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arXiv:quant-ph/0111018 · Physical Review A

Destabilization of dark states and optical spectroscopy in Zeeman-degenerate atomic systems

Dana J. Berkeland, M. G. Boshier

Published Feb 26, 2002• 186 citations
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Abstract

We present a general discussion of the techniques of destabilizing dark states in laser-driven atoms with either a magnetic field or modulated laser polarization. We show that the photon-scattering rate is maximized at a particular evolution rate of the dark state. We also find that the atomic-resonance curve is significantly broadened when the evolution rate is far from this optimum value. These results are illustrated with detailed examples of destabilizing dark states in some commonly trapped ions and supported by insights derived from numerical calculations and simple theoretical models.

DOI
10.1103/physreva.65.033413

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We present a general discussion of the techniques of destabilizing dark states in laser-driven atoms with either a magnetic field or modulated laser polarization. We show that the photon-scattering rate is maximized at a particular evolution rate of the dark state. We also find that the atomic-resonance curve is significantly broadened when the evolution rate is far from this optimum value. These results are illustrated with detailed examples of destabilizing dark states in some commonly trapped ions and supported by insights derived from numerical calculations and simple theoretical models.
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.
A significant problem in laser cooling of molecules is the presence of the dark Zeeman sublevels. Herein, a detailed theoretical and experimental study of destabilizing the dark states is reported in magnesium monofluoride molecules. By applying an external magnetic field, the Zeeman sublevels are made to be time dependent and nondegenerate, forcing the dark states to Larmor precess into the bright states. It is found that the laser induced fluorescence signal depends on the angle and the magnitude of the magnetic field. Theoretical calculations are performed by solving the density matrix equations for the multiple-level system, which shows good agreement with experimental data. This study may provide a useful perspective for continuous efforts toward laser cooling of MgF molecules.
Coherent dark states in atoms, created by simultaneous interaction of two coherent light fields with a 3-level system, are of prime importance in quantum state manipulation. They are used extensively in quantum sensing and quantum information applications to build atomic clocks, magnetometers, atomic interferometers and more. Here we study the formation and decay of coherent dark-states in an ensemble of laser-cooled free-falling atoms. We measure the optical-pumping rate into the dark-state in the σ+−σ−σ^+-σ^-σ+−σ− polarization configuration. We find that the pumping rate is linear with the optical field intensity, but about an order-of-magnitude slower than the rate predicted by the commonly used, but simplistic, three-level analytic formula. Using a numerical model we demonstrate that this discrepancy is due to the multi-level Zeeman manifold. Taking into account the slower pumping rate we explain quantitatively the relation between the light-shift and the duration of pumping into dark-state in Ramsey spectroscopy. We also measure the decay of the dark-state coherence and find that in our apparatus it is dominated by the mechanical motion of the atoms out of the probing region, while the atomic decoherence is negligible.
Theoretical study and computer modeling results of the spectra of coherent dark resonances resulted from excitation of Zeeman sublevels of the Fg=2→Fe=1 transition of the D1 line in 87Rb atoms by a frequency-modulated laser field are presented and discussed in detail. The influence of the nonlinear Zeeman effect on the structure of the coherent dark resonances is observed. It is shown that calculated for different values of the magnetic field spectra are in a good agreement with the experimental data.
The effect of a dc magnetic field on the rate at which a ground-level, Zeeman-degenerate atom is photoionized via a short-lived autoionizing level is calculated. We consider single-step as well as two-step photoionization; in the latter case we allow the light to be either resonant or far from resonance with an intermediate level. In all cases we find that the magnetic field may raise the fraction of the atoms available for photoionization and consequently increase the photoion fraction produced by a light pulse of given fluence. In the resonant case we find that if the magnetic-field Zeeman splitting of the ground and intermediate level is much larger than the rate at which population enters or leaves that level then the Zeeman-state populations are decoupled from one another and there exist simple conditions under which they obey rate equations. In the nonresonant case an additional condition for two-photon rate equations is that the optical Stark shift of the ground state be much smaller than the magnetic Zeeman splitting. These results apply specifically to excitation by lasers whose spectral widths are narrow compared to the homogeneous linewidths of the corresponding atomic transitions, but appear to be generalizable to the opposite limit, in which the laser spectral widths are much broader than the homogeneous linewidths.
Abstract We present a thorough analysis of a Zeeman slower for sodium atoms made of permanent magnets in a Halbach configuration. Due to the orientation of the magnetic field, the polarization of the slowing laser beam cannot be purely circular, leading to optical leakages into dark states. To circumvent this effect, we propose an atomic state preparation stage that is able to significantly increase the performance of the Zeeman slower. After a careful theoretical analysis of the problem, we experimentally implement an optical pumping stage leading to an increase in the magneto-optical trap loading rate by 3.5. Such a method is easy to set up and could be extended to other Zeeman slower architectures.