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Journal of the Optical Society of America B

Saturation of multistate atoms

Juha Javanainen

Published Apr 1, 1993• 13 citations
Publisher

Abstract

Position-averaged excited-state fraction as a function of laser intensity is computed for several angular-momentum degenerate atomic transitions for the lin ‖ lin optical molasses and the magnetic molasses trap field with either fixed or random temporal phases. The results are summarized in a concise, accurate functional form with three fitted parameters.

DOI
10.1364/josab.10.000572

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We present a semiclassical laser-cooling theory for an ion bound in a quadratic potential well, allowing for an arbitrary internal level scheme of the ion and an arbitrary polarization of the light field. The special case that the ion moves in a region much smaller than the wavelength of the exciting light (Lamb-Dicke limit), as well as an additional low-intensity limit, are worked out in detail. Explicit general expressions are given for the damping and diffusion tensors of the center-of-mass motion of the ion, and the light-induced renormalization of the mechanical oscillation frequencies is discussed. The formalism is implemented analytically using a computer program mathematica for an ion with a j=1/2\ensuremath{\rightarrow}j=3/2 transition moving in a one-dimensional optical molasses consisting of two counterpropagating laser beams with perpendicular linear polarizations (lin \ensuremath{\perp} lin). For a weakly bound ion at negligible saturation, the greatest lower limit of excitation energy turns out to be (33/20)1/2{)}^{1/2})1/2-1/2\ensuremath{\approxeq}0.78 vibrational quanta above the zero-point energy.
We present the theory for a technique, based on multistate variants of the stimulated Raman adiabatic passage (STIRAP) process, that allows efficient and robust preparation of a preselected superposition of two or three degenerate states (magnetic sublevels of an atom) and the measurement of their relative amplitudes and phases. Because the preparation utilizes adiabatic passage it is robust against small fluctuations of the Rabi frequencies and temporal shapes of the coupling fields. We here describe and, in the following companion paper we demonstrate, an approach to the experimental characterization of the superposition state, i.e., the measurement of the relative phases and the ratios of amplitudes of the components. That technique, termed phase-to-population mapping, is applicable to the characterization of a stream of identically prepared atoms and is based on laser-induced fluorescence after the atoms have undergone optical pumping cycles induced by an additional laser. The optical pumping process maps the phase into populations of a subset of levels by means of a filtering laser field, and is robust against variations in the intensity and detuning of that field. We describe four linkage patterns appropriate to the creation of superpositions of two or three degenerate states of angular momentum J=2J=2J=2, starting from J=0J=0J=0. We offer an interpretation, from three different perspectives, of the subsequent characterization procedure.
Deep laser cooling of 24Mg^{24}\mathrm{Mg}24Mg atoms has been theoretically studied. We propose a two-stage sub-Doppler cooling strategy using electrodipole transition $3\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{2}\ensuremath{\rightarrow}3\phantom{\rule{0.16em}{0ex}}{}^{3}{D}_{3}$ ($\ensuremath{\lambda}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}383.8$ nm). The first stage implies exploiting magneto-optical trap with ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ light beams, while at the second stage lin $\ensuremath{\perp}$ lin molasses is used. We focus on achieving a large number of ultracold atoms (${T}_{\mathrm{eff}}<10 \ensuremath{\mu}\mathrm{K}$) in a cold-atomic cloud. The calculations have been based on quantum treatment, taking into full account the recoil effect and beyond many widely used approximations. Steady-state values of average kinetic energy and linear momentum distributions of cold atoms have been analyzed for various light-field intensities and frequency detunings. The results of conducted quantum analysis have been significantly different from the results achieved under a semiclassical approximation based on the Fokker-Planck equation. The second cooling stage allows achieving sufficiently lower kinetic energies of the atomic cloud as well as increased fraction of ultracold atoms at certain conditions compared to the first one. We hope that the obtained results can help in overcoming current experimental problems in deep cooling of 24Mg^{24}\mathrm{Mg}24Mg atoms by means of laser field. Cold magnesium atoms cooled in a large amount to several $\ensuremath{\mu}\mathrm{K}$ are of huge interest to, for example, quantum metrology and to other many-body cold-atoms physics.