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arXiv:0706.3470 · Physical Review A

Coherent control and entanglement in the attosecond electron-recollision dissociation of D2+

Michael Spanner, Paul W. Brumer

Published Jul 17, 2007• 10 citations
arXivHTMLPDF

Abstract

We examine the attosecond electron recollision dissociation of $\mathrm{D}_{2}{}^{+}$ recently demonstrated experimentally [H. Niikura et al., Nature (London) 421, 826 (2003)] from a coherent control perspective. In this process, a strong laser field incident on ${\mathrm{D}}_{2}$ ionizes an electron, accelerates the electron in the laser field to eV energies, and then drives the electron to recollide with the parent ion, causing $\mathrm{D}_{2}{}^{+}$ dissociation. A number of results are demonstrated. First, a full dimensional strong field approximation model is constructed and shown to be in agreement with the original experiment. This is then used to rigorously demonstrate that the experiment is an example of coherent pump-dump control. Second, extensions to bichromatic coherent control are proposed by considering dissociative recollision of molecules prepared in a coherent superposition of vibrational states. Third, by comparing the results to similar scenarios involving field-free attosecond scattering of independently prepared $\mathrm{D}_{2}{}^{+}$ and electron wave packets, recollision dissociation is shown to provide an example of wave-packet coherent control of reactive scattering. Fourth, this analysis makes clear that it is the temporal correlations between the continuum electron and $\mathrm{D}_{2}{}^{+}$ wave packet, and not entanglement, that are crucial for the subfemtosecond probing resolution demonstrated in the experiment. This result clarifies some misconceptions regarding the importance of entanglement in the recollision probing of $\mathrm{D}_{2}{}^{+}$. Finally, signatures of entanglement between the recollision electron and the atomic fragments, detectable via coincidence measurements, are identified.

DOI
10.1103/physreva.76.013409

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Remote control of the dissociative ionization of H 2 based on electron- H 2 + entanglement

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The single ionization of ${\mathrm{H}}_{2}$ in strong laser fields creates the correlated electron-${{\mathrm{H}}_{2}}^{+}$ 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-${{\mathrm{H}}_{2}}^{+}$ 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 ${{\mathrm{H}}_{2}}^{+}$ can be controlled even though there is no direct laser-${{\mathrm{H}}_{2}}^{+}$ coupling. On the other hand, the photoelectron energy spectra can be manipulated via laser-${{\mathrm{H}}_{2}}^{+}$ coupling. This study demonstrates the entanglement of molecular quantum wave packets, and affords a route to remotely control molecular dissociative ionization.

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Entanglement and timing-based mechanisms in the coherent control of scattering processes

Michael Spanner, Paul W. Brumer

The coherent control of scattering processes is considered, with electron impact dissociation of used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a control scenario that relies on previously established entanglement requirements between the scattering partners. Specifically, initial state entanglement assures that all collisions in the scattering volume yield the desirable scattering configuration. Scattering is controlled by preparing the particular internal state wave function that leads to the favored collisional configuration in the collision volume. This insight allows coherent control to be extended to the case of time-dependent scattering. Specifically, we identify reactive scattering scenarios using incident wave packets of translational motion where coherent control is operational and initial state entanglement is unnecessary. Both the stationary and time-dependent scenarios incorporate extended coherence features, making them physically distinct. From a theoretical point of view, this work represents a large step forward in the qualitative understanding of coherently controlled reactive scattering. From an experimental viewpoint, it offers an alternative to entanglement-based control schemes. However, both methods present significant challenges to existing experimental technologies.

