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Journal of Physics B Atomic Molecular and Optical Physics

Determination of the absolute excited state density of a sodium target by means of beam deflection measurements

W. P. Wiersema, Albert Rudolph Schlatmann, S. Schippers, Reinhard Morgenstern

Published Aug 28, 1994• 2 citations
Publisher

Abstract

The average deflection of a laser excited, divergent sodium beam with a broad velocity distribution is measured by means of a Langmuir-Taylor detector and exploited for determining the absolute density of the excited state in the interaction area. Simulations of the excitation and deflection process point out that the knowledge of the velocity distribution of the sodium atoms plays a crucial part in obtaining reliable information from deflection measurements. From the comparison of simulated and experimental results we find that in our set-up typically 30% of the sodium atoms are in the excited state when both ground state levels are pumped with an intensity of 35 mW cm -2 from an electro-optically modulated CW laser beam; the corresponding excited state density is 1.5*10 9 cm -3 .

DOI
10.1088/0953-4075/27/16/019

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The average deflection of a laser excited, divergent sodium beam with a broad velocity distribution is measured by means of a Langmuir-Taylor detector and exploited for determining the absolute density of the excited state in the interaction area. Simulations of the excitation and deflection process point out that the knowledge of the velocity distribution of the sodium atoms plays a crucial part in obtaining reliable information from deflection measurements. From the comparison of simulated and experimental results we find that in our set-up typically 30% of the sodium atoms are in the excited state when both ground state levels are pumped with an intensity of 35 mW cm -2 from an electro-optically modulated CW laser beam; the corresponding excited state density is 1.5*10 9 cm -3 .
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.
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.
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.
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.
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.
A sodium atomic beam has been decelerated and laser cooled to a longitudinal beam temperature of less than 30 mK. Subsequently these slow atoms with a typical velocity of 100 m/sec were selectively deflected by laser-light forces. The deflection angle was typically 30°. The deflection scheme permits a stabilization of the transverse velocities in the deflected atomic beam down to the quantum-limit temperature for one dimension (0.7 × 240 μK). The experimentally achieved temperatures are of the order of 1 mK.