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AIP conference proceedings

Beyond ATI: Strong Field Quantum Control

P. H. Bucksbaum, David J. Wineland, Carl Wieman, Stephen J. Smith

Published Jan 1, 1994• 8 citations
Publisher

Abstract

Above‐threshold ionization (ATI) is the ionization of atoms by more than the minimum number photons necessary to overcome the Coulomb binding energy. Although ATI is contrary to the predictions of minimum‐order perturbation theory, it is the dominant mode of ionization whenever the light field becomes comparable to the static fields in the atom. We have learned a great deal by studying ATI over the past several years. We now know that by controlling these high intensity optical fields, we can control atomic and molecular processes such as ionization and dissociation. We can even engineer wave‐functions.

DOI
10.1063/1.2946021

Related papers

Multiphoton absorption above ionization threshold by atoms in strong laser fields

Zhifang Deng, Joseph H. Eberly

We present an atomic model to study above-threshold ionization (ATI). We show that when the laser field is sufficiently intense the usual perturbation theory is not valid. We solve the model dynamics exactly, and several interesting quantities, including the initial-state decay rate and photoelectron spectrum, are calculated. These quantities are related to recent ATI experiments, and qualitatively they agree with these experiments. We specify the strong-field condition for continuum–continuum transitions and explore its physical meaning. Finally some comments on perturbation theory are made.

Journal of the Optical Society of America B•Mar 1, 1985•143 citations

Phase and intensity control of integral and differential above-threshold ionization rates

Ricardo A. Blank, Moshe Shapiro

A theory of coherent control of above-threshold ionization (ATI) of hydrogen using light fields composed of a fundamental frequency and its third harmonic is developed. Phase control and intensity control over integral and differential quantities is demonstrated. Modulation of the first ATI kinetic-energy peak height by more than 70%, variation in the ratio of the first two peaks of up to a factor of 4, and separation in the alignment of the first two ATI peaks by as much as \ensuremath{\sim}50\ifmmode^\circ\else\textdegree\fi{}, as a function of the relative phase between the two fields, are demonstrated. Intensity control, in which both partial and total integral ATI rates attain a local maximum at a specific combination of light intensities, is predicted to occur.

Physical Review A•Nov 1, 1995•25 citations

Microscopic analysis of above-threshold ionization driven by squeezed light

Javier Rivera-Dean, Philipp Stammer, Carla Figueira de Morisson Faria +1 more

Above-threshold ionization (ATI) is a strong-field-driven process where electrons absorb more photons than required for ionization. While ATI dynamics and outputs are well-understood when driven by classical, perfectly coherent light, the recent development of nonclassical light sources for strong-field phenomena has spurred interest in their effect on the involved electron dynamics. In this work, we present a microscopic quantum optical theory describing ATI under the influence of strong squeezed light. We observe that squeezed light significantly enhances the coupling between light and matter, making their mutual backaction more important than under classical driving. This backaction profoundly impacts the electronic ionization times, as well as the nonclassical properties of the joint electron-light state. This results in pronounced entanglement features, both immediately after ionization and at later times. These entanglement features are reflected in the properties of the quantum optical state of the driving field, revealing notable non-Gaussian features that depend on both the amount of squeezing and the number of ionization events occurring during the interaction.

