Relativistic features and time delay of laser-induced tunnel ionization

Abstract

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.

Tunneling time in attosecond experiments and the time-energy uncertainty relation

“…The choice of Z ef f is easy recognized for many electron system and well-known in atomic, molecular and plasma physics [18][19][20]. We take one dimensional model along the x-axis as justified by Klaiber and Yakaboylu et al [22,23]. Augst et al [14] calculated the position of the barrier maximum xm by setting ∂V ef f (x)/∂x = 0 ⇒ xa = xm(Fa) = ( Z ef f /Fa) and by equating V ef f (xm) to the ionization potential V ef f (xa) = −Ip (compare fig 1, the lower green curve) they found an expression for the atomic field strength Fa,…”

“…Their conclusion supported with ab initio numerical tests, is that for long range potentials, ionization is not yet completed at the "moment" the electron exits the tunneling barrier in contrast to the usual assumption that ionization is completed once the electron emerges from the barrier. Indeed it is not difficult to see that the electric field of the laser pulse shift the electrons along the x-axis direction [22,23], compare fig 1, reaching the exit point with zero velocity, i.e. the electron is forced by the electric field to take and move along a preferred direction, and to reduce its kinetic energy to zero at th exit point xe (the field interacts only kinematic-ally with the electron since no photon absorbing), where it is still underling the attraction of the atomic potential V (xe) = −…”

“…where xe ≈ (xe − x 0 ), x 0 ≈ 0 is the initial point of the electron and assuming the electron moves along the x-axis direction [22,23]. , which is far from the "correct" exit point.…”

Recollision as a probe of magnetic-field effects in nonsequential double ionization

“…In ref. [27] non-dipole effects were accounted for in the ADK rate. It was shown that the most probable transverse velocity ranges from 0.33 I p /c to almost zero with increasing E 0 /(2I p ) 3/2 , with I p the ionization energy of the tunneling electron.…”

Under-the-Tunneling-Barrier Recollisions in Strong-Field Ionization

“…Although all alternative definitions of the tunneling delay time are equally valid theoretical concepts, the Wigner concept [20] is physically relevant to the measurement of the photoelectron momentum distribution in the attoclock setup in the quasistatic regime, as proved in a recent experiment [10]. However the Wigner definition of the time delay via the derivative of the wave function phase, and its generalization for the strong field tunneling problem [18,[21][22][23][24] is applicable only in the quasistatic limit, i.e., when the laser induced barrier is (quasi-)static. Therefore, there is need for a generalization of the Wigner concept to the nonadiabatic regimes [25][26][27] of the strong field ionization, which may explain the discrepancy between the theory and the attoclock experiment at large Keldysh parameters [10].…”