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

Resonance fluorescence line polarization studies of laser excited sodium transitions

Xian-Kun Meng

Published Jan 1, 1991• 0 citations
OpenAlex

Abstract

The resonant excitation of the sodium D2 transition by laser radiation was investigated experimentally in this thesis. Line polarization measurement of the resonance fluorescence was employed to investigate the excitation process. The sodium atoms, which were collimated in a very narrow beam, were excited by a monochromatic laser beam with the frequency tuned to resonance with the 32S 112(F=2) - 32P312 hyperfine transition. The direction of the laser beam was perpendicular to the atomic beam and the fluorescence photons were detected along a direction perpendicular to both the laser and atomic beams. The experimental measurements were performed to determine the effect due to the variation of the laser intensity and frequency on the line polarization. A theoretical expression of the line polarization as a function of density matrix elements of the upper excited hyperfine sub -states was derived. A full quantum electrodynamic theory was used to derive an atomic operator equation of motion which was needed to calculate atomic operator elements. These elements then yielded the corresponding density matrix elements. The experimental results and the theoretical modelling were in a good agreement. The first experimental results for the line polarization of the highly excited states, 42D512 and 42D312, are also presented. The use of two lasers enabled these highly excited states to be excited. The line polarization of the fluorescence for transitions from the 4D level down to lower states is derived in terms of the density matrix elements of the upper excited states. Two limiting cases for the theoretical predictions of the line polarization are considered.

Related papers

Line polarization of laser-excited Na D2 -transition resonance fluorescence

X-K. Meng, W. R. MacGillivray, M. C. Standage

The sodium ${\mathit{D}}_{2}$ transition is resonantly excited by \ensuremath{\pi}-polarized, narrow-band laser radiation. The line polarization of the resulting fluorescence detected normally to the plane containing the electric-field vector of the radiation and its propagation direction, as well as the atomic beam, is measured as a function of radiation intensity and tuning. The data are compared to calculations from a quantum-electrodynamic theory which includes all participating energy states in the hyperfine representation. The quantitative agreement is very good.

Physical Review A•Feb 1, 1992•16 citations

Superelastic electron scattering from the laser-excited 32P3/2 level of Na

Peter Mark Farrell

The atomic collision parameters ?, ?, ?, ?, P, |P| and |�| were determined from measurements of the pseudo Stokes parameters for superelastic scattering of 20 eV incident electrons at angles of 10� and 15� from the 32P312 excited state of sodium. Two depolarising factors K and K' for the pseudo Stokes parameters are defined for it and a laser excitation respectively to account for the depolarising influence due to optical pumping in the hyperfine structure of the 32P3t2 excited state. A theoretical model of the laser excitation of the sodium transition is developed to determine K and K'. The theory developed is a quantum -electrodynamic description of the resonant interaction of monochromatic light with the 32S in(F'=2) <-> 32P3a(F=3,2,1) hyperfine transitions of the sodium D2 line formualated in terms of the Heisenberg atomic operator. Off diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences and certain state coherences form a closed subset of the total system of equations. This subset is sufficiently small to enable numerical computation. As well as K and K', the model is used to calculate the probability of occupation of the various atomic states and the polarisation of the sideways scattered fluorescence from the laser excited atoms. The results of this model are compared with the predictions of four other models, a rate equation model which includes only the F=3 excited state, a semiclassical model based on the density operator, a low light intensity approximation to the semiclassical model and a high intensity model which uses a transformed basis for the states. For both it and a laser excitation it is shown that the QED calculated values converge to the values predicted by the high and low intensity approximations in the appropriate limits.

