We have experimentally and theoretically investigated the behavior of excited Na atoms under the combined influence of resonant laser light and a weak magnetic field. The use of weak magnetic fields gives another possibility to vary the polarization of the atoms, additional to variation of the polarization of the exciting laser. We calculated in detail the influence of weak magnetic fields on the density matrix describing the excited atoms, using generalized rate equations. We checked the results of our model experimentally, at the Na(3 2 S1/2, Fl=2) →(3 2 P3/2, Fu =3) transition, excited with circularly polarized light. We determined the polarization of the excited atoms, by measuring the fluorescence light at various angles, as a function of both magnetic field strength and laser irradiance. Model and experiment agreed very well. We applied our model to the associative ionization of the excited Na atoms. We measured the ion signal as a function of magnetic field. Analyzing the results, we could determine a specific associative ionization cross section, which is not accessible in our experimental geometry without the use of magnetic fields. Thereby we showed that the application of magnetic fields in polarization dependence studies can provide us with additional information about the process.
We present experimental results and a theoretical model that illustrate how competing eigenbases can determine the dynamics of a fluorescing atom. In the absence of a magnetic field, the atom can get trapped in a dark state, which inhibits fluorescence. In general, this will happen when the magnetic degeneracy of the ground state is greater than the one of the excited state. A canonical way to avoid optical pumping to dark states is to apply a magnetic field at an angle with respect to the polarization of the exciting light. This generates a competition of eigenbases which manifests as a crossover between two regimes dominated either by the laser or the magnetic field. We illustrate this crossover with fluorescence measurements on a single laser-cooled calcium ion in a Paul trap and find that it occurs at a critical laser intensity that is proportional to the external magnetic field. We contrast our results with numerical simulations of the atomic levels involved and also present a simple theoretical model that provides excellent agreement with experimental results and facilitates the understanding of the dynamics.
In a previous paper, I have presented a general theory of the optical pumping of atoms by a polarized multimode-laser beam, in the presence of a magnetic field. Equations of motion, valid at arbitrary laser intensities for the density matrix of the atomic system, have been obtained. In this paper, these equations are exactly solved for a linearly $\ensuremath{\sigma}$-polarized laser and levels having small angular momenta. More precisely, I consider the laser transitions ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=0$, ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=1$, and ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$. Two particular results are emphasized: (i) For $J=1\ensuremath{-}J=0$ and $J=1\ensuremath{-}J=1$ transitions and for the
J=2 level of a $J=1\ensuremath{-}J=2$ transition, the laser-induced Hanle effects keep a Lorentzian shape, independent of the laser intensity. For the $J=1\ensuremath{-}J=1$ transition, it is shown that the depolarizing relaxation processes play a leading part in the coupling induced by the laser between the transverse alignments of the two levels. On the other hand, the power broadenings of the Hanle effects are shown to be similar. For the
J=1 level of a $J=1\ensuremath{-}J=2$ transition, the Hanle-effect shape presents a departure from the Lorentzian one, owing to a coupling with the laser-induced hexadecapole moment in the
J=2 level. (ii) The populations of the levels exhibit a "zero-field saturation resonance" which is due to the coupling with the Zeeman coherences. These resonances, which reproduce the Hanle effects of the transition, can be observed on the $\ensuremath{\pi}$-polarized fluorescence from the levels. In general, these resonances appear as a saturation effect, i.e., they reduce the laser-induced fluorescence of the levels in zero magnetic field. However, for the ${J}_{b}=1\ensuremath{\rightarrow}{J}_{a}=2$ transition, the ${J}_{a}=2\ensuremath{\rightarrow}{J}_{f}=2 \ensuremath{\pi}$ fluorescence presents an anomalous behavior; the saturation resonance increases the zero-field laser-induced fluorescence. The theoretical study shows the prominent part played by the value of the
Jb=1 level lifetime in the interpretation of this anomaly. Other results, such as the laser-induced depolarization of the fluorescence, are also obtained. All the theoretical predictions have been experimentally checked and will be presented in forthcoming papers.
We investigate the population differences between ground-state hyperfine levels (
5S1/2,F=2 and
5S1/2, F=1) of an optically pumped
87Rb beam in a static magnetic field, taking into account the various kinds of atomic coherence (Zeeman, hyperfine, and optical). The pumping lasers are monochromatic and in resonance with the ${(5S}_{1/2},F=1\ensuremath{\leftrightarrow}{5P}_{1/2}{,F}^{\ensuremath{'}}=1)$ transition. By varying the polarization configuration of the pumping lasers, we find that the pumping efficiency is substantially enhanced when a $\ensuremath{\sigma}$-polarized laser and a $\ensuremath{\pi}$-polarized laser are counterpropagating. In this case, the pumping efficiency remains high even in a weak magnetic field, which explains qualitatively experimental data reported previously from a cesium beam experiment.
We report detailed studies of the dynamic response of spin coherence to a step input of optically resonant narrow-band laser radiation in the presence of a static transverse magnetic field. The evolution of the spins is observed with a cw optical probe beam using polarization-selective detection of the transmitted light. In extension of previous optical-pumping experiments, the dynamics of the system are studied systematically as a function of optical-resonance detuning and intensity. Our experiments are performed on the 3s
2S1/2 ground state of sodium, using the
D1 line for optical excitation. The experimental data are compared with theoretical predictions based on a Bloch-type equation of motion for an optically driven spin system in a J=(1/2 ground state.
We have studied theoretically and experimentally the effect of a relatively strong magnetic field on sub-Doppler laser cooling in a one-dimensional optical molasses. We used the operator description of laser cooling with the Larmor precession frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$ being much higher than the optical pumping rate. We found velocity-selective resonances (VSR) in the force at velocities
vr=n${\mathrm{\ensuremath{\omega}}}_{\mathit{Z}}$, with n=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2 for both the scattering and redistribution force operators. These depend on the relative direction of the magnetic field and the polarization vectors of the light beams. Analytical results for the force on the atom are obtained in two cases that illustrate the effect of the VSR on the force. These formulas are compared with numerical calculations of the force. We also discovered a redistribution mechanism that relies on the gradient of the eigenstates of the light-shift operator, with eigenvalues that are independent of position so that a ``Sisyphus cooling'' picture does not apply. The theory is compared with many experimental results and excellent agreement is found. We believe that all essential features of laser cooling at low intensity are well described by this operator theory.