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

Atoms

Two Photon Processes in an Atom Confined in Gaussian Potential

Sonia Lumb, Shalini Lumb, Vinod Prasad

Published Feb 17, 2016• 7 citations
Publisher

Abstract

Transitions of an atom under the effect of a Gaussian potential and loose spherical confinement are studied. An accurate Bernstein-polynomial (B-polynomial) method has been applied for the calculation of the energy levels and radial matrix elements. The transition probability amplitudes, transparency frequencies, and resonance enhancement frequencies for transitions to various excited states have been evaluated. The effect of the shape of confining potential on these spectral properties is studied.

DOI
10.3390/atoms4010006

Related papers

Effects of Debye plasmas on two-photon transitions in lithium atoms

S. Paul, Y. K. Ho

We have studied two-photon transition rates of atomic lithium within model potential by using the pseudostate summation approach. Transition amplitudes and absorption coefficients have been computed for $2s\text{\ensuremath{-}}3s$, $2s\text{\ensuremath{-}}4s$, and $2s\text{\ensuremath{-}}3d$ transitions with various Debye lengths. In the case of $2s\text{\ensuremath{-}}3s$ transition, two-photon transparency vanishes for smaller Debye length. Reverse incident occurred for $2s\text{\ensuremath{-}}3d$ transition. Here, we have found a two-photon transparency for lower values of Debye length. These two situations occur due to energy level shifting in the presence of a plasma environment. A detailed description of resonance enhancement frequency and transition amplitude has been analyzed.

Physical Review A•Oct 27, 2008•40 citations

Ground-State Entanglement Properties of Helium Atom in a Finite Spherical Cavity

Przemysław Kościk, Jayanta K. Saha

The effects of the spatial confinement on the ground-state entanglement properties of the helium atom have been studied. The finite oscillator potential is used to represent the confining potential. The transition to the free atom regime and the harmonic confinement regime are discussed in detail in dependence of the control parameters of the system.

Few-Body Systems•May 19, 2015•12 citations

Precision Spectroscopy of Radiation Transitions between Singlet Rydberg States of the Group IIb and Yb Atoms

Igor L. Glukhov, Aleksandr A. Kamenski, Vitaly D. Ovsiannikov +1 more

The measurements of microwave (μw) and radio-frequency (RF) radiation quantitative parameters may be based on the quantum–optical approach to determine the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions between opposite-parity Rydberg states nL 1L and n′L±1 1L±1 (where n′= n,n±1,n±2) of the singlet series in the alkaline–earth–metal-like atoms of group IIb (Zn, Cd, Hg) and Yb. The matrix elements determine the shifts of Rydberg-state energy levels in the field of resonance μw or RF radiation, splitting the resonance of electromagnetically induced transparency (EIT) for intensely absorbed probe radiation. Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data from the current literature on quantum defect values are performed for frequencies and matrix elements of transitions between singlet Rydberg states of 1S0-, 1P1-, 1D2-, and 1F3-series in Zn, Cd, Hg, and Yb atoms. The calculated data are approximated by polynomials in the powers of the principal quantum numbers. The polynomial coefficients are determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically calculated functions. These approximation expressions provide new possibilities for accurately evaluating the frequencies and matrix elements of dipole transitions between Rydberg states over a wide range of quantum numbers n >> 1, accompanied by the emission and absorption of μw and RF photons.

Photonics•Oct 13, 2023•5 citations

Laser-induced resonant transitions with Gaussian switching conditions

Predrag Krstić, R K Janve, D. Fussen

A simple closed-form formula is obtained for the transition probability of a two-state atom in a Gaussian laser pulse. The validity of the formula is tested by comparison with numerical results. The analytic formula is applicable over a wide range of the laser intensities, detunings and pulse durations. Particularly, it can be used for calculation of excitation probability when the Rabi frequency is of the order of or larger than a frequency associated with the pulse duration.

Journal of Physics B Atomic Molecular and Optical Physics•Mar 28, 1991•2 citations

Microwave Field Metrology Based on Rydberg States of Alkali-Metal Atoms

Vitaly D. Ovsiannikov, Vitaly G. Palchikov, Igor L. Glukhov

The high-precision determination of microwave radiation parameters may be based on measurements of the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions from even-parity nS1/2 and nD5/2 to odd-parity n′P3/2 and n′F7/2 (where n′ = n, n ± 1, n ± 2) for the Rydberg states of alkali-metal atoms. The matrix elements determine the splitting of Rydberg-state energy levels in the field of a resonance microwave (μw) radiation, which results in the splitting of the resonance in electromagnetic induced transparency (EIT). Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data of the current literature on quantum defect values were performed for the 2S, 2P, 2D and 2F series of the Rydberg states of Li, Na, K, Rb and Cs atoms. The calculated data were approximated by quadratic polynomials of the principal quantum number. The polynomial coefficients were determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically presented functions. The approximation equations may be used for the accurate evaluation of the frequencies and matrix elements of μw transitions in wide ranges of the Rydberg-state quantum numbers n >> 1.

