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During the last decade there has been a great deal of interest in ultra-cold atomic gases, atomic Bose-Einstein condensates (BECs) and the degenerate Fermi gases. Ultra-cold atomic gases are systems there the atomic physics meets the condensed matter physics. Unlike electrons or holes in solids, atoms forming quantum gases are electrically neutral particles and there is no vector potential type interaction coupling the atoms with a magnetic field. Consequently there is no direct analogy between the magnetic phenomena of solids and the degenerate atomic gases. The usual way to produce an articifial magnetic field is to rotate the atomic gases so that the vector potential will appear in the rotating frame of reference. Yet stirring an ultra-cold cloud of atoms in a controlled manner is a rather demanding task. A significant experimental advantage would be gained if a more direct way could be used to induce an effective magnetic field.
In the present contribution we consider an alternative method of creating an effective magnetic field based on light-induced gauge potentials for atoms with space-depended dark states [1-5]. A dark state is created if three-level Lambda-type atoms interact with two laser fields under conditions of electromagnetically induced transparency (EIT). If the dark state is space dependent, a vector gauge potential arises for the adiabatic center-of-mass motion. As shown in [1-3] the vector potential is associated with a non-vanishing magnetic field, if at least one of the two light beams has a vortex, i.e. an orbital angular momentum (OAM). Recently we have explored an alternative scheme [4] that does not require light beams to poses an OAM with respect to their propagation axis. This can be achieved by two counter-propagating and overlapping laser beams with shifted spatial profiles. This configuration allows a planar geometry and a non-vanishing flow of atoms, e.g. an atomic BEC moving along an atomic waveguide. Finally we have show that the adiabatic motion of ultra-cold, multi-level atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist [5]. A pair of such degenerate dark states emerges, e.g. if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component. 1. G. Juzeliunas and P. Öhberg, Phys. Rev. Lett. 93, 033602 (2004). 2. G. Juzeliunas, P. Öhberg, J. Ruseckas, and A. Klein, Phys. Rev. A 71, 053614 (2005). 3. P. Öhberg, G. Juzeliunas, J. Ruseckas and M. Fleischhauer. Phys. Rev. A 72, 053632 (2005). 4. G. Juzeliūnas, J. Ruseckas, P. Öhberg and M. Fleischhauer, Submitted to Phys. Rev. A; arXiv quant-ph/0511226. 5. J. Ruseckas, G. Juzeliunas, P. Öhberg, and M. Fleischhauer, Phys. Rev. Lett. 95, 010404 (2005). |
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