Signatures of nonadiabaticity, relativity and tunneling time delays in the photoelectron momentum distribution of laser-induced tunnel-ionization

We discuss the photoelectron momentum distribution in tunnel-ionization by taking into account nonadiabatic and relativistic effects as well as the tunneling time delay. For this purpose we first identify the tunneling barrier by defining a gauge invariantenergy operator for the quasistatic tunneling regime for both nonrelativisticand relativistic cases [1,2]. Then, we investigate the asymptotic momentum distribution for the maximal tunneling probability, and by tracing back toit at the tunnel exit, we show that the nonadiabatic dynamics as well as the magnetically induced Lorentz force give rise to transversal momentum shifts [3,4]. Finally, we discuss the tunneling time delay. In the well-known quasiclassical description of tunnel-ionization, the ionized electron emerges with a vanishing velocity at the tunnel exit by assuming instantaneous tunneling, and then fulfills the Newtonian equations of motion. In particular, we find a time delay between the quasiclassical trajectory and a quantum mechanical trajectory, and map this delay to a longitudinal momentum shift at the tunnel exit [2,5]. All these momentum shifts depend on the atomic ionization potential and can be rendered more visible in comparative measurements employing two species with different ionization energies.

[1] M. Klaiber, E. Yakaboylu, H. Bauke, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. Lett. 110, 153004 (2013).
[2] E. Yakaboylu, M. Klaiber, H. Bauke, K. Z. Hatsagortsyan, and C. H. Keitel, Phys. Rev. A 88, 063421 (2013).
[3] E. Yakaboylu, M. Klaiber, and K. Z. Hatsagortsyan, to be submitted.
[4] M. Klaiber, K.Z. Hatsagortsyan, C.H. Keitel, arXiv:1408.5712
[5] E. Yakaboylu, M. Klaiber, and K. Z. Hatsagortsyan, Phys. Rev. A 88, 063421 (2014).