Adiabatic stabilization against photoionization in a constant magnetic field

Abstract

An adiabatic stabilization against photoionization consists in the fact that an electron wave packet ͑or at least its part͒ in an ultrastrong laser field moves as a whole in the rhythm of the field in the neighborhood of the nucleus instead of throwing away its small parts every time it passes the nucleus ͓1͔. This phenomenon can also be described as the packet's trapping in the time-averaged potential seen by the electron ͑Kramers-Henneberger well͒. A necessary condition for the model stabilization in one dimension is that the laser pulse is such that the solution of the classical Newton equation, also in the absence of the binding potential, has the mean velocity ͑i.e., the velocity averaged over the oscillation period͒ equal to zero. This is true, for example, for trapezoid field envelopes or for a cosine electric field with a rectangular envelope, but not for a sine pulse with the latter envelope.It has been known for a long time that the effect of the stabilization is weaker for two-or three-dimensional systems ͓2͔. This has been confirmed by Vazquez de Aldana et al. ͓3,4͔, who have numerically investigated the photoionization of a two-dimensional atom and have demonstrated that the stabilization is essentially hindered. A reason for that is that, apart from the strong electric force in the direction of the pulse polarization, there exists a magnetic force that causes a drift of the packet away from the nucleus ͓3,4͔. Below we show classically and demonstrate by ab initio numerical computations that it is in general impossible to choose such a field ramp-up that the magnetic drift could be avoided and that the latter effect can be compensated by an additional properly chosen constant magnetic field. In our opinion this is an interesting theoretical observation concerning the dynamics of the process, even though the magnitude of this magnetic field is now far beyond the experimentally accessible range.The atomic model we adopt is a shallow ͑i.e., such that the ionization energy of the bound state is small͒ rectangular potential well, for which the effect of tearing up of the packet into smaller pieces is small for the field intensities considered in this paper. Our observations would be valid also for long-range potentials ͓5͔, for which the packet also remains a connected structure during the evolution, and are in contrast with our former results for a deep potential well ͓6͔, for which numerous pieces of the packet exhibited some special dynamical effects.Consider a laser pulse with the electric-field amplitude equal to E x (y,t)ϭE 0 f (), ϭtϪky, during the switch-on stage 0рр 1 and E x (y,t)ϭE 0 cos(ϩ) for Ͼ 1 . We assume that 1 ϭ2n, n being an integer number. We are not concerned with the switch-off stage because it has no influence on the stabilization. The magnetic field is B z ϭ(Ϫ1/c)E x ϩB c , where we have admitted a constant magnetic component in addition to the magnetic field of the laser. The Newton equations of motion in two spatial dimensions areIf we make the dipole approximation now and retain...

Entanglement between an auto-ionization system and a neighbor atom

“…(1) q depends on the experimental frequency resolution ∆E. It even holds that N (1) q (E) → 0 for ∆E → 0. This the fact that at least a 'small' group of states |E inside the frequency interval ∆E is needed to 'imprint' the entanglement.…”

“…Ionization is a process in which an electron is transferred from its bound discrete state into a continuum of free states, e.g., by interacting with an optical field. In a stationary optical field, an electron at an atom gradually leaves its bound state and moves into an ionized free state [1]. This process is irreversible.…”

Entanglement between an autoionizing system and a neighboring atom

“…In a stationary optical field, an electron at an atom gradually leaves its bound state and moves into an ionized free state [1]. This process is irreversible.…”

Recombination in strong laser fields: Manifestation of a slow drift

“…As it has been shown in the works devoted to the atomic stabilization, in laser fields of order of a few atomic units most of the electron wave packet moves as a whole, performing oscillations in the rhythm of the field. Additionally, long time oscillations of the packet are possible which are due to an asymmetry of the interaction of its different parts with the binding potential; in our earlier papers [4,5,6] we have called them a slow drift. The slow drift has the range equal to that of the classical oscillations of a free electron in the laser field and it was possible to give an analytic formula for its frequency in the case of the binding potential being a rectangular well.…”