arXiv:0706.3469•Physical Review A•Jul 17, 2007•10 citations

Coherent Control of Absorption and Entanglement via Ultrafast Strong Coupling

Axel Stenquist

This thesis investigates quantum dynamics induced in atoms by ultrashort pulses of light. The work is motivated by recent developments in free-electron lasers, which generate ultrashort pulses of intense, coherent light and enable coherent control of quantum dynamics. We develop theoretical models to study the processes of absorption and emission in laser-atom interactions. Additionally, we study photoionisation, which creates an ion and an electron, and the entanglement that can be generated between these particles. Finally, we have investigated how the spontaneous decay of the ion induces entanglement transfer from the ion-electron pair to the electron-photon pair.This thesis compiles seven papers. Paper I investigates the absorption of light from an attosecond pulse by an atom in a prepared coherent superposition of states. We show how the evolution of the phase of the superposition wave packet influences the attosecond transient absorption spectra. Paper II predicts the existence of Mollow-like triplets in the absorption spectra of strongly coupled atoms. We establish the conditions for the pulse envelope under which this triplet pattern can be supported.Paper III studies two-photon Rabi oscillations, establishing which systems can sustain such dynamics. We find that a two-photon Rabi oscillating system can induce giant counter-rotating oscillations in the population dynamics, enabling investigations of physical effects beyond the rotating-wave approximation.Paper IV studies ionisation from an atom strongly coupled by a dichromatic field, where interference between the two frequency components shapes the temporal symmetry of the atomic dynamics, allowing for coherent control of the photoelectron distribution.Paper V considers an experiment performed at a Free-Electron Laser facility where a helium atom is ionised and the resulting ion is subsequently strongly coupled. The photoelectron spectra are theoretically reproduced and the entanglement between the ion and photoelectron is studied. Paper VI investigates how the entanglement in the ion--electron pair, generated via photoionisation followed by strong coupling, can be coherently controlled by harnessing the time symmetry of the pulse. We find that the observable manifestation of the entanglement can be altered in such a way that the electron energy becomes associated with the ionic state, allowing the entanglement to be detected via coincidence measurements. Paper VII investigates how quantum correlations between the ion and the electron can be coherently controlled by sequential strong coupling of the ion. We find that both the build-up of entanglement and its manifestation can be controlled, and we establish a quantitative measure of the amplitude entanglement that explains the dynamics in an intuitive way. Paper VIII studies the process of entanglement transfer induced by the spontaneous decay of the ion. We find that the ion--electron entanglement generated during the ultrashort interaction with the laser field is transferred to the electron--photon system over the much longer timescale of fluorescence.

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Attosecond spatial control of ionizing electron wave packets

Li Zhang, Xinhua Xie, Stefan Roither +7 more

Summary form only given. Angstrom and attosecond control of free electron wave packets is one of the pinnacles of attosecond science. Orthogonally polarized two-color (OTC) laser fields allow to control the motion of field-ionizing electronic wave packets both in time and space[1]. In OTC pulses time and space are connected and thus an attosecond time scale is established in the polarization plane for both the emitted and the re-colliding wave packets[2,3].In this submission, we report on experiments that use OTC pulses for studying atomic single and double ionization. The three-dimensional momentum vector of electrons and ions created by single and double ionization of neon atoms was measured with the COLTRIMS technique as a function of the sub-cycle shape of the OTC pulses. We introduce a concept similar to attosecond streaking that allows reading sub-cycle timing information from the momentum vector of emitted electrons. The concept is then applied to gaining information about the influence of the long-range Coulomb potential on the trajectories of tunneling electrons.Fig.1 (a) shows the measured momentum distributions of electrons correlated with singly ionized neon in the polarization plane of the OTC field with relative phase Δφ between the two color components. The spectra show that the electron emission direction is sensitive to Δφ. Furthermore, the spectra feature a prominent x-shaped central structure and weaker fine-scale modulations due to wave packet interferences. To compare with simulated spectra with strong field approximation (SFA) and solving two-dimensional time-dependent Schrödinger equation (TDSE) with single active electron approximation, we conclude that Coulomb effect plays important role on the spatial distribution of released electron wave packets. In the conference, we will furthermore demonstrate control over the correlation between the two electrons emitted during double ionization upon electron recollision by tuning the shape of the electric field of the OTC pulses on the sub-cycle scale. The results of these experiments are in agreement with theoretical predictions [4].

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•May 1, 2013•0 citations

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The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.

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Lisa-Marie Koll, Laura Maikowski, Lorenz Drescher +2 more

Entanglement is one of the most intriguing aspects of quantum mechanics and lies at the heart of the ongoing second quantum revolution, where it is a resource that is used in quantum key distribution, quantum computing, and quantum teleportation. We report experiments demonstrating the crucial role that entanglement plays in pump-probe experiments involving ionization, which are a hallmark of the novel research field of attosecond science. We demonstrate that the degree of entanglement in a bipartite ion + photoelectron system, and, as a consequence, the degree of vibrational coherence in the ion, can be controlled by tailoring the spectral properties of the attosecond extreme ultraviolet laser pulses that are used to create them.

