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Deflection of a sodium atomic beam by optical forces

Gilford S. Summy

Published Jan 1, 1994• 0 citations
OpenAlex

Abstract

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.

Related papers

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

Complete determination of atomic states by photon momentum transfer

G. S. Summy, W. R. MacGillivray, M. C. Standage

Abstract. In this paper we present a theory which shows that the optical force on atoms due to spontaneous processes depends upon the quantum state of the atom at the time it begins interacting with the optical field. The momentum is treated as a classical variable and the theory used to model the interaction between the atom and radiation is based on a quantum electrodynamic technique. The formalism developed is quite general and, in principle, can be applied to the determination of initial atomic states prepared by a variety of mechanisms. An example of an application of the spontaneous force is presented which shows how it is possible to use the momentum absorbed by an atom from a coherent light field to determine the density matrix of the atomic state created by a collision process. For completeness, the derivation of a stimulated force model is included where it is shown that the resulting force on atoms also depends on their initial state. 1.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 28, 1996•2 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.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 28, 1997•5 citations

Electron superelastic scattering from states of atomic sodium and rubidium

B. V. Hall, Robert T. Sang, Max Shurgalin +3 more

This paper reports on the extension of the electron superelastic scattering technique to three new situations. The first considers scattering from the 32P3/2 level of Na that has been excited by two laser modes tuned, respectively, to the transitions from the two hyperfine states of the 32S1/2 ground level. Both coherent and noncoherent modes are treated in a full quantum electrodynamic model of the laser excitation. Under certain conditions, the time-averaged probability of finding an atom in the 32P3/2 level exceeds 0.5. The second situation is electron superelastic scattering from the 32D5/2 level of Na that has been resonantly excited from the ground level via a resonant intermediate level. With the first observation of superelastically scattered electrons from this higher lying level recently recorded, this paper considers the extension of the quantum electrodynamics (QED) model to describe the optical excitation process. Application of superelastic scattering to the 52S1/2–52P3/2 transition of Rb is the third situation considered. The superelastic scattering formalism is extended to allow for a nonzero spin flip cross section for this transition. The resulting optical pumping terms are calculated using the QED model and the method of their determination for the superelastic scattering experiment described. The experimental design necessary to measure all of the collision parameters for this transition is discussed.

Canadian Journal of Physics•Nov 1, 1996•4 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

Electron scattering from the optically prepared 3P state of sodium

Max Shurgalin

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.

•Jan 1, 1998•0 citations
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.
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.
Abstract. In this paper we present a theory which shows that the optical force on atoms due to spontaneous processes depends upon the quantum state of the atom at the time it begins interacting with the optical field. The momentum is treated as a classical variable and the theory used to model the interaction between the atom and radiation is based on a quantum electrodynamic technique. The formalism developed is quite general and, in principle, can be applied to the determination of initial atomic states prepared by a variety of mechanisms. An example of an application of the spontaneous force is presented which shows how it is possible to use the momentum absorbed by an atom from a coherent light field to determine the density matrix of the atomic state created by a collision process. For completeness, the derivation of a stimulated force model is included where it is shown that the resulting force on atoms also depends on their initial state. 1.
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 paper reports on the extension of the electron superelastic scattering technique to three new situations. The first considers scattering from the 32P3/2 level of Na that has been excited by two laser modes tuned, respectively, to the transitions from the two hyperfine states of the 32S1/2 ground level. Both coherent and noncoherent modes are treated in a full quantum electrodynamic model of the laser excitation. Under certain conditions, the time-averaged probability of finding an atom in the 32P3/2 level exceeds 0.5. The second situation is electron superelastic scattering from the 32D5/2 level of Na that has been resonantly excited from the ground level via a resonant intermediate level. With the first observation of superelastically scattered electrons from this higher lying level recently recorded, this paper considers the extension of the quantum electrodynamics (QED) model to describe the optical excitation process. Application of superelastic scattering to the 52S1/2–52P3/2 transition of Rb is the third situation considered. The superelastic scattering formalism is extended to allow for a nonzero spin flip cross section for this transition. The resulting optical pumping terms are calculated using the QED model and the method of their determination for the superelastic scattering experiment described. The experimental design necessary to measure all of the collision parameters for this transition is discussed.
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.
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.