Electromagnetically induced optical anisotropy of an ultracold atomic medium V.M. Datsyuk, I.M. Sokolov, and D.V. Kupriyanov Department of Theoretical Physics, State Polytechnic University, 195251, St.-Petersburg, Russia * M.D. Havey Department of Physics, Old Dominion University, Norfolk, VA 23529 † (Dated: September 25, 2007) We consider radiative transport in ultracold atomic systems under conditions of electromagnet- ically induced transparency. We calculate the macroscopic susceptibility and scattering tensors of the light and show that essential anisotropic optical properties such as dichroism and birefringence naturally appear. In such a case, light propagation through a spatially non-homogeneous atomic cloud is considered for an arbitrary direction of the probe light. We determine the polarization properties of the coherently transmitted probe light as well as the polarization dependence of light incoherently scattered in an arbitrary direction. Both the steady state regime and time-dependent case are discussed. Concrete calculations are performed for the case of an inhomogeneous and ultracold sample of 87 Rb atoms. PACS numbers: 34.50.Rk, 34.80.Qb, 42.50.Ct, 03.67.Mn I. INTRODUCTION In the last decade, control of optical properties of matter by means of auxiliary electromagnetic fields has attracted significant scientific and technical attention. Electromagnetically induced atomic coherence changes the optical properties of atomic samples in sometimes dramatic ways, and is responsible for such effects as co- herent population trapping, electromagnetically induced transparency, ”slow light”, ”stopped light,” to name a few [1–3]. Interest in these effects is partly determined by their possible applications in several broad fields, in- cluding optical communications, atomic timekeeping and atomic memories, light amplification and lasing without inversion. Recently more detailed attention has been paid to po- larization phenomena under electromagnetically induced transparency (EIT) in atomic media. Due to optical selection rules and different dipole moments of various atomic transitions, polarized coupling fields act differ- ently on different Zeeman sublevels and consequently dis- turbs them distinctly. On the one hand these general conditions lead to a strong influence of coupling light po- larization on EIT. On the other, they give the possibility of control of the polarization properties of the probe light by means of such effects as induced dichroism and bire- fringence. By now polarization phenomena under EIT have been investigated both for multilevel ladder-type [4–8] and for lambda-type atomic energy level configurations [9–11]. In the past few years, several groups have also experi- mentally studied the influence of a static magnetic field on the polarization sensitivity of EIT. Particularly, elec- * Electronic address: IMS@IS12093.spb.edu † Electronic address: mhavey@odu.edu tromagnetically induced magnetochiral anisotropy in a resonant medium has been predicted and experimentally demonstrated in [12, 13]. The influence of a magnetic field on creation and retrieval of polaritonic excitations in stopped light experiments has been considered in [14, 15]. In spite of no apparent lack of publications in this area, some aspects of polarization phenomena under EIT con- ditions have not been adequately explored. For exam- ple, nearly all theoretical studies have been done for a collinear geometry of control and probe light, i.e. in the case when the propagation direction of the fields coincide. At the same time, noncollinear geometry is interesting from several different points of view. First, some ex- periments on slow light and electromagnetically induced transparency have been done in such geometry, for ex- ample, the remarkable investigations of Hau et al. [16]. Second, noncollinearity of the pump and probe beams influences the line width of the EIT resonance. This is evidently very important for such quantum metrology de- vices as quantum frequency standards and high precision magnetometers based on narrow EIT resonances [17–19]. Finally, but more generally, we deal with a noncollinear geometry every time we consider incoherent light scatter- ing. In this case, the scattered light can propagate in an arbitrary direction with respect to the control light wave vector even if the initial directions of both fields coincide. Though incoherent scattering can be essential in exper- iments on EIT (see for example [20–22]) the anisotropic effect in such a case has not been studied in detail. The main goal of the present paper is to consider in detail optical anisotropy of atomic ensembles under conditions of electromagnetically induced transparency. Within the framework of that goal we will study po- larization properties of the light transmitted (coherently forward scattered) through the atomic ensemble in an arbitrary direction with respect to the propagation di- rection of the control field. We will consider both the steady state regime as well as the response to a tempo-