arXiv:2508.01621•Physical Review A•Oct 28, 2025•7 citations

Quantum Effects in Strong Field Physics

Boroumand, Neda

When matter is exposed to strong fields, electrons are ionized and a number of processes such as high harmonic generation (HHG), above threshold ionization (ATI), non-sequential ionization happen. These processes are usually investigated semiclassically, i.e. matter is treated by quantum mechanics, and radiation is treated classically. In particular HHG which is the generation of ultrashort coherent extreme ultraviolet (XUV) pulses, has enabled a wealth of novel ultrashort spectroscopic methods in atomic, molecular, and condensed matter physics. Further, ionization has applications in micro-machining. Strong field physics continues to have numerous open questions. As an illustration, the mechanisms underlying dominant HHG pathways in solids remain insufficiently understood. It is not clear which mechanism dominates HHG in various materials. Possible pathways are the interband and intraband contributions. Furthermore, many of these processes in strong field physics have been described by single active electron (SAE) approximation. This approach relies on the assumption that the interaction between a single electron and the intense laser field dominates all other interactions. However, this is clearly not the case especially in solids where interactions with the lattice and other electrons can be important. In addition, quantum optical aspects of strong field physics have generated increasing interest, yet they remain partially explored. This chapter involves treating electromagnetic fields using the formalism of second quantization. Quantum optical properties, such as squeezing, entanglement and the negativity of the Wigner function, are of fundamental importance for the field of quantum information and quantum computation. The central theme of my thesis is the development of quantum optical and statistical theoretical frameworks for describing intense laser field processes such as ionization and HHG in atomic and molecular gases and in solids. The second chapter focuses on gaining a detailed understanding of the mathematical steps involved in the Keldysh theory of ionization to establish a solid theoretical foundation. Through this analysis we identified an additional factor of two compared to Keldysh’s original derivation of atomic ionization rates. The third chapter addresses the inadequately understood mechanisms that govern dominant high harmonic generation (HHG) pathways in solids. One approach to clarify these mechanisms involves introducing real (resonant) and virtual processes. We developed the strong field adiabatic following (SFAF) formalism which is based on Dyson expansion using the von-Neumann equation of density matrix. Using SFAF a diagnostic method is obtained to separate virtual and resonant channels. Through this separation, and by comparing with experimental results, we identified the need to incorporate many-body effects. The fourth chapter explores the fact that a solid is a complex many body system in which the SAE approximation is very crude. The electron interacts with holes, other electrons, collective excitations such as plasmons, and phonons. Our work is based on the idea that all theses effects can be treated as a quantum statistical heat bath of bosonic harmonic oscillators. We apply this to our SFAF formalism. In the ionization case, this work has settled a long standing issue which is the fact that simple phenomenological approaches such as the relaxation time approximation 𝑇2 result in nonphysical enhancement of ionization. In chapter five, we have investigated ways to transfer quantum optical properties on the otherwise classical high harmonic radiation. The goal is to use HHG to scale quantum sources to smaller wavelengths. Quantum properties can be imprinted by perturbing HHG with a quantum field, such as bright squeezed vacuum (BSV). In this chapter, the theory of quantum sideband high harmonic generation (QSHHG) in atoms and solids is derived to find ways by which to transfer quantum properties from the perturbative BSV to the harmonic sideband. The theoretical framework is a quantum generalization of the semi-classical Lewenstein model of HHG. It gives closed-form solutions for the HHG and QSHHG wavefunctions. Knowing the wavefunction, we can identify the quantum properties of QSHHG. The additional photons absorbed and emitted from the quantum perturbation, here BSV, create entanglement between individual harmonic sidebands and between the harmonic sidebands and the BSV. We show how this entanglement can be used to create a variety of non-classical states commonly used in quantum information science, such as high-purity single-photon states, Schrödinger cat states, and photon-added squeezed vacuum states. Some of these non-Gaussian states with negative Wigner functions have been shown to provide a quantum computational advantage over their Gaussian counterparts. Additionally, they play a significant role in quantum metrology, enhancing precision measurements beyond classical limits. This chapter has opened a path to quantum engineering of HHG.

•Nov 25, 2025•0 citations

Phase Dependence of Intense Field Ionization: A Study Using Two Colors

Douglass W. Schumacher, Frederick Weihe, Harm Geert Muller +1 more

We present the first measurement of the ionization rate from above-threshold ionization (ATI) in an optical field whose phase dependence is known and controllable. Our method uses a harmonic two-color light field with a calibrated phase difference between the $1\ensuremath{\omega}$ and $2\ensuremath{\omega}$ fields. Our measurements confirm many of the predictions of recent semiclassical theories, but show an important discrepancy: An asymmetry in the ATI rates relative to the sign of the two-color phase difference supports recently suggested modifications to the models to include electron-core rescattering during ionization.

Physical Review Letters•Sep 5, 1994•197 citations

Time delays in above-threshold ionization

Stefan Nagele, S. D. López, D. G. Arbó +1 more

We theoretically analyze time-resolved above-threshold ionization as probed by an interferometric measurement technique. We investigate the time delays in the ATI process as a function of the number of involved photons and the intensity of the ionizing UV field and identify IR-probe field induced contributions to the time shifts.

