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Physical Review A

Time correlation in two-electron transitions produced in fast collisions of atoms with matter and light

James H. McGuire, Alexander Godunov, S. G. Tolmanov, Kh. Kh. Shakov, R. Dörner, H. Schmidt‐Böcking, R. M. Dreizler

Published Apr 13, 2001• 18 citations
Publisher

Abstract

Time connection between electrons in dynamic atomic systems is considered. We describe time correlation in terms of the Dyson time ordering operator T. In this paper we decompose T into an uncorrelated term ${T}_{\mathrm{unc}},$ plus a correlated term ${T}_{\mathrm{cor}}=T\ensuremath{-}{T}_{\mathrm{unc}},$ which interconnects the time-dependent external interactions. We show that time correlation between electrons requires both ${T}_{\mathrm{cor}}$ and spatial electron-electron correlation. Two examples are analyzed. In transfer ionization the time correlation operator incoherently changes the shape of an electron-electron Thomas peak. In double excitation the influence of ${T}_{\mathrm{cor}}$ in amplitudes for coherently interfering pathways changes resonance intensities and profiles.

DOI
10.1103/physreva.63.052706

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Time connection between electrons in dynamic atomic systems is considered. We describe time correlation in terms of the Dyson time ordering operator T. In this paper we decompose T into an uncorrelated term Tunc,{T}_{\mathrm{unc}},Tunc​, plus a correlated term Tcor=T\ensuremath−Tunc,{T}_{\mathrm{cor}}=T\ensuremath{-}{T}_{\mathrm{unc}},Tcor​=T\ensuremath−Tunc​, which interconnects the time-dependent external interactions. We show that time correlation between electrons requires both Tcor{T}_{\mathrm{cor}}Tcor​ and spatial electron-electron correlation. Two examples are analyzed. In transfer ionization the time correlation operator incoherently changes the shape of an electron-electron Thomas peak. In double excitation the influence of Tcor{T}_{\mathrm{cor}}Tcor​ in amplitudes for coherently interfering pathways changes resonance intensities and profiles.
We propose an independent time approximation (ITA), defined by simplifying the chronological operator, namely, TTunc, where Tunc is the uncorrelated limit of the chronological operator T. The concept of the time correlation is analogous to spatial electron correlation. In both cases `correlation' is the difference between an exact result and an uncorrelated limit. In the uncorrelated ITA the time correlation operator Tcor = T-Tunc is neglected and causality between electrons is lost. In second-order calculations of a two-electron transition the ITA reduces computer time by over two orders of magnitude. Greater savings are expected when higher orders or more electrons are included.
Correlation is often significant in electron scattering from atoms, nuclei and bulk matter. Mathematically, as well as conceptually, correlation and entanglement are defined in the same way. Both correlation and entanglement connote mixing. Both are described as a deviation from a product (uncorrelated) form. In quantum optics the term entanglement is used to describe the spatial mixing of states of a system by external electromagnetic fields. In static systems correlation arises from interparticle fields that mix wavefunctions. Correlation dynamics, intrinsic in scattering from few and many body systems, adds the dimension of time to the basic conceptual framework. Time correlation, described here, mixes the time evolution of the particles. This time entanglement, which is non-local, requires both spatial correlation and quantum time ordering. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Universality of the dynamic characteristic relationship between the characteristic time t c and the two-electron Coulomb interaction energy V ¯ 12 of the ground state in the two-photon double ionization process is investigated via changing the parameters of the two-electron atomic system and the corresponding laser conditions. The numerical results show that the product t c V ¯ 12 keeps constant around 4.1 in the cases of changing the nucleus charge, the electron charge, the electron mass, and changing simultaneously the nucleus charge and the electron charge. These results demonstrate that the dynamic characteristic relationship in the two-photon double ionization process is universal. This work sheds more light on the dynamic characteristic relationship in ultrafast processes and may find its application in measurements of attosecond pulses.
We calculate photoelectron spectra for a two-electron atom under the influence of two external driving fields, using an essential states formalism. We focus on the regime of coherence transfer, in which electron-electron correlation transfers field-induced photocoherence from one electron to the other. In the case studied here, two laser fields are resonant with coupled atomic transitions, in the manner familiar from three-level dark-state spectroscopy. Dynamical two-electron effects are monitored via the photoelectron energy spectrum. We show that the distribution of the photoelectron energies can be singly, doubly, or triply peaked depending on the relative laser intensities. The electron spectra are independent of the turn-on sequence of the fields. \textcopyright{} 1996 The American Physical Society.
Excitation energy transfer is a photophysical process upon which many chemical and biological phenomena are built. From natural small systems to synthetic multichromophoric macromolecules, energy transfer deals with the process of migration of electronic excitation energy from an excited donor to an acceptor. Although this phenomenon has been extensively studied in the past, the rapid evolution of quantum-enabled technologies has motivated the question on whether nonclassical sources of light, such as entangled photon pairs, may provide us with a better control (or enhancement) of energy transfer at the nanoscale. In this work, we provide a comprehensive study of the joint excitation of two non-interacting two-level atoms by time-frequency correlated photon pairs -- whose central frequencies are not resonant with the individual particles -- generated by means of spontaneous parametric down conversion (SPDC). We demonstrate that while strong frequency anti-correlation between photons guarantees a large two-photon excitation (TPE) probability, photons bearing a sine cardinal spectral shape exhibit a $\sim$3.8 times larger TPE signal than photons with a Gaussian spectrum. More importantly, we find that suppression of time-ordered excitation pathways does not substantially modify the TPE probability for two-photon states with a Gaussian spectral shape; whereas photons with a sine cardinal spectrum exhibit the strongest TPE signals when two-photon excitation pathways are not suppressed. Our results not only help elucidating the role of time-frequency correlations in resonance energy transfer with SPDC photons, but also provide valuable information regarding the optimal source to be used in its experimental implementation.
The concept of coherence is analyzed in a system of interacting radiation and matter. Using the projection technique, the reduced field density operator is found, and with it the first and higher order field correlation functions are computed. It is proved that the inelastically scattered field is, for the most part, incoherent in any order at any time interval after collision with an atomic ensemble, except some specific time intervals and positions, where the order of coherence is determined by the atomic correlations considered.