Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Distortion of atomic states by time-dependent electric fields

Predrag Krstić, Yukap Hahn

Published Dec 1, 1993• 21 citations
Publisher

Abstract

A class of approximate solutions of the Schr\"odinger equation for an atom in a time-dependent electric field that scales with the applied field F as FF(t)dt is derived and their bounds of validity are carefully examined. The class covers a wide region of applicable electric fields and its time constants. An extensive comparison of these solutions with the results of numerical calculations on a truncated basis of up to 465 hydrogenic states shows surprising agreement. One of these solutions is found to be very effective in field dressing of high Rydberg states. The resulting field dressing is proposed for the description of the plasma field effects on atomic reaction rates, but its range of applicability can be extended to the other atomic problems that involve time-dependent electric fields.

DOI
10.1103/physreva.48.4515

Related papers

Distortion of atomic states by time-dependent electric fields. II. Coupling to the continuum

Predrag Krstić, Yukap Hahn

The previously derived approximation for an atom in time-dependent electric fields [P. Krsti\ifmmode \acute{c}\else \'{c}\fi{} and Y. Hahn, Phys. Rev. A 48, 4515 (1993)] is improved for electric pulses of both short and long duration. The transitions that involve a distorted continuum are studied in detail, and the phenomenon of momentum coherence is shown to greatly enhance the transition amplitudes. A detailed comparison with the recent experiment of Jones, You, and Bucksbaum [Phys. Rev. Lett. 70, 1236 (1993)] is presented, where a half-cycle high-power laser pulse was used to ionize Rydberg atoms.

Physical Review A•Dec 1, 1994•48 citations

Collisions of Rydberg atoms in an electric field: Calculations using hydrogenic wave functions in parabolic coordinates

A. P. Hickman

The theory of collisions of Rydberg atoms with rare-gas atoms is generalized to include the effects of an applied static electric field. Two effects occur. First, the field causes the states to split, and the increased energy separations lead to a decrease in the inelastic cross sections. Second, there is a change in the form of the wave functions, because the various Stark states in the field have electron charge distributions that may be localized in very different regions of space. The present work focuses on this second effect. With the description of the initial and final Stark states of the Rydberg atom by the proper electronic wave functions obtained in parabolic coordinates, cross sections are obtained for a variety of specific transitions of Rydberg atoms ($n=10, 15, \mathrm{and} 20$) caused by collisions. The calculations are strictly valid for hydrogen, but exhibit general features that are expected to apply to other Rydberg atoms as well. The results show a dramatic effect on the cross section for particular transitions depending on the degree of overlap of the initial and final charge distributions. In addition, it is observed that transitions are favored that involve small changes in the azimuthal quantum number $m$. The origin of this tendency is discussed.

Physical Review A•Jul 1, 1983•18 citations

Atoms in strong, oscillating electric fields: momentum-space solutions of the time-dependent, three-dimensional Schrödinger equation

Lee A. Collins, A. L. Merts

We have developed a procedure for solving the three-dimensional, time-dependent Schrödinger equation by expanding the total system wave function in a Volkov basis and by propagating the resulting first-order differential equations in time. We discuss applications to several model systems representing an atom in an intense, oscillating electric field.

Journal of the Optical Society of America B•Apr 1, 1990•17 citations

The temporal picture for Bloch electron dynamics in homogeneous electric fields

G. J. Iafrate, V. N. Sokolov

The transient picture for a Bloch electron accelerating in an arbitrarily time-dependent homogeneous electric field is developed. The temporal sequence for the analysis includes the instant after electron injection, followed by the time required for a small change in electron wavenumber away from initial injection, leading to the final time evolution over many Bloch periods. The time-dependent behavior is studied using the properties of the Schrödinger equation. The electric field is described through the vector potential gauge, and the instantaneous eigenstates of the Bloch, electric-field-dependent Hamiltonian are used as basis states in describing the Bloch dynamics in the electric field. For each temporal sequence considered, the solution to the Schrödinger equation is established and comparatively discussed. The expectation value of the momentum is obtained for the special case of first order in a constant electric field; the resulting velocity derived is a field-dependent generalization of the natural Zitterbewegung-like behavior discussed in the recent literature. The early-time and long-time limits of the momentum expectation value and its time derivative demonstrate that the resistance to Bloch acceleration after initial band injection varies from real mass to effective mass dynamics as the electron accelerates through the band under the influence of electric field. This changing inertia from early injection of a free-mass electron is the result of the {\it real mass} electron {\it dressing-up} into the states of the crystal to become {\it an effective mass} electron. The ramifications of this temporal {\it dressing} behavior are discussed in considering the general dynamics of Bloch electrons subject to ultrastrong electric fields.

