Detailed studies of non-linear magneto-optical resonances at D1 excitation of Rb-85 and Rb-87 for partially resolved hyperfine F-levels

Experimental signals of non-linear magneto-optical resonances at D1 excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The D1 transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. Great care was taken to obtain accurate experimental signals and avoid systematic errors. The experimental signals were reproduced very well at each hyperfine transition and over a wide range of laser power densities, beam diameters, and laser detunings from the exact transition frequency. The bright resonance expected at the F_g=1 --> F_e=2 transition of Rb-87 has been observed. A bright resonance was observed at the F_g=2 --> F_e=3 transition of Rb-85, but displaced from the exact position of the transition due to the influence of the nearby F_g=2 --> F_e=2 transition, which is a dark resonance whose contrast is almost two orders of magnitude larger than the contrast of the bright resonance at the F_g=2 --> F_e=3 transition. Even in this very delicate situation, the theoretical model described in detail the experimental signals at different laser detunings.Comment: 11 pages, 9 figure

Nonlinear magneto-optical resonances at D1 excitation of 85Rb and 87Rb in an extremely thin cell

Nonlinear magneto-optical resonances have been measured in an extremely thin cell (ETC) for the D1 transition of rubidium in an atomic vapor of natural isotopic composition. All hyperfine transitions of both isotopes have been studied for a wide range of laser power densities, laser detunings, and ETC wall separations. Dark resonances in the laser induced fluorescence (LIF) were observed as expected when the ground state total angular momentum F_g was greater than or equal to the excited state total angular momentum F_e. Unlike the case of ordinary cells, the width and contrast of dark resonances formed in the ETC dramatically depended on the detuning of the laser from the exact atomic transition. A theoretical model based on the optical Bloch equations was applied to calculate the shapes of the resonance curves. The model averaged over the contributions from different atomic velocity groups, considered all neighboring hyperfine transitions, took into account the splitting and mixing of magnetic sublevels in an external magnetic field, and included a detailed treatment of the coherence properties of the laser radiation. Such a theoretical approach had successfully described nonlinear magneto-optical resonances in ordinary vapor cells. Although the values of certain model parameters in the ETC differed significantly from the case of ordinary cells, the same physical processes were used to model both cases. However, to describe the resonances in the ETC, key parameters such as the transit relaxation rate and Doppler width had to be modified in accordance with the ETC's unique features. Agreement between the measured and calculated resonance curves was satisfactory for the ETC, though not as good as in the case of ordinary cells.Comment: v2: substantial changes and expanded theoretical model; 13 pages, 10 figures; accepted for publication in Physical Review

Conversion of bright magneto-optical resonances into dark at fixed laser frequency for D2 excitation of atomic rubidium

Nonlinear magneto-optical resonances on the hyperfine transitions belonging to the D2 line of rubidium were changed from bright to dark resonances by changing the laser power density of the single exciting laser field or by changing the vapor temperature in the cell. In one set of experiments atoms were excited by linearly polarized light from an extended cavity diode laser with polarization vector perpendicular to the light's propagation direction and magnetic field, and laser induced fluorescence (LIF) was observed along the direction of the magnetic field, which was scanned. A low-contrast bright resonance was observed at low laser power densities when the laser was tuned to the Fg=2 --> Fe=3 transition of Rb-87 and near to the Fg=3 --> Fe=4 transition of Rb-85. The bright resonance became dark as the laser power density was increased above 0.6mW/cm2 or 0.8 mW/cm2, respectively. When the Fg=2 --> Fe=3 transition of Rb-87 was excited with circularly polarized light in a second set of experiments, a bright resonance was observed, which became dark when the temperature was increased to around 50C. The experimental observations at room temperature could be reproduced with good agreement by calculations based on a theoretical model, although the theoretical model was not able to describe measurements at elevated temperatures, where reabsorption was thought to play a decisive role. The model was derived from the optical Bloch equations and included all nearby hyperfine components, averaging over the Doppler profile, mixing of magnetic sublevels in the external magnetic field, and a treatment of the coherence properties of the exciting radiation field.Comment: 9 pages, 7 figure

Cascade coherence transfer and magneto-optical resonances at 455 nm excitation of Cesium

We present and experimental and theoretical study of nonlinear magneto-optical resonances observed in the fluorescence to the ground state from the 7P_{3/2} state of cesium, which was populated directly by laser radiation at 455 nm, and from the 6P_{1/2} and 6P_{3/2} states, which were populated via cascade transitions that started from the 7P_{3/2} state and passed through various intermediate states. The laser-induced fluorescence (LIF) was observed as the magnetic field was scanned through zero. Signals were recorded for the two orthogonal, linearly polarized components of the LIF. We compared the measured signals with the results of calculations from a model that was based on the optical Bloch equations and averaged over the Doppler profile. This model was adapted from a model that had been developed for D_1 and D_2 excitation of alkali metal atoms. The calculations agree quite well with the measurements, especially when taking into account the fact that some experimental parameters were only estimated in the model.Comment: small changes to text of previous version; 12 pages, 8 figure

Twenty-three unsolved problems in hydrology (UPH) – a community perspective

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through on-line media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focussed on process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come