Excitation of Rydberg wave packets in the tunneling regime

Abstract

In the tunneling regime for strong laser field ionization of atoms, experimental studies have shown that a substantial fraction of atoms survive the laser pulse in many Rydberg states. To explain the origin of such trapping of population into Rydberg states, two mechanisms have been proposed : the first involves AC-Stark-shifted multiphoton resonances and the second, called frustrated tunneling ionization, leads to the recombination of tunneled electrons into Rydberg states. We use a very accurate spectral method based on complex sturmian functions to solve the time dependent Schrödinger equation for hydrogen in a linearly polarized infrared pulse and to calculate the tunneling probability in terms of the atomic ground state width. We examine the probability of excitation into Rydberg states as a function of the peak intensity for various pulse durations and two wavelengths, 800 nm and 1800 nm and try to explain the results in light of the two aforementioned mechanisms. For long pulses of 800 nm wavelength, the extreme sensitivity of the trapping of population into high-lying Rydberg states to the peak intensity, the well defined value and parity of the angular momentum of the populated Rydberg states and the presence of Freeman resonances can be explained using a multiphotonic excitation mechanism. For strong pulses of 1800 nm wavelength, in the so-called adiabatic or quasi-static tunneling regime, the oscillations of the excitation probability as a function of intensity are in phase opposition to the ionization probability and we observe a migration towards high values of the angular momentum with different distributions in the angular momentum at the maxima and minima of the oscillations. We also present a detailed study of how the excited state wave packet builds up in time during the interaction of the atom with the pulse.

Quantum dynamics of atomic Rydberg excitation in strong laser fields

“…Since the energies of the Rydberg states are near the threshold so that their Stark shifts are all close to the Stark shift U p of the continuum, multiphoton resonance between the Rydberg and the initial states occurs at intensities that are separated by ∆U p = ω [1]. In addition, the dipole selection rule only allows even-order (odd-order) multiphoton transitions between states of equal (opposite) parity, which gives rise to a ∆U p = 2 ω separation between consecutive peaks for a transition between two states with specified parity [17,19]. Apparently, these features are beyond the scope of the semiclassical picture of the RSE.…”

Angular momentum distribution in Rydberg states excited by a strong laser pulse

“…Theoretical analysis of the angular momentum distribution in the populated Rydberg states is less advanced. Predictions of Floquet theory for a monochromatic laser field [35] and results of numerical calculations for laser pulses with a trapezoidal envelope [32] yield that the angular momentum of the excited Rydberg states has the same parity as N p − 1, where N p is the minimum number of photons needed to ionize the atom. Furthermore, the angular quantum number of the states with the largest population in numerical calculations [9,10,32] agrees well with semiclassical estimations [36], initially performed for low-energy angular resolved photoelectron distributions.…”

“…Recent theoretical studies of the excitation mechanism in strong fields mainly consider the distribution of the population as a function of the principal quantum number of the excited states [9,10,25,31,32]. It was shown that the modulation of the excitation probability is related to the channel closing effect [9,10,32,35]. The latter phenomenon occurs at threshold intensities at which the absorption of one more photon is needed to ionize the atom due to the shift of the ionization threshold by the ponderomotive energy.…”

Static field limit of excitation probabilities in laser-atom interactions

“…As briefly described in [25], our numerical method to solve the TDSE is based on a spectral method, which consists in expanding the total wave function in a basis composed of products of spherical harmonics and complex radial Coulomb Sturmian functions. These Sturmian functions depend on a nonlinear parameter which allows one to monitor the region of the bound state spectrum we want to describe accurately.…”

“…This is the objective of the present paper. Several attempts have been made to study this problem by solving numerically the time dependent Schrödinger equation (TDSE) [20,21,25]. However, such a calculation is tremendously difficult and still out of reach in the limit where the frequency tends to zero.…”