Journal of Physics Conference Series•Sep 7, 2015•0 citations
Above‐threshold ionization (ATI) is the ionization of atoms by more than the minimum number photons necessary to overcome the Coulomb binding energy. Although ATI is contrary to the predictions of minimum‐order perturbation theory, it is the dominant mode of ionization whenever the light field becomes comparable to the static fields in the atom. We have learned a great deal by studying ATI over the past several years. We now know that by controlling these high intensity optical fields, we can control atomic and molecular processes such as ionization and dissociation. We can even engineer wave‐functions.
We present an atomic model to study above-threshold ionization (ATI). We show that when the laser field is sufficiently intense the usual perturbation theory is not valid. We solve the model dynamics exactly, and several interesting quantities, including the initial-state decay rate and photoelectron spectrum, are calculated. These quantities are related to recent ATI experiments, and qualitatively they agree with these experiments. We specify the strong-field condition for continuum–continuum transitions and explore its physical meaning. Finally some comments on perturbation theory are made.
A theory of coherent control of above-threshold ionization (ATI) of hydrogen using light fields composed of a fundamental frequency and its third harmonic is developed. Phase control and intensity control over integral and differential quantities is demonstrated. Modulation of the first ATI kinetic-energy peak height by more than 70%, variation in the ratio of the first two peaks of up to a factor of 4, and separation in the alignment of the first two ATI peaks by as much as \ensuremath{\sim}50\ifmmode^\circ\else\textdegree\fi{}, as a function of the relative phase between the two fields, are demonstrated. Intensity control, in which both partial and total integral ATI rates attain a local maximum at a specific combination of light intensities, is predicted to occur.
Above-threshold ionization (ATI) is a strong-field-driven process where electrons absorb more photons than required for ionization. While ATI dynamics and outputs are well-understood when driven by classical, perfectly coherent light, the recent development of nonclassical light sources for strong-field phenomena has spurred interest in their effect on the involved electron dynamics. In this work, we present a microscopic quantum optical theory describing ATI under the influence of strong squeezed light. We observe that squeezed light significantly enhances the coupling between light and matter, making their mutual backaction more important than under classical driving. This backaction profoundly impacts the electronic ionization times, as well as the nonclassical properties of the joint electron-light state. This results in pronounced entanglement features, both immediately after ionization and at later times. These entanglement features are reflected in the properties of the quantum optical state of the driving field, revealing notable non-Gaussian features that depend on both the amount of squeezing and the number of ionization events occurring during the interaction.
When matter is exposed to strong fields, electrons are ionized and a number of processes such as high harmonic generation (HHG), above threshold ionization (ATI), non-sequential ionization happen. These processes are usually investigated semiclassically, i.e. matter is treated by quantum mechanics, and radiation is treated classically. In particular HHG which is the generation of ultrashort coherent extreme ultraviolet (XUV) pulses, has enabled a wealth of novel ultrashort spectroscopic methods in atomic, molecular, and condensed matter physics. Further, ionization has applications in micro-machining. Strong field physics continues to have numerous open questions. As an illustration, the mechanisms underlying dominant HHG pathways in solids remain insufficiently understood. It is not clear which mechanism dominates HHG in various materials. Possible pathways are the interband and intraband contributions. Furthermore, many of these processes in strong field physics have been described by single active electron (SAE) approximation. This approach relies on the assumption that the interaction between a single electron and the intense laser field dominates all other interactions. However, this is clearly not the case especially in solids where interactions with the lattice and other electrons can be important. In addition, quantum optical aspects of strong field physics have generated increasing interest, yet they remain partially explored. This chapter involves treating electromagnetic fields using the formalism of second quantization. Quantum optical properties, such as squeezing, entanglement and the negativity of the Wigner function, are of fundamental importance for the field of quantum information and quantum computation. The central theme of my thesis is the development of quantum optical and statistical theoretical frameworks for describing intense laser field processes such as ionization and HHG in atomic and molecular gases and in solids. The second chapter focuses on gaining a detailed understanding of the mathematical steps involved in the Keldysh theory of ionization to establish a solid theoretical foundation. Through this analysis we identified an additional factor of two compared to Keldysh’s original derivation of atomic ionization rates. The third chapter addresses the inadequately understood mechanisms that govern dominant high harmonic generation (HHG) pathways in solids. One approach to clarify these mechanisms involves introducing real (resonant) and virtual processes. We developed the strong field adiabatic following (SFAF) formalism which is based on Dyson expansion using the von-Neumann equation of density matrix. Using SFAF a diagnostic method is obtained to separate virtual and resonant channels. Through this separation, and by comparing with experimental results, we identified the need to incorporate many-body effects. The fourth chapter explores the fact that a solid is a complex many body system in which the SAE approximation is very crude. The electron interacts with holes, other electrons, collective excitations such as plasmons, and phonons. Our work is based on the idea that all theses effects can be treated as a quantum statistical heat bath of bosonic harmonic oscillators. We apply this to our SFAF formalism. In the ionization case, this work has settled a long standing issue which is the fact that simple phenomenological approaches such as the relaxation time approximation 𝑇2 result in nonphysical enhancement of ionization. In chapter five, we have investigated ways to transfer quantum optical properties on the otherwise classical high harmonic radiation. The goal is to use HHG to scale quantum sources to smaller wavelengths. Quantum properties can be imprinted by perturbing HHG with a quantum field, such as bright squeezed vacuum (BSV). In this chapter, the theory of quantum sideband high harmonic generation (QSHHG) in atoms and solids is derived to find ways by which to transfer quantum properties from the perturbative BSV to the harmonic sideband. The theoretical framework is a quantum generalization of the semi-classical Lewenstein model of HHG. It gives closed-form solutions for the HHG and QSHHG wavefunctions. Knowing the wavefunction, we can identify the quantum properties of QSHHG. The additional photons absorbed and emitted from the quantum perturbation, here BSV, create entanglement between individual harmonic sidebands and between the harmonic sidebands and the BSV. We show how this entanglement can be used to create a variety of non-classical states commonly used in quantum information science, such as high-purity single-photon states, Schrödinger cat states, and photon-added squeezed vacuum states. Some of these non-Gaussian states with negative Wigner functions have been shown to provide a quantum computational advantage over their Gaussian counterparts. Additionally, they play a significant role in quantum metrology, enhancing precision measurements beyond classical limits. This chapter has opened a path to quantum engineering of HHG.
We present the first measurement of the ionization rate from above-threshold ionization (ATI) in an optical field whose phase dependence is known and controllable. Our method uses a harmonic two-color light field with a calibrated phase difference between the $1\ensuremath{\omega}$ and $2\ensuremath{\omega}$ fields. Our measurements confirm many of the predictions of recent semiclassical theories, but show an important discrepancy: An asymmetry in the ATI rates relative to the sign of the two-color phase difference supports recently suggested modifications to the models to include electron-core rescattering during ionization.