Attosecond probing of instantaneous ac Stark shifts in helium atoms

Based on the numerical solutions of the time-dependent Schrödinger equation within the single-active-electron approximation, we propose a method for observing instantaneous atomic level shifts in an oscillating strong infrared (IR) field with sub-IR-cycle time resolution, by using a single tunable attosecond (SA) pulse to probe excited states of the perturbed atom. The ionization probability in the combined fields depends on both the frequency of the attosecond pulse and the time delay between both pulses, since the IR field periodically shifts SA-pulse-excited energy levels into and out of resonance. (Some figures in this article are in colour only in the electronic version) The energetic shift of atomic levels in external electric fields is a well-known phenomenon and usually referred to as ‘Stark shift’. For static fields that are much weaker than intraatomic Coulomb fields, Stark shifts can be calculated using perturbation theory [1]. For oscillating external fields in the optical and near-IR range, perturbation theory breaks down at intensities of about 10 W cm [2], orders of magnitudes below the peak intensities available in state-of-theart ultrashort laser laboratories. If such strong external fields are maintained over many optical cycles, cycle-averaged level shifts can be evaluated, e.g. by exploiting the quasi periodicity of the external field using the non-perturbative Floquet theory [3–5]. However, for the recently developed strong few-cycle IR laser pulses [6–10], atomic level shifts are non-perturbative in nature and also render the continuum-wave Floquet picture inapplicable. Modern pump-probe experiments combine extended ultraviolet (XUV) attosecond pulses of sub-IR-cycle pulse lengths (1 as = 10 s) with phase-coherent IR laser pulses to observe electronic dynamics in atoms, molecules and solids [11–16]. The role of laser-dressed highly excited energy levels in atomic excitation and ionization has been studied recently using attosecond technology [17, 18]. In this communication, we show that the attosecond pump-probe technique should also enable the measurement of instantaneous level shifts of low-lying bound atomic states in alternating optical electric