© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

The Journal of Chemical Physics

Rydberg state decay in inhomogeneous electric fields

T. P. Softley, R. J. Rednall

Published May 8, 2000• 7 citations

Abstract

An extension of the model of Merkt and Zare [J. Chem. Phys. 101, 3495 (1994)] is presented to describe the effects of static inhomogeneous electric fields, which arise experimentally from combinations of applied (or stray) homogeneous fields and the presence of charged particles, on Rydberg states of atoms and molecules. The effect of an arbitrary number of charged particles is included and the effects of nonzero quantum defects are investigated. A quantization axis rotation procedure is defined, allowing clear distinction between homogeneous and inhomogeneous field effects. Calculations are reported of the time-dependent decay of a coherent population of eigenstates for n=20, 33, and 50, involving diagonalization of the full n2×n2 matrix. Calculations are also carried out for n=100 by pre-diagonalization of the full homogeneous field perturbation followed by a restricted basis set diagonalization for the inhomogeneous part of the perturbation. The inclusion of nonzero quantum defects has a substantial impact on the ml mixing, confining significant mixing to a narrow range of radial and angular positions of the ion. An applied homogeneous field of order the Inglis-Teller field is required in combination with the field due to the ions. The dynamics are very different according to whether np or nf series carry the transition probability. For np-state population, the maximum stabilization is achieved at ion-Rydberg distances of around 5n2a0, with the ion almost perpendicular to the applied homogeneous field. For an initial nf population the ion perturbation may have a destabilizing effect at sufficiently small homogeneous field (⩽0.1FIT). Significant effects of laser polarization on the stability are reported. Calculations for a realistic pseudo-random distribution of ions and Rydbergs suggest that ml mixing by ions will never reach the complete mixing limit, but that at least an order of magnitude stabilization is achievable under a restricted range of conditions.

DOI: 10.1063/1.481423

Related papers

Control of atomic and molecular motion via the Stark effect in Rydberg states

A L Goodgame, T. P. Softley

A novel theoretical study of the control of translational motion of atomic and molecular Rydberg states in inhomogeneous static electric fields is presented. Simulations have been carried out demonstrating that, under realistic conditions, the deflection and focusing of Rydberg atoms and molecules should be achievable. Advantage is taken of the high susceptibility of the Rydberg states to external electric fields, allowing the use of much smaller fields than would be necessary for ground state neutrals. The simulations presented are for trajectories of Rydberg states with n = 18-20 in the fields of an electric dipole, quadrupole and hexapole. A deflection of 7 mm is predicted for n = 18 Rydberg states travelling parallel to the dipole after 100 µs time of flight. In the hexapole n = 20 Rydberg states are refocused to a spot size of the order of the laser beam waist (10 µm) after 20 µs. It is demonstrated that the hexapole can also act as a cylindrical lens if its axis is perpendicular to the Rydberg beam direction. Spontaneous emission and black-body decay rates are also calculated, and their variation with the applied field is investigated. The potential applications of this work might include the use of focusing and deflection for controlled low-energy collisions of Rydberg molecules with surfaces.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 7, 1999•17 citations

Atomic Rydberg-state excitation in strong spatially inhomogeneous fields

Shilin Hu, xiaopeng Yi, Li Shuai Guo +2 more

We investigated the Rydberg-state excitation process of a hydrogen atom subjected to spatially homogeneous and inhomogeneous laser fields by means of ab initio calculations. It is found that, comparing with atoms exposed to spatially homogeneous laser fields, the excitation probability decreases and the electron tends to occupy the states with lower principal quantum numbers and angular quantum numbers for atoms in spatially inhomogeneous laser pulses. Furthermore, calculations of a quantum model without taking into account ionization of the electron after it is coherently captured by the Rydberg state are inconsistent with the above-stated findings by ab initio calculations. Analysis indicates that the aforementioned intriguing features can be attributed to the enhanced ionization of the Rydberg states by inhomogeneous laser fields since the distributions of Rydberg states of high principal quantum numbers and angular quantum numbers locate far away from the core where the inhomogeneous electric fields become significant.