arXiv:2108.11772•Physical Review Letters•Jan 24, 2022•91 citations
We examine the attosecond electron recollision dissociation of D2+\mathrm{D}_{2}{}^{+}D2​+ recently demonstrated experimentally [H. Niikura et al., Nature (London) 421, 826 (2003)] from a coherent control perspective. In this process, a strong laser field incident on D2{\mathrm{D}}_{2}D2​ ionizes an electron, accelerates the electron in the laser field to eV energies, and then drives the electron to recollide with the parent ion, causing D2+\mathrm{D}_{2}{}^{+}D2​+ dissociation. A number of results are demonstrated. First, a full dimensional strong field approximation model is constructed and shown to be in agreement with the original experiment. This is then used to rigorously demonstrate that the experiment is an example of coherent pump-dump control. Second, extensions to bichromatic coherent control are proposed by considering dissociative recollision of molecules prepared in a coherent superposition of vibrational states. Third, by comparing the results to similar scenarios involving field-free attosecond scattering of independently prepared D2+\mathrm{D}_{2}{}^{+}D2​+ and electron wave packets, recollision dissociation is shown to provide an example of wave-packet coherent control of reactive scattering. Fourth, this analysis makes clear that it is the temporal correlations between the continuum electron and D2+\mathrm{D}_{2}{}^{+}D2​+ wave packet, and not entanglement, that are crucial for the subfemtosecond probing resolution demonstrated in the experiment. This result clarifies some misconceptions regarding the importance of entanglement in the recollision probing of D2+\mathrm{D}_{2}{}^{+}D2​+. Finally, signatures of entanglement between the recollision electron and the atomic fragments, detectable via coincidence measurements, are identified.
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.
The coherent control of scattering processes is considered, with electron impact dissociation of used as an example. The physical mechanism underlying coherently controlled stationary state scattering is exposed by analyzing a control scenario that relies on previously established entanglement requirements between the scattering partners. Specifically, initial state entanglement assures that all collisions in the scattering volume yield the desirable scattering configuration. Scattering is controlled by preparing the particular internal state wave function that leads to the favored collisional configuration in the collision volume. This insight allows coherent control to be extended to the case of time-dependent scattering. Specifically, we identify reactive scattering scenarios using incident wave packets of translational motion where coherent control is operational and initial state entanglement is unnecessary. Both the stationary and time-dependent scenarios incorporate extended coherence features, making them physically distinct. From a theoretical point of view, this work represents a large step forward in the qualitative understanding of coherently controlled reactive scattering. From an experimental viewpoint, it offers an alternative to entanglement-based control schemes. However, both methods present significant challenges to existing experimental technologies.
This thesis investigates quantum dynamics induced in atoms by ultrashort pulses of light. The work is motivated by recent developments in free-electron lasers, which generate ultrashort pulses of intense, coherent light and enable coherent control of quantum dynamics. We develop theoretical models to study the processes of absorption and emission in laser-atom interactions. Additionally, we study photoionisation, which creates an ion and an electron, and the entanglement that can be generated between these particles. Finally, we have investigated how the spontaneous decay of the ion induces entanglement transfer from the ion-electron pair to the electron-photon pair.This thesis compiles seven papers. Paper I investigates the absorption of light from an attosecond pulse by an atom in a prepared coherent superposition of states. We show how the evolution of the phase of the superposition wave packet influences the attosecond transient absorption spectra. Paper II predicts the existence of Mollow-like triplets in the absorption spectra of strongly coupled atoms. We establish the conditions for the pulse envelope under which this triplet pattern can be supported.Paper III studies two-photon Rabi oscillations, establishing which systems can sustain such dynamics. We find that a two-photon Rabi oscillating system can induce giant counter-rotating oscillations in the population dynamics, enabling investigations of physical effects beyond the rotating-wave approximation.Paper IV studies ionisation from an atom strongly coupled by a dichromatic field, where interference between the two frequency components shapes the temporal symmetry of the atomic dynamics, allowing for coherent control of the photoelectron distribution.Paper V considers an experiment performed at a Free-Electron Laser facility where a helium atom is ionised and the resulting ion is subsequently strongly coupled. The photoelectron spectra are theoretically reproduced and the entanglement between the ion and photoelectron is studied. Paper VI investigates how the entanglement in the ion--electron pair, generated via photoionisation followed by strong coupling, can be coherently controlled by harnessing the time symmetry of the pulse. We find that the observable manifestation of the entanglement can be altered in such a way that the electron energy becomes associated with the ionic state, allowing the entanglement to be detected via coincidence measurements. Paper VII investigates how quantum correlations between the ion and the electron can be coherently controlled by sequential strong coupling of the ion. We find that both the build-up of entanglement and its manifestation can be controlled, and we establish a quantitative measure of the amplitude entanglement that explains the dynamics in an intuitive way. Paper VIII studies the process of entanglement transfer induced by the spontaneous decay of the ion. We find that the ion--electron entanglement generated during the ultrashort interaction with the laser field is transferred to the electron--photon system over the much longer timescale of fluorescence.
