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arXiv:2005.05018 · Physical Review A

Competition between factors determining bright versus dark atomic states within a laser mode

Bryan Hemingway, Thomas G. Akin, Steven Peil, J. V. Porto

Published May 7, 2020• 1 citation
arXivHTMLPDF

Abstract

We observe bimodal fluorescence patterns from atoms in a fast atomic beam when the laser excitation occurs in the presence of a magnetic field and the atoms sample only a portion of the laser profile. The behavior is well explained by competition between the local intensity of the laser, which tends to generate a coherent-population-trapping (CPT) dark state in the $J=1$ to ${J}^{\ensuremath{'}}=0$ system, and the strength of an applied magnetic field that can frustrate the CPT process. This work is relevant for understanding and optimizing the detection process for clocks or other coherent systems utilizing these transitions and could be applicable to in situ calibration of the laser-atom interaction, such as the strength of the magnetic field or laser intensity at a specific location.

DOI
10.1103/physreva.101.053410

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We observe bimodal fluorescence patterns from atoms in a fast atomic beam when the laser excitation occurs in the presence of a magnetic field and the atoms sample only a portion of the laser profile. The behavior is well explained by competition between the local intensity of the laser, which tends to generate a coherent-population-trapping (CPT) dark state in the J=1J=1J=1 to J\ensuremath′=0{J}^{\ensuremath{'}}=0J\ensuremath′=0 system, and the strength of an applied magnetic field that can frustrate the CPT process. This work is relevant for understanding and optimizing the detection process for clocks or other coherent systems utilizing these transitions and could be applicable to in situ calibration of the laser-atom interaction, such as the strength of the magnetic field or laser intensity at a specific location.
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.
Summary form only given. We have performed a series of experiments on coherent population trapping (CPT) in the presence of strong magnetic flux densities up to 1 mT. CPT can be observed in /spl Lambda/-systems where two ground states are coupled to a common excited state by two near-resonant light fields. Effective formation of ground state coherences takes place when the frequency difference of the light fields precisely matches the ground state splitting. This process leads to reduced absorption in the medium and thus reduced fluorescence intensity ("dark resonance") at the optical resonance frequency.
Formation of a coherent population trapping (CPT) resonance is studied in the interaction of a beam of atoms with two spatially separated domains of the dichromatic field. Various resonance excitation schemes are compared depending on the choice of operation transitions and type of the polarisation scheme. In the case of a single-velocity atomic beam, the dependence of the CPT resonance profile is studied as a function of principal parameters of the system: beam velocity, distance between optical fields, laser beam dimensions and intensities, and applied permanent magnetic field. Influence of the atomic beam angular divergence and residual beam velocity spread on the resonance quality parameter is estimated.
Phase-dependent coherent population trapping (CPT) was observed using a thermal Na atomic beam irradiated by four laser fields derived from two dye lasers. Investigations were made on Λ- and double Λ-systems created in the D 1 line, both with and without magnetic field that lifts degeneracy of the Zeeman sublevels. In all cases a sharp decrease of fluorescence intensity was observed for certain values of the relative phase of the light waves, indicating that the occurrence of CPT depends on this phase. The shape of the phase dependence as well as its behaviour with respect to laser intensity fits well theoretical predictions.
Coherent population trapping (CPT) is theoretically examined as a magnetic-field diagnostic for high-\ensuremath{\beta} hydrogen plasma. Time-dependent quantum mechanical Bloch equations, which describe the evolution of the 2sss and 3ppp level populations of the hydrogen atom under CPT conditions, were solved numerically. When the frequency difference of two copropagating lasers equals the energy difference between the atoms' levels subject to the local magnetic field, a discernable CPT dark line in the H\ensuremath{\alpha} emission is predicted, enabling the possibility of noninvasive, localized magnetic-field measurements. The effects of fine and hyperfine level structure, Doppler broadening, plasma-generated electric fields, and degree-of-hydrogen ionization are included in the model. A shift in dark-line position of 15% of the linewidth is predicted to be caused by contributions from the entire H\ensuremath{\alpha} manifold. The laser-induced H\ensuremath{\alpha} fluorescence is estimated to be an order of magnitude stronger than the background H\ensuremath{\alpha} emission.
We present a set of exploratory experimental studies of velocity-selective coherent population trapping (VSCPT) on the $2{}^{3}{S}_{1}\ensuremath{\rightarrow}2{}^{3}{P}_{1}$ transition of Helium, including the effect of an external magnetic field along the propagation direction of the light. We also investigate in detail the effects of the laser detuning and the atom-laser interaction time in determining the shape and width of the VSCPT velocity distribution. Our data corroborates some previous theory and calculations. We demonstrate that the only observable effect of a magnetic field applied along the direction of light propagation is to shift the center of the VSCPT peaks in the atomic velocity distribution by an amount proportional to the magnitude of the applied field. We present a semiclassical picture that describes the atomic motion of VSCPT in such a B field.