Physical Review A•Mar 7, 2023•11 citations

Confinement of High- and Low-Field-Seeking Rydberg Atoms Using Time-Varying Inhomogeneous Electric Fields

Adam Deller, S. D. Hogan

Helium atoms in high- and low-field-seeking Rydberg states with linear and quadratic Stark shifts have been confined in two dimensions and guided over a distance of 150 mm using time-varying inhomogeneous electric fields. This was achieved with an electrode structure composed of four parallel cylindrical rods to which voltages were applied to form oscillating and rotating saddle-point fields. These two modes of operation result in time-averaged pseudopotentials that confine samples in high- and low-field-seeking states about the axis of the device. The experimental data have been compared to the results of numerical particle trajectory calculations that include effects of blackbody radiation and electric field ionization. The results highlight important contributions from single-photon blackbody-induced transitions that cause large changes in the principal quantum number of the Rydberg atoms.

arXiv:1902.09392•Physical Review Letters•Feb 8, 2019•8 citations

Deflection and deceleration of hydrogen Rydberg molecules in inhomogeneous electric fields

Yoshihiro Yamakita, Simon R. Procter, A L Goodgame +2 more

Hydrogen molecules are excited in a molecular beam to Rydberg states around n=17-18 and are exposed to the inhomogeneous electric field of an electric dipole. The large dipole moment produced in the selected Stark eigenstates leads to strong forces on the H2 molecules in the inhomogeneous electric field. The trajectories of the molecules are monitored using ion-imaging and time of flight measurements. With the dipole rods mounted parallel to the beam direction, the high-field-seeking and low-field-seeking Stark states are deflected towards and away from the dipole, respectively. The magnitude of the deflection is measured as a function of the parabolic quantum number k and of the duration of the applied field. It is also shown that a large deflection is observed when populating the (17d2)1 state at zero field and switching the dipole field on after a delay. With the dipole mounted perpendicular to the beam direction, the molecules are either accelerated or decelerated as they move towards the dipole. The Rydberg states are found to survive for over 100 micros after the dipole field is switched off before being ionized at the detector and the time of flight is measured. A greater percentage change in kinetic energy is achieved by initial seeding of the beam in helium or neon followed by inhomogeneous field deceleration/acceleration. Molecular dynamics trajectory simulations are presented highlighting the extent to which the trajectories can be predicted based on the known Stark map. The spectroscopy of the populated states is discussed in detail and it is established that the N+=2, J=1, MJ=0 states populated here have a special stability with respect to decay by predissociation.

The Journal of Chemical Physics•Jul 6, 2004•87 citations

Electrostatic Trapping of N2 Molecules in High Rydberg States

M. H. Rayment, S. D. Hogan

N_{2} molecules traveling in pulsed supersonic beams have been excited from their X ^{1}Σ_{g}^{+} ground electronic state to long-lived Rydberg states with principal quantum numbers between 39 and 48 using a resonance-enhanced two-color three-photon excitation scheme. The Rydberg states populated had static electric dipole moments exceeding 5000 D which allowed deceleration of the molecules to rest in the laboratory-fixed frame of reference and three-dimensional trapping using inhomogeneous electric fields. The trapped molecules were confined for up to 10 ms, with effective trap decay time constants increasing with principal quantum number, and ranging from 450 to 700 μs. These observations, and comparison with the results of similar measurements with He atoms, indicate that the decay dynamics of the trapped Rydberg N_{2} molecules are dominated by spontaneous emission and do not exhibit significant contributions from effects of intramolecular interactions that lead to non-radiative decay.