•Jan 1, 1992•0 citations

Photon deflection of a state prepared sodium beam

Benjamin T. H. Varcoe

This thesis presents a theoretical and experimental investigation of the deflection of an atomic beam by an interaction with a near resonant laser. This investigation focuses on the sensitivity of this force to the initial state of an atom. The term deflection spectroscopy is applied to a specific application of the deflection force as a probe of a collisionally created density matrix. For the purpose of demonstrating the state sensitivity, a method of state preparation is presented that can produce both an and off diagonal density matrix elements in the ground state of sodium, simulating those occurring in a collisional excitation. The atomic collision parameter L1 was determined from a measurement of the deflected momentum of a state prepared atomic beam. A full quantum electrodynamic description of the interaction is used to describe the laser - atom interaction. Incorporated in the description is both the preparation of a ground state and a full description of the momentum exchange. The QED equations are applied to the 32S112 to 32P312 transition of atomic sodium for all possible modes of excitation from the "pure" polarisations, circular (a) and linear (it) to an elliptical polarisation involving combinations and relative phase shifts of these two polarisations. In addition the deflection of a J=2 metastable state is considered, and a set of deflection pseudo -Stokes parameters are developed for both the metastable state and the optically prepared sodium ground state. Comparisons between theory and experiment are made. Both fluorescence measurements and transverse momentum measurements are performed and were compared with theory. All aspects of the interaction were investigated with the theory performing well under all experimental conditions. It was found the deflection was sensitive to the preparation of the atomic ground state of sodium and hence it was demonstrated that atom deflection can be used to determine atomic collision parameters.

•Jan 1, 1997•0 citations

Superelastic Electron Scattering from Laser Excited States of Sodium

Sang, Robert

This thesis presents the results of a series of experiments in which electrons are superelastically scattered from various laser excited states of sodium. The atoms, once in the optically prepared state, are forced to relax via the superelastic collision with an electron. The rate of detection of superelastically scattered electrons was measured as a function of the laser polarisation which enabled pseudo Stokes parameters to be determined. These pseudo Stokes parameters are functions of both optical pumping parameters and atomic collision parameters. The optical pumping parameters describe the laser-atom interaction and the atomic collision parameters describe the electron-atom collision process. Three different laser excitation mechanisms were used to optically pump the atoms into various excited states. The first of these used a single laser tuned to the 32S 112(F'=2 hyperfine state)-~32P312 transition. The excited atoms underwent a superelastic collision with an electron leaving the atom in the ground state and pseudo Stokes parameters were measured as a function of both scattering angle and incident electron energy. The second superelastic experiment, utilised a folded step excitation mechanism which employed two lasers tuned from the two hypethne states of the 32S112 ground state respectively to the 32P312 excited state. Power broadening effects in the single laser experiment cause the atoms to be optically pumped into the F= 1 hyperfine ground state. The laser powers used were not great enough to power broaden the hyperfine ground states and as such the F'= 1 sublevel effectively acted as a sink. The folded step excitation method enabled the excited state population to be increased so that data at larger scattering angles could be obtained. Stokes parameters from both of these experiments which had an incident energy range of 10eV to 30eV and an angular range of 5°-25° were compared to three current electron-atom scattering theories and previous experimental data. Overall, fair to good agreement was found between theory and experiments for the individual Stokes parameters. Losses of coherence was observed at small scattering angles (50.200) at 20eV and 25eV incident electron energies which were poorly modelled by the three different theories. The third superelastic experiment involved the use of two lasers of specified polarisation to stepwise excite the atoms to the 32D512 excited state. Superelastic collisions with incident electron energies of 20eV from the 32D512-*32P312~312 collision were studied at three different scattering angles and pseudo Stokes parameters for the case where the polarisations of the radiation from the lasers were parallel were measured. The single step and folded step laser-atom interactions for it excitation were modelled using a full quantum electrodynamical treatment so that the optical pumping parameters from the single and folded step experiments could be investigated. Equations of motion were derived in the Heisenberg picture and it is shown that for the single laser case 59 equations of motion are required to fully model the interaction and for the folded step ease 78 equations of motion are required. The results of calculations demonstrated that the optical pumping parameters were sensitive to laser intensity, laser detuning and the Doppler width of the atomic beam. The theoretical quantum electrodynamical calculation results were in good agreement with the experimental results.

•Jan 1, 2007•0 citations

Optical pumping of the Na D2 transition with elliptically polarized light

Benjamin T. H. Varcoe, Robert T. Sang, W. R. Macgillivary +2 more

The quantum electrodynamic description of circularly and linearly polarized, single mode radiation exciting atomic transitions in a hyperfine manifold is extended to the more general case of elliptic polarization. Calculations for the sodium D2 line are tested by observing the line polarization of the resonance flourescence scattered perpendicular to the plane containing laser and atomic beams as a function of the laser polarization. Very good agreement between the calculations and the measurements is achieved. It is demonstrated that predetermined populations and substate coherences can be engineered by optically pumping the transition with the appropriately polarized radiation.

