians, which constitute non-Hermitian extensions of anharmonic
oscillators, ii) the spiked harmonic oscillator, which exhibits explicit
supersymmetry and iii) the -x^4-potential, which serves as a toy model for the
quantum field theoretical phi^4-theory.Comment: 14 pages, 3 figures, to appear in Laser Physics, minor typos
correcte
Time evolution of non-Hermitian Hamiltonian systems
We provide time-evolution operators, gauge transformations and a perturbative
treatment for non-Hermitian Hamiltonian systems, which are explicitly
time-dependent. We determine various new equivalence pairs for Hermitian and
non-Hermitian Hamiltonians, which are therefore pseudo-Hermitian and in
addition in some cases also invariant under PT-symmetry. In particular, for the
harmonic oscillator perturbed by a cubic non-Hermitian term, we evaluate
explicitly various transition amplitudes, for the situation when these systems
are exposed to a monochromatic linearly polarized electric field.Comment: 25 pages Latex, 1 eps figure, references adde
Classical and quantum-mechanical treatments of nonsequential double ionization with few-cycle laser pulses
We address nonsequential double ionization induced by strong, linearly
polarized laser fields of only a few cycles, considering a physical mechanism
in which the second electron is dislodged by the inelastic collision of the
first electron with its parent ion. The problem is treated classically, using
an ensemble model, and quantum-mechanically, within the strong-field and
uniform saddle-point approximations. In the latter case, the results are
interpreted in terms of "quantum orbits", which can be related to the
trajectories of a classical electron in an electric field. We obtain highly
asymmetric electron momentum distributions, which strongly depend on the
absolute phase, i.e., on the phase difference between the pulse envelope and
its carrier frequency. Around a particular value of this parameter, the
distributions shift from the region of positive to that of negative momenta, or
vice-versa, in a radical fashion. This behavior is investigated in detail for
several driving-field parameters, and provides a very efficient method for
measuring the absolute phase. Both models yield very similar distributions,
which share the same physical explanation. There exist, however, minor
discrepancies due to the fact that, beyond the region for which electron-impact
ionization is classically allowed, the yields from the quantum mechanical
computation decay exponentially, whereas their classical counterparts vanish.Comment: 12 pages revtex, 12 figures (eps files
Non-sequential double ionization below laser-intensity threshold: Anticorrelation of electrons without excitation of parent ion
Two-electron correlated spectra of non-sequential double ionization below
laser-intensity threshold are known to exhibit back-to-back scattering of the
electrons, viz., the anticorrelation of the electrons. Currently, the widely
accepted interpretation of the anticorrelation is recollision-induced
excitation of the ion plus subsequent field ionization of the second electron.
We argue that another mechanism, namely simultaneous electron emission, when
the time of return of the rescattered electron is equal to the time of
liberation of the bounded electron (the ion has no time for excitation), can
also explain the anticorrelation of the electrons in the deep below
laser-intensity threshold regime. Our conclusion is based on the results of the
numerical solution of the time-dependent Schr\"{o}dinger equation for a model
system of two one-dimensional electrons as well as an adiabatic analytic model
that allows for a closed-form solution.Comment: 6 pages and 3 figure
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