Eur. Phys. J. D 48, 111–119 (2008) DOI: 10.1140/epjd/e2008-00068-4 T HE EUROPEAN P HYSICAL JOURNAL D Characterization of a magnetic trap by polarization dependent Zeeman spectroscopy C.V. Nielsen, J.K. Lyngsø, A. Thorseth, M. Galouzis, K.T. Therkildsen, E.D. van Ooijen, and J.W. Thomsen a The Niels Bohr Institute, Universitetsparken 5, 2100 Copenhagen, Denmark Received 18 July 2007 / Received in final form 18 January 2008 Published online 18 April 2008 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2008 Abstract. This paper demonstrates a detailed experimental study of our cloverleaf magnetic trap for sodium atoms. By using polarization dependent Zeeman spectroscopy of our atomic beam, passing the magnetic trap region, we have determined important trap parameters such as gradients, their curvatures and corresponding trap frequencies. Experimental findings are compared to theoretical calculations as well as complementary methods of characterizing the trap. PACS. 32.60.+i Zeeman and Stark effects – 42.30.-d Imaging and optical processing – 07.55.Ge Magnetometers for magnetic field measurements 1 Introduction The interest in cooling and magnetic trapping of neutral atoms and molecules has accelerated significantly during the past ten years. The workhorse in most cases is the magneto-optical trap (MOT) [1], in which atoms can be cooled and confined to a temperature of typically 100 μK at densities of the order of 10 11 cm -3 . The temperature is mainly limited by photon rescattering [2] and therefore other trapping and cooling schemes must be used to cir- cumvent this problem. Most commonly used techniques are optical dipole trapping [3,4] or magnetic trapping. In the latter case, one exploits the interaction between the permanent dipole moment of paramagnetic atoms or molecules with a magnetic field gradient. Several coil ge- ometries have been developed to generate a magnetic field with a local minimum, like a TOP trap [5], Quick trap [6], Baseball trap and a Ioffe-Pritchard trap [7]. All these traps possess a non-zero magnetic field minimum, B 0 , to prevent Majorana losses [8]. Atoms trapped in such magnetic traps (low field seek- ers) can be cooled further by applying evaporative cool- ing techniques [9,10]. Here the most energetic atoms are removed by spin-flipping to a high-field seeking state by applying a resonant radio frequency field. The remaining atoms rethermalize to lower temperatures. For optimal transfer from MOT to magnetic trap and for optimizing the process of forced evaporation [5], where the radio frequency field is continuously lowered with a certain rate, it is desirable to know trapping parameters such as the magnetic field gradient and B 0 . Furthermore, at low temperatures and high densities, where degeneracy a e-mail: jwt@fys.ku.dk is reached, it is essential to know the trapping frequencies in order to determine important experimental parameters such as the critical temperature (T c ). Measuring the magnetic field with Hall probes is usually performed, but as the actual trap region to be analyzed is in vacuum and relatively small, in situ char- acterization with this method is difficult. Numerical cal- culation of the coil geometry can easily be performed at high accuracy, but do not account for possible defects in the field caused by magnetized elements, possible short- cuts between windings, changes in geometry, etc. The motivation of this work was the need for a fast and accurate determination of the trap parameters. Previous work on magnetic field cartography have been done using the mechanical Hanle effect [11]. However, this method lacks spatial resolution and works best at low magnetic fields. A more sophisticated method of measuring mag- netic fields with high sensitivity and resolution have been demonstrated using imaging of Bose-Einstein condensed atoms [12,13]. Our method follows suggestions put for- ward in Courteille et al. [14], which presents a fast and accurate determination of the trap parameters prior to Bose-Einstein condensation. In this paper we present a detailed experimental investigation of our magnetic clover- leaf trap for sodium atoms. Essentially, we image the po- larization dependent fluorescence of thermal atoms pass- ing the magnetic trap monitored by a thin sheet of near resonant light. Experimental findings are compared to the theory presented in [14] and to complementary experimen- tal methods of obtaining trap parameters. The paper is organized as follows. A short introduc- tion of the experimental setup is given, where the prop- erties of the magnetic trap is emphasized. Subsequently, the polarization dependent Zeeman spectroscopy method