Journal of Modern Optics•Apr 1, 1999•13 citations

Polarization rotation spectral profiles for the D2 line of 87 Rb atoms: theory and experiment

Geol Moon, Seung-Chul Yang, Jin‐Tae Kim +1 more

Abstract We present a theoretical and experimental study of the polarization rotation of a linearly polarized probe beam scanning across all of the neighboring hyperfine levels ( F e = 1 and 2) with a circularly polarized pumping beam resonant on the F g = 2 → F e = 3 transition of the D2 line of 87 Rb atoms. The experimental results match well with the results calculated from the full-level density matrix equations considering laser phase noise, which hinders observations of narrow lines with linewidths of ∼90 kHz, as calculated in polarization rotation spectra for the first time.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 23, 2019•4 citations
The resonant excitation of the sodium D2 transition by laser radiation was investigated experimentally in this thesis. Line polarization measurement of the resonance fluorescence was employed to investigate the excitation process. The sodium atoms, which were collimated in a very narrow beam, were excited by a monochromatic laser beam with the frequency tuned to resonance with the 32S 112(F=2) - 32P312 hyperfine transition. The direction of the laser beam was perpendicular to the atomic beam and the fluorescence photons were detected along a direction perpendicular to both the laser and atomic beams. The experimental measurements were performed to determine the effect due to the variation of the laser intensity and frequency on the line polarization. A theoretical expression of the line polarization as a function of density matrix elements of the upper excited hyperfine sub -states was derived. A full quantum electrodynamic theory was used to derive an atomic operator equation of motion which was needed to calculate atomic operator elements. These elements then yielded the corresponding density matrix elements. The experimental results and the theoretical modelling were in a good agreement. The first experimental results for the line polarization of the highly excited states, 42D512 and 42D312, are also presented. The use of two lasers enabled these highly excited states to be excited. The line polarization of the fluorescence for transitions from the 4D level down to lower states is derived in terms of the density matrix elements of the upper excited states. Two limiting cases for the theoretical predictions of the line polarization are considered.
The sodium D2{\mathit{D}}_{2}D2​ transition is resonantly excited by \ensuremath{\pi}-polarized, narrow-band laser radiation. The line polarization of the resulting fluorescence detected normally to the plane containing the electric-field vector of the radiation and its propagation direction, as well as the atomic beam, is measured as a function of radiation intensity and tuning. The data are compared to calculations from a quantum-electrodynamic theory which includes all participating energy states in the hyperfine representation. The quantitative agreement is very good.
The atomic collision parameters ?, ?, ?, ?, P, |P| and |�| were determined from measurements of the pseudo Stokes parameters for superelastic scattering of 20 eV incident electrons at angles of 10� and 15� from the 32P312 excited state of sodium. Two depolarising factors K and K' for the pseudo Stokes parameters are defined for it and a laser excitation respectively to account for the depolarising influence due to optical pumping in the hyperfine structure of the 32P3t2 excited state. A theoretical model of the laser excitation of the sodium transition is developed to determine K and K'. The theory developed is a quantum -electrodynamic description of the resonant interaction of monochromatic light with the 32S in(F'=2) <-> 32P3a(F=3,2,1) hyperfine transitions of the sodium D2 line formualated in terms of the Heisenberg atomic operator. Off diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences and certain state coherences form a closed subset of the total system of equations. This subset is sufficiently small to enable numerical computation. As well as K and K', the model is used to calculate the probability of occupation of the various atomic states and the polarisation of the sideways scattered fluorescence from the laser excited atoms. The results of this model are compared with the predictions of four other models, a rate equation model which includes only the F=3 excited state, a semiclassical model based on the density operator, a low light intensity approximation to the semiclassical model and a high intensity model which uses a transformed basis for the states. For both it and a laser excitation it is shown that the QED calculated values converge to the values predicted by the high and low intensity approximations in the appropriate limits.
This thesis presents a theoretical and experimental investigation of the deflection of an atomic beam by an interaction with a near resonant laser. This investigation focuses on the sensitivity of this force to the initial state of an atom. The term deflection spectroscopy is applied to a specific application of the deflection force as a probe of a collisionally created density matrix. For the purpose of demonstrating the state sensitivity, a method of state preparation is presented that can produce both an and off diagonal density matrix elements in the ground state of sodium, simulating those occurring in a collisional excitation. The atomic collision parameter L1 was determined from a measurement of the deflected momentum of a state prepared atomic beam. A full quantum electrodynamic description of the interaction is used to describe the laser - atom interaction. Incorporated in the description is both