Plasmon signatures in high harmonic generation

High harmonic generation in complex multi-electron systems is investigated theoretically. The harmonic spectra exhibit two cutoffs. The first cutoff is in good agreement with the well established, single active electron cutoff law. The second cutoff presents a signature of multi-electron dynamics. The strong laser field excites nonlinear plasmon oscillations. Electrons that are ionized from one of the multi-plasmon states and recombine to the ground state gain additional energy, thereby creating the second plateau. This finding gives experimental access to a so far hardly explored regime of quantum physics the non-perturbative, nonlinear dynamics of multi-electron systems. Submitted to: J. Phys. B: At. Mol. Phys. ‡ Present address: Institute of Chemistry, Karl-Franzens-University Graz, Heinrichstraße 28, A-8010 Graz, Austria Plasmon signatures in high harmonic generation 2 When an intense laser pulse is focused onto a noble gas jet, high harmonic generation (HHG) takes place. High harmonic radiation is created in a three step process [1]. The valence electron is set free by tunnel ionization. In the continuum, the electron is accelerated and follows the quiver motion of the laser field. When the laser field changes sign, the electron is driven back towards the parent ion. Finally, the electron recombines to the ground state upon recollision, and an xuv photon is emitted. The theory of HHG is based on the single-active-electron (SAE) approximation [2]. It is assumed that only the valence electron interacts with the strong laser field. The residual electron core remains frozen and does not contribute to the interaction. As a result, the valence electron and the core electrons are regarded as uncorrelated. HHG has been performed with noble gas atoms, noble gas clusters [3], and with small molecules [4, 5]. All experiments so far were found to be in agreement with SAE theory. Experimental [6, 7, 8] and theoretical [9] evidence was found that SAE theories cannot describe optical field ionization of highly polarizable systems, such as large molecules and metallic clusters. Due to the high electron mobility and polarizability, a factorization into valence and core electrons is no longer valid and the complete, correlated multi-electron (ME) dynamics has to be taken into account. This raises the question as to which extent the SAE approximation is applicable to non-perturbative phenomena in complex materials [10, 11]. In this article, HHG in highly polarizable electron systems is investigated by a 1D multi-configuration time-dependent Hartree-Fock (MCTDHF) analysis. MCTDHF is currently the only method that can properly model non-perturbative, correlated ME quantum dynamics [12, 13]. Our analysis reveals the following key result. In contrast to HHG in noble gases, where the harmonic spectrum exhibits one plateau and cutoff, a second cutoff is identified in complex, highly polarizable materials. The first cutoff is found to be in agreement with the SAE cutoff law [1]. The second cutoff originates from the ME nature of the bound electrons. The strong laser field excites nonlinear, collective electron oscillations. This results in a population of multi-plasmon states that oscillate at a multiple of the plasmon frequency. The second plateau is generated by electrons that ionize from the multi-plasmon states and recombine to the ground state. The energy difference between excited and ground state determines the difference between first and second cutoff. The identified plasmon signature presents a novel tool for the investigation of nonlinear, non-perturbative ME dynamics in complex materials. Our analysis has still another implication. At lower intensities, just below the threshold for ionization, the plasmon frequency and its first few harmonics are still excited very efficiently. This process presents an interesting alternative to HHG, as it does not underly the limitations of HHG arising from dephasing and spreading of the electron wavefunction in the continuum [14]. Nonlinear plasmon oscillations hold the potential for the realization of efficient, coherent xuv-sources. Finally, a 3D numerical analysis of non-perturbative ME dynamics is currently computationally out of reach. Although 3D effects may affect the quantitative structure of the calculated spectra, the essential physics underlying HHG and the nonlinear excitation of multi-plasmon frequencies is contained in our 1D analysis. Ionization potential and polarizability of our model potentials were chosen to be close to values that are representative for highly polarizable, complex materials. Therefore, our 1D analysis of HHG in ME systems gives a reasonable approximation to the ”real world” process. The 1DMCTDHF analysis is based on the solution of the 1D Schrödinger equation Plasmon signatures in high harmonic generation 3 for the f -electron potential V = ∑f i=1 [ −Vn(xi)− xiE(t) + ∑f j>i Ve(xi − xj) ]