Photonics•Sep 3, 2022•7 citations

Double-Photon Contributions to Multiple-Photon Processes. II. Resonance Case

Norah V. Cohan

We study the contribution to the transition probability of a multiple-photon process for which resonance occurs of the part of the interaction operator quadratic in the vector potential. We consider only the case in which this vector potential is constant within the region of space to which the system is confined. Under this assumption we show that the ratio of the contribution from the quadratic term in the vector potential to that from the linear term is proportional to the square of the energy difference between the initial state of the whole system (material system plus radiation field) and the intermediate state for which resonance occurs. As this energy difference is negligible near resonance, the quadratic term in the vector potential (or double-photon contributions) can be neglected when calculating transition probabilities for multiple-photon processes near resonances in the dipole approximation.

Physical Review•Feb 25, 1968•0 citations
Transitions of an atom under the effect of a Gaussian potential and loose spherical confinement are studied. An accurate Bernstein-polynomial (B-polynomial) method has been applied for the calculation of the energy levels and radial matrix elements. The transition probability amplitudes, transparency frequencies, and resonance enhancement frequencies for transitions to various excited states have been evaluated. The effect of the shape of confining potential on these spectral properties is studied.
We have studied two-photon transition rates of atomic lithium within model potential by using the pseudostate summation approach. Transition amplitudes and absorption coefficients have been computed for $2s\text{\ensuremath{-}}3s$, $2s\text{\ensuremath{-}}4s$, and $2s\text{\ensuremath{-}}3d$ transitions with various Debye lengths. In the case of $2s\text{\ensuremath{-}}3s$ transition, two-photon transparency vanishes for smaller Debye length. Reverse incident occurred for $2s\text{\ensuremath{-}}3d$ transition. Here, we have found a two-photon transparency for lower values of Debye length. These two situations occur due to energy level shifting in the presence of a plasma environment. A detailed description of resonance enhancement frequency and transition amplitude has been analyzed.
The measurements of microwave (μw) and radio-frequency (RF) radiation quantitative parameters may be based on the quantum–optical approach to determine the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions between opposite-parity Rydberg states nL 1L and n′L±1 1L±1 (where n′= n,n±1,n±2) of the singlet series in the alkaline–earth–metal-like atoms of group IIb (Zn, Cd, Hg) and Yb. The matrix elements determine the shifts of Rydberg-state energy levels in the field of resonance μw or RF radiation, splitting the resonance of electromagnetically induced transparency (EIT) for intensely absorbed probe radiation. Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data from the current literature on quantum defect values are performed for frequencies and matrix elements of transitions between singlet Rydberg states of 1S0-, 1P1-, 1D2-, and 1F3-series in Zn, Cd, Hg, and Yb atoms. The calculated data are approximated by polynomials in the powers of the principal quantum numbers. The polynomial coefficients are determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically calculated functions. These approximation expressions provide new possibilities for accurately evaluating the frequencies and matrix elements of dipole transitions between Rydberg states over a wide range of quantum numbers n >> 1, accompanied by the emission and absorption of μw and RF photons.
The high-precision determination of microwave radiation parameters may be based on measurements of the spectral characteristics of radiation transitions between the Rydberg states of atoms. Frequencies and matrix elements are calculated for dipole transitions from even-parity nS1/2 and nD5/2 to odd-parity n′P3/2 and n′F7/2 (where n′ = n, n ± 1, n ± 2) for the Rydberg states of alkali-metal atoms. The matrix elements determine the splitting of Rydberg-state energy levels in the field of a resonance microwave (μw) radiation, which results in the splitting of the resonance in electromagnetic induced transparency (EIT). Numerical computations based on the single-electron quantum defect method (QDM) and the Fues’ model potential (FMP) approach with the use of the most reliable data of the current literature on quantum defect values were performed for the 2S, 2P, 2D and 2F series of the Rydberg states of Li, Na, K, Rb and Cs atoms. The calculated data were approximated by quadratic polynomials of the principal quantum number. The polynomial coefficients were determined with the use of a standard curve-fitting interpolation polynomial procedure for numerically presented functions. The approximation equations may be used for the accurate evaluation of the frequencies and matrix elements of μw transitions in wide ranges of the Rydberg-state quantum numbers n >> 1.
We study the contribution to the transition probability of a multiple-photon process for which resonance occurs of the part of the interaction operator quadratic in the vector potential. We consider only the case in which this vector potential is constant within the region of space to which the system is confined. Under this assumption we show that the ratio of the contribution from the quadratic term in the vector potential to that from the linear term is proportional to the square of the energy difference between the initial state of the whole system (material system plus radiation field) and the intermediate state for which resonance occurs. As this energy difference is negligible near resonance, the quadratic term in the vector potential (or double-photon contributions) can be neglected when calculating transition probabilities for multiple-photon processes near resonances in the dipole approximation.