We present an experimental scheme performing scalar magnetometry based on the fitting of Rb D 2 line spectra recorded by derivative selective reflection spectroscopy from an optical nanometric-thick cell. To demonstrate its efficiency, the magnetometer is used to measure the inhomogeneous magnetic field produced by a permanent neodimuim-iron-boron alloy ring magnet at different distances. The computational tasks are realized by relatively cheap electronic components: an Arduino Due board for the external control of the laser and acquisition of spectra, and a Raspberry Pi computer for the fitting. The coefficient of variation of the measurements remains under 5% in the magnetic field range of 40 -200 mT, limited only by the size of the oven and translation stage used in our experiment. The proposed scheme is expected to operate with a high measurement precision also for stronger magnetic fields (> 500 mT), in the hyperfine Paschen-Back regime, where the evolution of the atomic transitions can be calculated with a high accuracy.
Abstract⎯We study the nonlinear mean-field dynamics of molecule formation at coherent photo-and magneto-association of an atomic Bose-Einstein condensate for the case when the external field configuration is defined by the quasi-linear level crossing Demkov-Kunike model, characterized by a bell-shaped pulse and finite variation of the detuning. We present a general approach to construct an approximation describing the temporal dynamics of the molecule formation in the weak interaction regime and apply the developed method to the nonlinear Demkov-Kunike problem. The presented approximation, written as a scaled solution to the linear problem associated to the nonlinear one we treat, contains fitting parameters which are determined through a variational procedure. Assuming that the parameters involved in the solution of the linear problem are not modified, we suggest an analytical expression for the scaling parameter.
Abstract-In the framework of a basic semiclassical time dependent nonlinear two state problem, we study the weak coupling limit of the nonlinear Landau-Zener transition at coherent photo and magneto associ ation of an atomic Bose-Einstein condensate. Using an exact third order nonlinear differential equation for the molecular state probability, we develop a variational approach which enables us to construct an accurate analytic approximation describing time dynamics of the coupled atom molecular system for the case of weak coupling. The approximation is written in terms of the solution to an auxiliary linear Landau-Zener problem with some effective Landau-Zener parameter. The dependence of this effective parameter on the input Lan dau-Zener parameter is found to be unexpected: as the generic Landau-Zener parameter increases, the effective Landau-Zener parameter first monotonically increases (starting from zero), reaches its maximal value and then monotonically decreases again reaching zero at some point. The constructed approximation quantitatively well describes many characteristics of the time dynamics of the system, in particular, it provides a highly accurate formula for the final transition probability to the molecular state. The present result for the final transition probability improves the accuracy of the previous approximation by Ishkhanyan et al.
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