arXiv:2403.12315•Physical Review Letters•Mar 12, 2024•4 citations

Properties of Rydberg autoionizing states in electric fields

V. L. Jacobs, J. Davis

The linear-Stark-effect approximation is employed to investigate the effects of electric fields on autoionizing doubly excited atomic states corresponding to relatively large values of the outer-electron principal quantum number $n$. By assuming that a statistical distribution of the inner-electron magnetic sublevels has been established, simple expressions are derived which relate the autoionization and radiative transition rates in the presence of an electric field to the respective field-free rates. It is pointed out that the multiphoton laser excitation of the doubly excited states can give rise to a nonstatistical distribution of the magnetic sublevels and to complex interference terms involving transition amplitudes associated with different values of the outer-electron angular momentum quantum number $l$. The results of calculations are presented for the autoionization and radiative-transition rates which play the most important role in the dielectronic recombination of the Li-like ${\mathrm{Fe}}^{+23}$ ion through the $2p\ensuremath{\rightarrow}2s$ inner-electron transition, where the contributions from large-$n$ values are particularly important. In these calculations it is assumed that the magnetic sublevels are statistically populated and only the simple expressions for the transition rates are employed. The effects of the electric field on the dominant (inner-electron) radiative decay rate can be neglected, but the electric field mixing of the outer-electron $l$ substates substantially increases the autoionization rates from the higher-$l$ sublevels.

Physical Review A•Feb 1, 1979•49 citations

An extension of the model of Merkt and Zare [J. Chem. Phys. 101, 3495 (1994)] is presented to describe the effects of static inhomogeneous electric fields, which arise experimentally from combinations of applied (or stray) homogeneous fields and the presence of charged particles, on Rydberg states of atoms and molecules. The effect of an arbitrary number of charged particles is included and the effects of nonzero quantum defects are investigated. A quantization axis rotation procedure is defined, allowing clear distinction between homogeneous and inhomogeneous field effects. Calculations are reported of the time-dependent decay of a coherent population of eigenstates for n=20, 33, and 50, involving diagonalization of the full n2×n2 matrix. Calculations are also carried out for n=100 by pre-diagonalization of the full homogeneous field perturbation followed by a restricted basis set diagonalization for the inhomogeneous part of the perturbation. The inclusion of nonzero quantum defects has a substantial impact on the ml mixing, confining significant mixing to a narrow range of radial and angular positions of the ion. An applied homogeneous field of order the Inglis-Teller field is required in combination with the field due to the ions. The dynamics are very different according to whether np or nf series carry the transition probability. For np-state population, the maximum stabilization is achieved at ion-Rydberg distances of around 5n2a0, with the ion almost perpendicular to the applied homogeneous field. For an initial nf population the ion perturbation may have a destabilizing effect at sufficiently small homogeneous field (⩽0.1FIT). Significant effects of laser polarization on the stability are reported. Calculations for a realistic pseudo-random distribution of ions and Rydbergs suggest that ml mixing by ions will never reach the complete mixing limit, but that at least an order of magnitude stabilization is achievable under a restricted range of conditions.

A novel theoretical study of the control of translational motion of atomic and molecular Rydberg states in inhomogeneous static electric fields is presented. Simulations have been carried out demonstrating that, under realistic conditions, the deflection and focusing of Rydberg atoms and molecules should be achievable. Advantage is taken of the high susceptibility of the Rydberg states to external electric fields, allowing the use of much smaller fields than would be necessary for ground state neutrals. The simulations presented are for trajectories of Rydberg states with n = 18-20 in the fields of an electric dipole, quadrupole and hexapole. A deflection of 7 mm is predicted for n = 18 Rydberg states travelling parallel to the dipole after 100 µs time of flight. In the hexapole n = 20 Rydberg states are refocused to a spot size of the order of the laser beam waist (10 µm) after 20 µs. It is demonstrated that the hexapole can also act as a cylindrical lens if its axis is perpendicular to the Rydberg beam direction. Spontaneous emission and black-body decay rates are also calculated, and their variation with the applied field is investigated. The potential applications of this work might include the use of focusing and deflection for controlled low-energy collisions of Rydberg molecules with surfaces.

We investigated the Rydberg-state excitation process of a hydrogen atom subjected to spatially homogeneous and inhomogeneous laser fields by means of ab initio calculations. It is found that, comparing with atoms exposed to spatially homogeneous laser fields, the excitation probability decreases and the electron tends to occupy the states with lower principal quantum numbers and angular quantum numbers for atoms in spatially inhomogeneous laser pulses. Furthermore, calculations of a quantum model without taking into account ionization of the electron after it is coherently captured by the Rydberg state are inconsistent with the above-stated findings by ab initio calculations. Analysis indicates that the aforementioned intriguing features can be attributed to the enhanced ionization of the Rydberg states by inhomogeneous laser fields since the distributions of Rydberg states of high principal quantum numbers and angular quantum numbers locate far away from the core where the inhomogeneous electric fields become significant.

