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Physical Review A

Quantitative analysis of the deflection of a sodium beam by laser radiation

Bernardo Jaduszliwer, GF Shen, Benjamin B. Bederson

Published Jun 1, 1986• 7 citations
Publisher

Abstract

We have performed experimental and theoretical studies of the deflection of a sodium atomic beam by a laser tuned to the 3 ${\mathrm{}}^{2}$${S}_{1/2}$,F=2--3 ${\mathrm{}}^{2}$${P}_{3/2}$,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.

DOI
10.1103/physreva.33.3792

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Physical Review Letters•Oct 12, 1992•21 citations
We have performed experimental and theoretical studies of the deflection of a sodium atomic beam by a laser tuned to the 3 {\mathrm{}}^{2}$${S}_{1/2},F=2--3 {\mathrm{}}^{2}$${P}_{3/2},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 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 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.
We report the efficient transverse deflection of all atoms in a well-collimated sodium atomic beam by the spontaneous radiation pressure of a beam of resonance light which illuminates the atomic beam at right angles. Our results are obtained using two cw single-mode dye lasers to excite the two ground-state levels of sodium; this enables all atoms to interact with the light and it also eliminates optical pumping of the ground state. We obtained deflection angles greater than 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ rad which was ten times the divergence angle of the undeflected atomic beam; these deflections are due to the spontaneous scattering of more than 200 photons by each atom. The distribution of deflection angles is well described by a simple calculation. Fitting theory to experiment indicates that a fractional atomic excitation of 24 percent was obtained at an intensity of approximately 1 W/cm2{\mathrm{cm}}^{2}cm2. When single-frequency light was used, only a fraction of the atoms were deflected, and the deflection angles were much smaller due to optical pumping.
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 report here measurements of two-body photoassociative ionization collisions between sodium atoms within an ultranarrow velocity class selected from a well-collimated, thermal atomic beam. Doppler-shifted excitation of the Na(3s2{\mathrm{}}^{2}2S1/2{\mathit{S}}_{1/2}S1/2​;F=1)\ensuremath{\rightarrow}Na(5p2{\mathrm{}}^{2}2P3/2{\mathit{P}}_{3/2}P3/2​) transition at 285 nm by a single-mode laser defines the narrow velocity class that subsequently populates the F=2 hyperfine level of the Na ground state by optical pumping. Probe laser beam excitation tuned near the Na(3s2{\mathrm{}}^{2}2S1/2{\mathit{S}}_{1/2}S1/2​;F=2)\ensuremath{\rightarrow}Na(3p2{\mathrm{}}^{2}2P3/2{\mathit{P}}_{3/2}P3/2​;F=3) transition produced photoassociative ionization with an average collision energy EK{\mathit{E}}_{\mathit{K}}EK​ corresponding to a temperature of 5.3 mK (EK{\mathit{E}}_{\mathit{K}}EK​=3/2kT). We determine the rate constant for the process as a function of probe beam intensity and polarization.
Two intersecting laser beams of orthogonal circular polarization near resonant to the homogeneously broadened D1 transition of Na vapor were observed to deflect each other upon contact. The experimental results are in good agreement with calculations based on a model which includes diffraction and a local nonlinear atomic susceptibility wihch fully takes into account saturation and optical pumping effects. The contact deflection (or ``bouncing'') was also observed when both beams were tuned to the atomic resonance frequency.