cond-mat.mes-hallCross-listedarXiv:2602.23965•Mar 2, 2026

Time-Dependent Logarithmic Perturbation Theory for Quantum Dynamics: Formulation and Applications

Juan Carlos del Valle, Paul Bergold, Karolina Kropielnicka

We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schrödinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant. The resulting hierarchy of equations defining the perturbative corrections is governed by a gauge-rotated Hamiltonian of the unperturbed system and leads to closed-integral expressions for the time-dependent corrections based on Duhamel's formula. This closed-integral structure of corrections is a hallmark of time-independent logarithmic perturbation theory and is preserved in the present extension. This structure, in particular, provides a computable expression for the instantaneous energy shift. Furthermore, dynamic energy shifts arise naturally within this framework in the form of time-averaged expectation values of pseudopotentials and can be related, for example, to AC Stark shifts and electric polarizabilities. As an illustration, we apply the method to the harmonic oscillator and the hydrogen atom, both driven by a time-dependent laser field. The harmonic oscillator provides a proof of principle for which the exact solution is recovered, while the hydrogen atom illustrates the method applied to atomic systems. Supported by numerical simulations, we demonstrate the applicability to obtain relevant physical observables with high accuracy. The present approach offers a promising alternative for analytical studies of time-dependent multi-photon processes in the perturbative regime.

quant-pharXiv:2604.14812•Apr 17, 2026

On the electrostatic deceleration of argon atoms in high Rydberg states by time-dependent inhomogeneous electric fields

E. Vliegen, Frédéric Merkt

Argon atoms in a pulsed supersonic expansion are prepared in selected Stark components of Rydberg states with effective principal quantum number in the range n * = 15–25. When traversing regions of inhomogeneous electric fields, these atoms get accelerated or decelerated depending on whether the Stark states are low- or high-field seeking states. Using a compact electrode design, which enables the application of highly inhomogeneous and time-dependent electric fields, the Rydberg atoms experience kinetic energy changes of up to 1.2 × 10 −21 J (i.e. 60 cm −1 in spectroscopic units) in a single acceleration/deceleration stage of 3 mm length. The resulting differences in the velocities of the low- and high-field seeking states are large enough that the corresponding distributions of times of flight to the Rydberg particle detector are fully separated. As a result, efficient spectral searches of the Rydberg states best suited for acceleration/deceleration experiments are possible. Numerical simulations of the particle trajectories are used to analyse the time-of-flight distributions and to optimize the time dependence of the inhomogeneous electric fields. The decay of the Rydberg states by fluorescence, collisions and transitions induced by black-body radiation takes place on a timescale long enough not to interfere significantly with the deceleration during the first ∼5 µs.