the preparation of a ground state and a full description of the momentum exchange. The QED equations are applied to the 32S112 to 32P312 transition of atomic sodium for all possible modes of excitation from the "pure" polarisations, circular (a) and linear (it) to an elliptical polarisation involving combinations and relative phase shifts of these two polarisations. In addition the deflection of a J=2 metastable state is considered, and a set of deflection pseudo -Stokes parameters are developed for both the metastable state and the optically prepared sodium ground state. Comparisons between theory and experiment are made. Both fluorescence measurements and transverse momentum measurements are performed and were compared with theory. All aspects of the interaction were investigated with the theory performing well under all experimental conditions. It was found the deflection was sensitive to the preparation of the atomic ground state of sodium and hence it was demonstrated that atom deflection can be used to determine atomic collision parameters.
This thesis presents the results of a series of experiments in which electrons are superelastically scattered from various laser excited states of sodium. The atoms, once in the optically prepared state, are forced to relax via the superelastic collision with an electron. The rate of detection of superelastically scattered electrons was measured as a function of the laser polarisation which enabled pseudo Stokes parameters to be determined. These pseudo Stokes parameters are functions of both optical pumping parameters and atomic collision parameters. The optical pumping parameters describe the laser-atom interaction and the atomic collision parameters describe the electron-atom collision process. Three different laser excitation mechanisms were used to optically pump the atoms into various excited states. The first of these used a single laser tuned to the 32S 112(F'=2 hyperfine state)-~32P312 transition. The excited atoms underwent a superelastic collision with an electron leaving the atom in the ground state and pseudo Stokes parameters were measured as a function of both scattering angle and incident electron energy. The second superelastic experiment, utilised a folded step excitation mechanism which employed two lasers tuned from the two hypethne states of the 32S112 ground state respectively to the 32P312 excited state. Power broadening effects in the single laser experiment cause the atoms to be optically pumped into the F= 1 hyperfine ground state. The laser powers used were not great enough to power broaden the hyperfine ground states and as such the F'= 1 sublevel effectively acted as a sink. The folded step excitation method enabled the excited state population to be increased so that data at larger scattering angles could be obtained. Stokes parameters from both of these experiments which had an incident energy range of 10eV to 30eV and an angular range of 5°-25° were compared to three current electron-atom scattering theories and previous experimental data. Overall, fair to good agreement was found between theory and experiments for the individual Stokes parameters. Losses of coherence was observed at small scattering angles (50.200) at 20eV and 25eV incident electron energies which were poorly modelled by the three different theories. The third superelastic experiment involved the use of two lasers of specified polarisation to stepwise excite the atoms to the 32D512 excited state. Superelastic collisions with incident electron energies of 20eV from the 32D512-*32P312~312 collision were studied at three different scattering angles and pseudo Stokes parameters for the case where the polarisations of the radiation from the lasers were parallel were measured. The single step and folded step laser-atom interactions for it excitation were modelled using a full quantum electrodynamical treatment so that the optical pumping parameters from the single and folded step experiments could be investigated. Equations of motion were derived in the Heisenberg picture and it is shown that for the single laser case 59 equations of motion are required to fully model the interaction and for the folded step ease 78 equations of motion are required. The results of calculations demonstrated that the optical pumping parameters were sensitive to laser intensity, laser detuning and the Doppler width of the atomic beam. The theoretical quantum electrodynamical calculation results were in good agreement with the experimental results.
The quantum electrodynamic description of circularly and linearly polarized, single mode radiation exciting atomic transitions in a hyperfine manifold is extended to the more general case of elliptic polarization. Calculations for the sodium D2 line are tested by observing the line polarization of the resonance flourescence scattered perpendicular to the plane containing laser and atomic beams as a function of the laser polarization. Very good agreement between the calculations and the measurements is achieved. It is demonstrated that predetermined populations and substate coherences can be engineered by optically pumping the transition with the appropriately polarized radiation.
Abstract We present a theoretical and experimental study of the polarization rotation of a linearly polarized probe beam scanning across all of the neighboring hyperfine levels ( F e = 1 and 2) with a circularly polarized pumping beam resonant on the F g = 2 → F e = 3 transition of the D2 line of 87 Rb atoms. The experimental results match well with the results calculated from the full-level density matrix equations considering laser phase noise, which hinders observations of narrow lines with linewidths of ∼90 kHz, as calculated in polarization rotation spectra for the first time.