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Annual Meeting Optical Society of America

Two-color multiphoton ionization and a numerical test of essential states theory

L. Roso, Joseph H. Eberly, Kazimierz Rza̧żewski

Published Jan 1, 1989• 0 citations
Publisher

Abstract

The various essential states (ES) models of multiphoton ionization (MPI) are the only models that permit an analytical solution for the temporal dynamics of MPI. One specific comparison of experimental data1 with ES predictions did not give good agreement. This may have been due to the simplifying assumptions of any essential states model or to the intrinsic difficulties of MPI spectroscopy. One of the important simplifications of ES models, the reliance on the rotating wave approximation (RWA) in the continuum, has recently been overcome.2

DOI
10.1364/oam.1989.fm3

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The various essential states (ES) models of multiphoton ionization (MPI) are the only models that permit an analytical solution for the temporal dynamics of MPI. One specific comparison of experimental data1 with ES predictions did not give good agreement. This may have been due to the simplifying assumptions of any essential states model or to the intrinsic difficulties of MPI spectroscopy. One of the important simplifications of ES models, the reliance on the rotating wave approximation (RWA) in the continuum, has recently been overcome.2
We present the unambiguous determination of quantum phases in the multiphoton ionization (MPI) of potassium atoms by using a multichannel photoelectron interferometry scheme based on trichromatic pulse shaping. The colors of the laser field are chosen to produce three energetically separated photoelectron interferograms in the continuum. While the red pulse is two-photon resonant with the 3d3d3d state resulting in a (2+1)(2+1)(2+1) resonance-enhanced MPI (REMPI), a (1+2)(1+2)(1+2) REMPI occurs via the nonresonant intermediate 4p4p4p state with an initial green or blue pulse. We show that ionization via a nonresonant intermediate state lifts the degeneracy of photoelectron interferograms from pathways consisting of permutations of the colors. The analysis of the interferograms reveals a phase shift of $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2$ depending on the sign of the detunings in the (1+2)(1+2)(1+2) REMPI pathways. In addition, we demonstrate that the photoionization time delay in the resonant (2+1)(2+1)(2+1) REMPI pathway gives rise to a linear spectral phase in the photoelectron spectra. Insights into the underlying MPI processes are gained through an analytic perturbative description and numerical simulations of a trichromatic driven three-level system coupled to the continuum.
Atomic and molecular free electron vortices (FEVs), characterized by their spiral-shaped momentum distribution, have recently attracted a great deal of attention due to their varied shapes and their unusual topological properties. Shortly after their theoretical prediction by the single-photon ionization (SPI) of He atoms using pairs of counterrotating circularly polarized attosecond pulses, FEVs have been demonstrated experimentally by the multiphoton ionization (MPI) of alkali atoms using single-color and bichromatic circularly polarized femtosecond pulse sequences. Recently, we reported on the analysis of the experimental results employing a numerical model based on the ab initio solution of the time-dependent Schrödinger equation (TDSE) for a two-dimensional (2D) atom interacting with a polarization-shaped ultrashort laser field. Here, we apply the 2D TDSE model to study molecular FEVs created by SPI and MPI of a diatomic molecule using polarization-tailored single-color and bichromatic femtosecond pulse sequences. We investigate the influence of the coupled electron-nuclear dynamics on the vortex formation dynamics and discuss the effect of CEP- and rotational averaging on the photoelectron momentum distribution. By analyzing how the molecular structure and dynamics is imprinted in the photoelectron spirals, we explore the potential of molecular FEVs for ultrafast spectroscopy.
Driving quantum systems periodically in time plays an essential role in the coherent control of quantum states. The rotating-wave approximation (RWA) is a good approximation technique for weak and nearly resonance driven fields. However, these experiments sometimes require large detuning and strong driving fields, for which the RWA may not hold. In this work, we experimentally, numerically, and analytically explore strongly driven two-mode Josephson circuits in the regime of strong driving and large detuning. Specifically, we investigate beam-splitter and two-mode squeezing interaction between the two modes induced by driving a two-photon sideband transition. Using numerical simulations, we observe that the RWA is unable to correctly capture the amplitude of the sideband transition rates. We verify this finding using an analytical model that is based on perturbative corrections. We find that the breakdown of the RWA in the regime studied does not lead to qualitatively different dynamics, but gives the same results as the RWA theory at higher drive strengths, enhancing the coupling rates compared to what one would predict. This is an interesting consequence compared to the carrier transition case, where the breakdown of the RWA results in qualitatively different time evolution of the quantum state. Our work provides an insight into the behavior of time-periodically driven systems beyond the RWA. We also provide a robust theoretical framework for including these findings in the calculation and calibration of quantum protocols in circuit quantum electrodynamics.