Journal of Physics B Atomic Molecular and Optical Physics•May 20, 2005•36 citations
A class of approximate solutions of the Schr"odinger equation for an atom in a time-dependent electric field that scales with the applied field F as FF(t)dt is derived and their bounds of validity are carefully examined. The class covers a wide region of applicable electric fields and its time constants. An extensive comparison of these solutions with the results of numerical calculations on a truncated basis of up to 465 hydrogenic states shows surprising agreement. One of these solutions is found to be very effective in field dressing of high Rydberg states. The resulting field dressing is proposed for the description of the plasma field effects on atomic reaction rates, but its range of applicability can be extended to the other atomic problems that involve time-dependent electric fields.
The previously derived approximation for an atom in time-dependent electric fields [P. Krsti\ifmmode \acute{c}\else \'{c}\fi{} and Y. Hahn, Phys. Rev. A 48, 4515 (1993)] is improved for electric pulses of both short and long duration. The transitions that involve a distorted continuum are studied in detail, and the phenomenon of momentum coherence is shown to greatly enhance the transition amplitudes. A detailed comparison with the recent experiment of Jones, You, and Bucksbaum [Phys. Rev. Lett. 70, 1236 (1993)] is presented, where a half-cycle high-power laser pulse was used to ionize Rydberg atoms.
The theory of collisions of Rydberg atoms with rare-gas atoms is generalized to include the effects of an applied static electric field. Two effects occur. First, the field causes the states to split, and the increased energy separations lead to a decrease in the inelastic cross sections. Second, there is a change in the form of the wave functions, because the various Stark states in the field have electron charge distributions that may be localized in very different regions of space. The present work focuses on this second effect. With the description of the initial and final Stark states of the Rydberg atom by the proper electronic wave functions obtained in parabolic coordinates, cross sections are obtained for a variety of specific transitions of Rydberg atoms (n=10,15,and20n=10, 15, \mathrm{and} 20n=10,15,and20) caused by collisions. The calculations are strictly valid for hydrogen, but exhibit general features that are expected to apply to other Rydberg atoms as well. The results show a dramatic effect on the cross section for particular transitions depending on the degree of overlap of the initial and final charge distributions. In addition, it is observed that transitions are favored that involve small changes in the azimuthal quantum number mmm. The origin of this tendency is discussed.
The transient picture for a Bloch electron accelerating in an arbitrarily time-dependent homogeneous electric field is developed. The temporal sequence for the analysis includes the instant after electron injection, followed by the time required for a small change in electron wavenumber away from initial injection, leading to the final time evolution over many Bloch periods. The time-dependent behavior is studied using the properties of the Schrödinger equation. The electric field is described through the vector potential gauge, and the instantaneous eigenstates of the Bloch, electric-field-dependent Hamiltonian are used as basis states in describing the Bloch dynamics in the electric field. For each temporal sequence considered, the solution to the Schrödinger equation is established and comparatively discussed. The expectation value of the momentum is obtained for the special case of first order in a constant electric field; the resulting velocity derived is a field-dependent generalization of the natural Zitterbewegung-like behavior discussed in the recent literature. The early-time and long-time limits of the momentum expectation value and its time derivative demonstrate that the resistance to Bloch acceleration after initial band injection varies from real mass to effective mass dynamics as the electron accelerates through the band under the influence of electric field. This changing inertia from early injection of a free-mass electron is the result of the {\it real mass} electron {\it dressing-up} into the states of the crystal to become {\it an effective mass} electron. The ramifications of this temporal {\it dressing} behavior are discussed in considering the general dynamics of Bloch electrons subject to ultrastrong electric fields.
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schrödinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant. The resulting hierarchy of equations defining the perturbative corrections is governed by a gauge-rotated Hamiltonian of the unperturbed system and leads to closed-integral expressions for the time-dependent corrections based on Duhamel's formula. This closed-integral structure of corrections is a hallmark of time-independent logarithmic perturbation theory and is preserved in the present extension. This structure, in particular, provides a computable expression for the instantaneous energy shift. Furthermore, dynamic energy shifts arise naturally within this framework in the form of time-averaged expectation values of pseudopotentials and can be related, for example, to AC Stark shifts and electric polarizabilities. As an illustration, we apply the method to the harmonic oscillator and the hydrogen atom, both driven by a time-dependent laser field. The harmonic oscillator provides a proof of principle for which the exact solution is recovered, while the hydrogen atom illustrates the method applied to atomic systems. Supported by numerical simulations, we demonstrate the applicability to obtain relevant physical observables with high accuracy. The present approach offers a promising alternative for analytical studies of time-dependent multi-photon processes in the perturbative regime.
Argon atoms in a pulsed supersonic expansion are prepared in selected Stark components of Rydberg states with effective principal quantum number in the range n * = 15–25. When traversing regions of inhomogeneous electric fields, these atoms get accelerated or decelerated depending on whether the Stark states are low- or high-field seeking states. Using a compact electrode design, which enables the application of highly inhomogeneous and time-dependent electric fields, the Rydberg atoms experience kinetic energy changes of up to 1.2 × 10 −21 J (i.e. 60 cm −1 in spectroscopic units) in a single acceleration/deceleration stage of 3 mm length. The resulting differences in the velocities of the low- and high-field seeking states are large enough that the corresponding distributions of times of flight to the Rydberg particle detector are fully separated. As a result, efficient spectral searches of the Rydberg states best suited for acceleration/deceleration experiments are possible. Numerical simulations of the particle trajectories are used to analyse the time-of-flight distributions and to optimize the time dependence of the inhomogeneous electric fields. The decay of the Rydberg states by fluorescence, collisions and transitions induced by black-body radiation takes place on a timescale long enough not to interfere significantly with the deceleration during the first ∼5 µs.