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Photon deflection of a state prepared sodium beam

Benjamin T. H. Varcoe

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

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.

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•Jan 1, 1994•0 citations

Experimental determination of atomic state-dependent optical forces

G. S. Summy, Benjamin T. H. Varcoe, W. R. MacGillivray +1 more

An experimental demonstration of the state-dependent nature of the forces exerted on an atom by resonant radiation is reported. Sodium atoms, which are contained in a highly collimated beam, are initially prepared in a particular ground hyperfine substate by optical pumping. They are then deflected by resonant laser radiation of known polarization. Measurements of the magnitude of the deflection show a dependence on the way the atoms were initially prepared, confirming the predictions of a recently developed theoretical model. The experimental data show good agreement with calculations of the theory using a full quantum electrodynamic description of the sodium transition involved.

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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.

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Electron scattering from the optically prepared 3P state of sodium

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Resonance fluorescence line polarization studies of laser excited sodium transitions

Xian-Kun Meng

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.

•Jan 1, 1991•0 citations
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.
A detailed investigation of the momentum absorbed by an atom from resonant light is presented in this thesis. The major topic to be addressed concerns the dependence of absorbed momentum upon the initial quantum state of the atom. This dependence is exploited for the purpose of showing that the absorbed momentum can be used to investigate processes where determining this initial state is important. A specific example where this technique can be applied, electron -atom collision studies, is discussed. It is found that in this case, where the determination of coherences between substates of the electron excited level is critical, the method based upon momentum absorption produces the same general formalism as experiments using the superelastic and electron -photon coincidence techniques. A method for creating coherences between substates in the ground level with rf magnetic fields is described. This is proposed as a way of testing the sensitivity of the optical forces to ground state coherences. A quantum electrodynamic theory is used to describe the photon -atom interaction. This allows all of the atomic states that are important in the interaction to be included. The QED theory provides a solution to the density matrix of the atoms as a function of time, which in turn is used to calculate the average momentum transferred to the atom. Several different atomic systems are considered some hypothetical and some real. The systems to be examined include: a two level system, a J=1 J=2 transition, and the 32S111 (F=2) -> 32P312 transition of atomic sodium. Although the latter example is a complex system requiring the solution to a set of at least 59 first order partial differential equations, its theoretical consideration is vital for comparison to the experimental data.
An experimental demonstration of the state-dependent nature of the forces exerted on an atom by resonant radiation is reported. Sodium atoms, which are contained in a highly collimated beam, are initially prepared in a particular ground hyperfine substate by optical pumping. They are then deflected by resonant laser radiation of known polarization. Measurements of the magnitude of the deflection show a dependence on the way the atoms were initially prepared, confirming the predictions of a recently developed theoretical model. The experimental data show good agreement with calculations of the theory using a full quantum electrodynamic description of the sodium transition involved.
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.
We have performed experimental and theoretical studies of the deflection of a sodium atomic beam by a laser tuned to the 3 2{\mathrm{}}^{2}2S1/2{S}_{1/2}S1/2​,F=2--3 2{\mathrm{}}^{2}2P3/2{P}_{3/2}P3/2​,F=3 transition. The intensity profile of the deflected beam was measured at different laser power levels and for different laser polarizations. Calculations using a constant force derived from a two-level atom yield deflections which are too large. The results of more realistic simulation calculations agree very well with the measured deflection. Those calculations incorporate the atomic-beam spatial and velocity distributions as well as the laser frequency distribution and polarization state. Optical pumping, loss of atoms to the nonresonant F=1 ground state, and Doppler shifting of the atoms out of resonance are all considered, as also are the statistics and angular distributions of the spontaneous photons.
An experimental investigation of electron - impact induced transitions from the laser - excited 3P state of sodium atom to the 4S and 3D excited states is presented, the main objective being measurement of the atomic collision parameters ( ACPs ) that are related to individual scattering amplitudes. These parameters are complementary to the differential excitation cross - sections and provide finer details on the collisional excitation process. The experiment involved the preparation of the 3P - state with coherent laser radiation of a particular polarisation and measuring the rate of electrons scattered from the laser - excited state as function of laser polarisations. The ACPs were then deduced from these measurements and optical pumping parameters, which account for the optical preparation of the 3P - state. To formulate different measurement schemes, a measurement theory based on the general description of transitions between states of different angular momentum using density matrix formalism is derived. The investigation of the 3P - 4S transition is very similar to the studies of the 3S - 3P excitation performed by superelastic method involving the 3P - 3S scattering in the 'time - inverse' geometry. 'Standard' ACPs are used and, similarly to the superelastic method, the measurements for the 3P - 4S excitation performed in the 'time - inverse' geometry also reveal ACPs for the 4S - 3P de -excitation process. For the more complex 3P - 3D transition, however, the 'standard' ACPs may be less informative. It is shown that certain sums of individual magnetic sublevel excitation probabilities can be measured which may be considered as atomic collision parameters for transitions between P and D - states.
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.