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Annual Meeting Optical Society of America

Atomic excitation by a pulse train II: sodium

Lee C. Bradley

Published Jan 1, 1990• 0 citations
Publisher

Abstract

Compared to a hypothetical two-level atom, the sodium atom has a more complex structure with both Zeeman and hyperfine levels. When an assembly of such atoms is illuminated by a pulse train, the excitation is made more complex by the phenomenon of optical pumping. It is well known that pro longed excitation of the 2S1/2 - 2P3/2 transition by circularly polarized light leads to a steady state in which the atoms oscillate exclusively between the F = 2, MF = 2 ground level and the F = 3, MF = 3 excited level. The pumping is comparatively slow, so the temporal behavior is important, and the steady state may not be attained in practice. The dynamics of this process will be explained.

DOI
10.1364/oam.1990.tue6

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Compared to a hypothetical two-level atom, the sodium atom has a more complex structure with both Zeeman and hyperfine levels. When an assembly of such atoms is illuminated by a pulse train, the excitation is made more complex by the phenomenon of optical pumping. It is well known that pro longed excitation of the 2S1/2 - 2P3/2 transition by circularly polarized light leads to a steady state in which the atoms oscillate exclusively between the F = 2, MF = 2 ground level and the F = 3, MF = 3 excited level. The pumping is comparatively slow, so the temporal behavior is important, and the steady state may not be attained in practice. The dynamics of this process will be explained.
Optical experiments in alkali-metal atomic gases are usually interpreted in terms of the J=1/2 ground state, treating the electronic ground state as a degenerate two-level system. While this simplified level scheme has been quite successful in describing many experimental results, the nuclear spin can lead to significant modifications of the behavior. Apart from the obvious differences, such as the existence of hyperfine splitting, some more subtle effects are present that modify the dynamical as well as the equilibrium behavior of the system. An an example, the optical pumping process in the true atomic ground state is nonexponential and slower by at least an order of magnitude, compared to a hypothetical atom with nuclear spin zero. The limitations of the J=1/2 model are analyzed theoretically and experimentally for atomic sodium, and experimental methods are demonstrated that can help disentangle the contributions from different hyperfine components.
An assembly of ground-state two-level atoms with a Maxwellian velocity distribution is considered to be illuminated by a near-resonant train of Gaussian pulses whose pulse separation is of the same order of magnitude as the natural decay time of the upper state by spontaneous emission. The equations of motion of the density matrix, including spontaneous decay, are numerically integrated over the duration of one pulse and are analytically integrated between pulses. In this way, the transition matrix is derived. The time evolution of the system is then followed by successive multiplications of the state vector by the transition matrix. Steady state is attained after a few pulses. Because the pulse train has side bands separated by the pulse repetition frequency, corresponding velocity groups are preferentially excited. The response (defined as the time-average spontaneous emission of the assembly) is found to be a quasi-sinusoidal function of the number of Rabi flops per pulse. Frequency modulation of the pulse train leads to smaller variation in the response and, consequently, to considerably higher response.
Optical experiments in alkali-metal atomic gases are usually interpreted in terms of the J=1/2 ground state, treating the electronic ground state as a degenerate two-level system. While this simplified level scheme has been quite successful in describing many experimental results, the nuclear spin can lead to significant modifications of the behavior. Apart from the obvious differences, such as the existence of hyperfine splitting, some more subtle effects are present that modify the dynamical as well as the equilibrium behavior of the system. An an example, the optical pumping process in the true atomic ground state is nonexponential and slower by at least an order of magnitude, compared to a hypothetical atom with nuclear spin zero. The limitations of the J=1/2 model are analyzed theoretically and experimentally for atomic sodium, and experimental methods are demonstrated that can help disentangle the contributions from different hyperfine components.
A new method has been designed for obtaining the hyperfine optical pumping of Na vapor. The pumping lamp is placed in a magnetic field and the light emitted in the field direction is used for excitation after crossing a circular polarizer selecting one of the Zeeman lines. This method has two interesting features: (i) The atoms can be pumped either in the lower or in the upper hyperfine sublevel by simply rotating a polarizer by an angle of $\frac{1}{2}\ensuremath{\pi}$; (ii) the hyperfine pumping is obtained using both the D1{D}_{1}D1​ and D2{D}_{2}D2​ resonance lines without filtering losses. The pumping efficiency is good and it has been possible to measure the spin-exchange cross section between sodium atoms by studying the hyperfine relaxation rates as a function of the sodium density. The result is ${\ensuremath{\sigma}}_{\mathrm{ex}}=(1.109\ifmmode\pm\else\textpm\fi{}0.005)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2.
The steady-state absorption of a beam of sodium atoms irradiated by a train of pulses from a mode-locked dye laser has been measured. The sodium atoms were prepared as two-level systems by optical pumping with a two-mode laser. Absorption spectra on the 589.0-nm D2 line were recorded over 20 GHz with a frequency-stabilized, tunable, mode-locked dye laser having a bandwidth of 3.7 GHz and a mode spacing of 82 MHz. The laser-pulse profile was determined from the spectral profile assuming transform-limited pulses and was incorporated in theoretical calculations of excitation spectra obtained by numerical integration of the optical Bloch equations. By comparison of measured absorption spectra and theoretical excitation spectra the validity of the weak-field solution as well as the predicted saturation behavior were fully verified by the experimental results. For the highest level of irradiation applied, the laser pulses were identified as π pulses.