Summary form only given. Angstrom and attosecond control of free electron wave packets is one of the pinnacles of attosecond science. Orthogonally polarized two-color (OTC) laser fields allow to control the motion of field-ionizing electronic wave packets both in time and space[1]. In OTC pulses time and space are connected and thus an attosecond time scale is established in the polarization plane for both the emitted and the re-colliding wave packets[2,3].In this submission, we report on experiments that use OTC pulses for studying atomic single and double ionization. The three-dimensional momentum vector of electrons and ions created by single and double ionization of neon atoms was measured with the COLTRIMS technique as a function of the sub-cycle shape of the OTC pulses. We introduce a concept similar to attosecond streaking that allows reading sub-cycle timing information from the momentum vector of emitted electrons. The concept is then applied to gaining information about the influence of the long-range Coulomb potential on the trajectories of tunneling electrons.Fig.1 (a) shows the measured momentum distributions of electrons correlated with singly ionized neon in the polarization plane of the OTC field with relative phase Δφ between the two color components. The spectra show that the electron emission direction is sensitive to Δφ. Furthermore, the spectra feature a prominent x-shaped central structure and weaker fine-scale modulations due to wave packet interferences. To compare with simulated spectra with strong field approximation (SFA) and solving two-dimensional time-dependent Schrödinger equation (TDSE) with single active electron approximation, we conclude that Coulomb effect plays important role on the spatial distribution of released electron wave packets. In the conference, we will furthermore demonstrate control over the correlation between the two electrons emitted during double ionization upon electron recollision by tuning the shape of the electric field of the OTC pulses on the sub-cycle scale. The results of these experiments are in agreement with theoretical predictions [4].
The past thirty years witnessed rapid developing of strong field physics that leads to the first generation of attosecond (10−18 s) pulses. The duration of available pulses has recently been reduced to less than 100 as, approaching the Kepler period of a classical electron revolving around the nucleus. For the first time, electron motions inside atoms, molecules and solids can be traced, probed and even steered in real time. It pushed the study on ultrafast dynamic processes into a new frontier, giving birth to attosecond physics. The development of attosecond pulses provides unprecedented coherent ultrashort XUV (extreme ultra-violet) of soft X-ray sources that enable imaging the atomic structure and resolving the related quantum dynamics for matter science. In particular, it allows the probing and monitoring of electron dynamics in the natural time scale of attoseconds with atomic spatial resolution. The generation and applications of attosecond pulses are directly related to the control and manipulation of the sub-cycle electron dynamics. Recent studies on the correlated multielectron dynamics have provided insight into the optical and dynamical properties of matter in the perspectives of time, phase and entanglement. It deepens our understanding on some of the fundamental questions, e.g., how the single or multiple photons are absorbed and how short are the quantum processes such as photoionization, tunneling ionization and charge migration. Although currently attosecond pulses are limited by the flux and pulse duration, the combination of attosecond pulses with intense infrared laser pulses paves new ways of controlling and probing electron dynamics in the domains of energy, time and space that lays the foundation for petahertz optoelectronics and attosecond pulse based transient spectroscopy. In this review, we will first briefly summarize the advancement of strong field and ultrafast physics including the relevant experimental findings, the theoretical explorations, the related technologies and the possible applications. Then we focus on the sub-cycle electron or multielectron dynamics and their manifestation on the ionization and coherent radiation properties. We start with the time behavior of Fano resonance and how it can be probed in time domain. In section 2, the correlated electron dynamics is discussed in term of anti-screening effect and Pauli effect that influence strong field ionization and high harmonic generation processes. In section 3, the coherent emission with frequency from terahertz to soft XUV and their joint measurement are discussed by emphasizing the generation mechanism of terahertz wave in two-color laser pulses. The developed high-harmonic and terahertz wave spectroscopy (HATS) is shown capable of imaging the molecular structure and dynamics. In section 4, the time-resolving of electron and hole dynamics and their coherence is proposed based on attosecond transient absorption technique. The coherence of ionization and the correlated electron dynamics is hinted crucial for electron-hole interaction. The topics are very limited and mainly selected from the perspectives of our group.
Entanglement is one of the most intriguing aspects of quantum mechanics and lies at the heart of the ongoing second quantum revolution, where it is a resource that is used in quantum key distribution, quantum computing, and quantum teleportation. We report experiments demonstrating the crucial role that entanglement plays in pump-probe experiments involving ionization, which are a hallmark of the novel research field of attosecond science. We demonstrate that the degree of entanglement in a bipartite ion + photoelectron system, and, as a consequence, the degree of vibrational coherence in the ion, can be controlled by tailoring the spectral properties of the attosecond extreme ultraviolet laser pulses that are used to create them.