Helium atoms in high- and low-field-seeking Rydberg states with linear and quadratic Stark shifts have been confined in two dimensions and guided over a distance of 150 mm using time-varying inhomogeneous electric fields. This was achieved with an electrode structure composed of four parallel cylindrical rods to which voltages were applied to form oscillating and rotating saddle-point fields. These two modes of operation result in time-averaged pseudopotentials that confine samples in high- and low-field-seeking states about the axis of the device. The experimental data have been compared to the results of numerical particle trajectory calculations that include effects of blackbody radiation and electric field ionization. The results highlight important contributions from single-photon blackbody-induced transitions that cause large changes in the principal quantum number of the Rydberg atoms.

Hydrogen molecules are excited in a molecular beam to Rydberg states around n=17-18 and are exposed to the inhomogeneous electric field of an electric dipole. The large dipole moment produced in the selected Stark eigenstates leads to strong forces on the H2 molecules in the inhomogeneous electric field. The trajectories of the molecules are monitored using ion-imaging and time of flight measurements. With the dipole rods mounted parallel to the beam direction, the high-field-seeking and low-field-seeking Stark states are deflected towards and away from the dipole, respectively. The magnitude of the deflection is measured as a function of the parabolic quantum number k and of the duration of the applied field. It is also shown that a large deflection is observed when populating the (17d2)1 state at zero field and switching the dipole field on after a delay. With the dipole mounted perpendicular to the beam direction, the molecules are either accelerated or decelerated as they move towards the dipole. The Rydberg states are found to survive for over 100 micros after the dipole field is switched off before being ionized at the detector and the time of flight is measured. A greater percentage change in kinetic energy is achieved by initial seeding of the beam in helium or neon followed by inhomogeneous field deceleration/acceleration. Molecular dynamics trajectory simulations are presented highlighting the extent to which the trajectories can be predicted based on the known Stark map. The spectroscopy of the populated states is discussed in detail and it is established that the N+=2, J=1, MJ=0 states populated here have a special stability with respect to decay by predissociation.

N_{2} molecules traveling in pulsed supersonic beams have been excited from their X ^{1}Σ_{g}^{+} ground electronic state to long-lived Rydberg states with principal quantum numbers between 39 and 48 using a resonance-enhanced two-color three-photon excitation scheme. The Rydberg states populated had static electric dipole moments exceeding 5000 D which allowed deceleration of the molecules to rest in the laboratory-fixed frame of reference and three-dimensional trapping using inhomogeneous electric fields. The trapped molecules were confined for up to 10 ms, with effective trap decay time constants increasing with principal quantum number, and ranging from 450 to 700 μs. These observations, and comparison with the results of similar measurements with He atoms, indicate that the decay dynamics of the trapped Rydberg N_{2} molecules are dominated by spontaneous emission and do not exhibit significant contributions from effects of intramolecular interactions that lead to non-radiative decay.

The linear-Stark-effect approximation is employed to investigate the effects of electric fields on autoionizing doubly excited atomic states corresponding to relatively large values of the outer-electron principal quantum number

n

. By assuming that a statistical distribution of the inner-electron magnetic sublevels has been established, simple expressions are derived which relate the autoionization and radiative transition rates in the presence of an electric field to the respective field-free rates. It is pointed out that the multiphoton laser excitation of the doubly excited states can give rise to a nonstatistical distribution of the magnetic sublevels and to complex interference terms involving transition amplitudes associated with different values of the outer-electron angular momentum quantum number

l

. The results of calculations are presented for the autoionization and radiative-transition rates which play the most important role in the dielectronic recombination of the Li-like

{\mathrm{Fe}}^{+23}

ion through the $2p\ensuremath{\rightarrow}2s$ inner-electron transition, where the contributions from large-

n

values are particularly important. In these calculations it is assumed that the magnetic sublevels are statistically populated and only the simple expressions for the transition rates are employed. The effects of the electric field on the dominant (inner-electron) radiative decay rate can be neglected, but the electric field mixing of the outer-electron

l

substates substantially increases the autoionization rates from the higher-

l

sublevels.