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Physical Review A

Manipulating quantum entanglement of quasiparticles in many-electron systems by attosecond x-ray pulses

Shaul Mukamel, Haitao Wang

Published Jun 24, 2010• 6 citations
Publisher

Abstract

Photoexcited electrons and holes in molecules or in semiconductors constitute a bipartite entangled system. We show that this entanglement can be coherently controlled by broadband x-ray pulses which create valence excitation wave packets through a stimulated Raman process. A novel measure of electron correlations in excited states is then provided by the time dependence of the concurrence. In a simulation study we demonstrate the control of entanglement of electrons and holes in CO that can be achieved by tuning a soft x-ray pulse to different core transitions: the carbon $K$ edge (296 eV), the oxygen $K$ edge (540 eV), and the $2\ensuremath{\sigma}\ensuremath{\rightarrow}1{\ensuremath{\pi}}^{*}$ transition (191 eV).

DOI
10.1103/physreva.81.062334

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Photoexcited electrons and holes in molecules or in semiconductors constitute a bipartite entangled system. We show that this entanglement can be coherently controlled by broadband x-ray pulses which create valence excitation wave packets through a stimulated Raman process. A novel measure of electron correlations in excited states is then provided by the time dependence of the concurrence. In a simulation study we demonstrate the control of entanglement of electrons and holes in CO that can be achieved by tuning a soft x-ray pulse to different core transitions: the carbon KKK edge (296 eV), the oxygen KKK edge (540 eV), and the 2\ensuremathσ\ensuremath→1\ensuremathπ∗2\ensuremath{\sigma}\ensuremath{\rightarrow}1{\ensuremath{\pi}}^{*}2\ensuremathσ\ensuremath→1\ensuremathπ∗ transition (191 eV).
Recent techniques in x-ray free electron lasers allow the generation of highly coherent, intense x-ray pulses with time lengths on the order of femtoseconds. Here we explore the possibilities of using such x-ray pulses to control matter based on coherence. In particular we propose a theoretical scheme to perform stimulated Raman adiabatic passage in the x-ray regime by using inner-hole excited states. Numerical results in two well-known systems, the neon atom and the carbon monoxide molecule, show a robust control of population transfer. In the molecule, vibrational selectivity is achieved with femtosecond x-ray pulses. This work supports the possibility of using two-color x-ray pulses for coherent control.
This work theoretically investigates possibilities of using the Stimulated Raman Adiabatic Passage (STIRAP) and its variants to control a coherent superposition of quantum states. We present a generalization of the so-called fractional STIRAP (f-STIRAP), demonstrating precise control over the mixing ratio of quantum states in the wave packet. In contrast to conventional f-STIRAP, designed to drive a system from an eigenstate into a coherent superposition, our scheme enables arbitrary control over the composition of an already existing superposition state. We demonstrate that an approximate version of this technique -- where analytically designed laser pulses with composite envelopes are replaced by simple Gaussian pulses -- achieves comparable performance in controlling the dynamics of the wave packet. A limiting case of this scheme, utilizing two pulses with identical Gaussian envelopes and tuned delay and relative phase, is also explored, revealing experimentally accessible pathways for manipulating quantum coherence. We apply our developed techniques to control the ultrafast charge migration in the spin-orbit split ground electronic states of xenon cation via intermediate valence- and core-excited states. Finally, we propose concrete experimental realizations of the developed control schemes in combination with attosecond transient absorption spectroscopy as a method to probe the system.
Nonstationary molecular states which contain electronic coherences can be impulsively created and manipulated by using recently developed ultrashort optical and x-ray pulses via photoexcitation, photoionization, and Auger processes. We propose several stimulated-Raman detection schemes that can monitor the subsequent phase-sensitive electronic and nuclear dynamics. Three detection protocols of an x-ray broadband probe are compared: frequency-dispersed transmission, integrated photon number change, and total pulse energy change. In addition, each can be either linear or quadratic in the x-ray probe intensity. These various signals offer different gating windows into the molecular response, which is described by correlation functions of electronic polarizabilities. Off-resonant and resonant signals are compared.
Abstract Coherent control uses interference between quantum pathways to enhance or suppress transitions to a target quantum state. In stimulated Raman excitation, such control can be achieved through interference between two indistinguishable pathways connecting the same initial and final states, with the relative phase between the pathways modulating the population transfer to the final state. Extending this strategy to the extreme ultraviolet (XUV) and X-ray regimes would enable control of ultrafast electronic dynamics and site-selective core excitations. However, Raman coupling at short wavelengths competes with photoionization and intermediate-state decay, whereas intense fields with stable and adjustable relative phases remain difficult to produce. Here we use two-colour pulses from a seeded coherent free-electron laser to excite helium from its ground state to a bound metastable state via stimulated XUV Raman excitation. We implement phase-coherent control by creating two interfering Raman pathways through the ionization continuum and modulate the transferred population by varying their relative phases. Blocking one pathway removes the modulation, confirming its interferometric origin, and time-dependent Schrödinger equation calculations reproduce the measured phase dependence. Our results establish phase-controlled stimulated Raman excitation in the XUV regime, providing a strategy for the coherent control of atomic and molecular processes at short wavelengths.
The single ionization of H2{\mathrm{H}}_{2}H2​ in strong laser fields creates the correlated electron-H2+{{\mathrm{H}}_{2}}^{+}H2​+ pair. Based on such a correlation, we conceive a strategy to control the energy spectra of the freed electron or dissociative fragments by simulating the time-dependent Schr\"odinger equation. Two attosecond pulses in a train produce the replica of electron-H2+{{\mathrm{H}}_{2}}^{+}H2​+ pairs, which are to be steered by a time-delayed phase-stabilized (mid)infrared laser pulse. By controlling the behavior of the freed electron, the dissociation of H2+{{\mathrm{H}}_{2}}^{+}H2​+ can be controlled even though there is no direct laser-H2+{{\mathrm{H}}_{2}}^{+}H2​+ coupling. On the other hand, the photoelectron energy spectra can be manipulated via laser-H2+{{\mathrm{H}}_{2}}^{+}H2​+ coupling. This study demonstrates the entanglement of molecular quantum wave packets, and affords a route to remotely control molecular dissociative ionization.
Quantitative control and measurement of quantum entanglement are essential for advancing quantum technologies. Photoionization induced by ultrashort laser pulses provides a unique platform for studying entanglement between photoelectrons and residual ions, representing one of the most intriguing quantum phenomena in attosecond physics. Although extensive studies have focused on the coherence properties within either the emitted electrons or the ions individually, the electron-ion entanglement has remained largely unexplored. In this work, we bridge this gap by investigating the resonance-enhanced multiphoton ionization of argon atoms driven by two time-delayed ultrashort ultraviolet pulses. Employing state-of-the-art first-principles multi-electron simulations, we demonstrate the ability to reconstruct and precisely manipulate the purity of electron quantum states through detailed analysis of the photoelectron angular distributions. Our results reveal distinct scattering-phase differences among various electron configurations within the same partial wave channel, providing unequivocal evidence of electron-ion correlation and entanglement. With the fast development of free-electron lasers, this study establishes an experimentally feasible framework for directly controlling quantum entanglement in ultrafast ionization processes, offering new insights and powerful methodologies for exploring complex electron dynamics in many-electron systems.