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Physical Review A

Electromagnetically induced optical anisotropy of an ultracold atomic medium

V. M. Datsyuk, Igor M. Sokolov, Dmitriy V. Kupriyanov, Mark D. Havey

Published Mar 11, 2008• 32 citations
Publisher

Abstract

We consider radiative transport in ultracold atomic systems under conditions of electromagnetically 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 nonhomogeneous 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 $^{87}\text{R}\text{b}$ atoms.

DOI
10.1103/physreva.77.033823

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We consider radiative transport in ultracold atomic systems under conditions of electromagnetically 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 nonhomogeneous 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 87Rb^{87}\text{R}\text{b}87Rb atoms.
From a macroscopic viewpoint, atomic vapours appear homogeneous and isotropic. As we have seen during the discussion of the microscopic dynamics that light induces in atomic systems, however, the interaction with light as well as external fields can break the rotational and translational symmetries and make the system both inhomogeneous and anisotropic. This microscopic anisotropy appears directly in the optical properties of the system. This chapter discusses the propagation of light in such a medium and describes experiments that analyse the transmitted light to obtain information about the microscopic state of the medium. Isotropic atoms The Lorentz–Lorenz model Outline The interaction of electromagnetic radiation with matter, in particular light, has inspired philosophers of nature for many centuries and has led to heated debates like the one between Newton and Goethe. The original interest was with the difference in absorption of various materials as a function of the optical wavelength and with the refraction of light, i.e., its dispersion. The first theoretical analysis that connected these macroscopic effects to microscopic properties of the material was the Lorentz–Lorenz theory of dispersion (Lorentz 1880; Lorenz 1881), which was put forward shortly after the Maxwell equations and published in the year after Maxwell's death. (See Figure 6.1.) This theory models the material as a collection of dipoles, driven by the electromagnetic wave. We give here a brief summary of the theory, since its physical content is still the foundation of today's description although the mathematical formalism has changed significantly.
We show that under conditions typical of electromagnetically induced transparency (EIT) in an ultracold atomic sample in a magneto-optical trap, a significant portion of the incident probe pulse is transferred into Rayleigh and Raman scattering channels. The light scattered into the Rayleigh channel emerges from the sample with an EIT time delay. We show that a proper description of the probe light propagation in the sample should include, in the diffusion dynamics, a spin polariton generated by the two-photon EIT process. The results have important implications for studies of weak light localization and for manipulation of single and few photon states in ultracold atomic gases.
We report on systematic numerical and experimental investigations of electromagnetically induced transparency (EIT) to determine temperatures in an ultracold atomic gas. The technique relies on the strong dependence of EIT on atomic motion (i.e., Doppler shifts), when the relevant atomic transitions are driven with counterpropagating probe and control laser beams. Electromagnetically induced transparency permits thermometry with satisfactory precision over a large temperature range, which can be addressed by the appropriate choice of Rabi frequency in the control beam. In contrast to time-of-flight techniques, thermometry by EIT is fast and nondestructive, i.e., essentially it does not affect the ultracold medium. In an experimental demonstration we apply both EIT and time-of-flight measurements to determine temperatures along different symmetry axes of an anisotropic ultracold gas. As an interesting feature we find that the temperatures in the anisotropic atom cloud vary in different directions.
The propagation of a probe field through a four-level Y-type atomic system is described in the presence of two additional coherent radiation fields, namely, the control field and the coupling field. An expression for the probe response is derived analytically from the optical Bloch equations under steady state condition to study the absorptive properties of the system under probe field propagation through an ensemble of stationary atoms as well as in a Doppler broadened atomic vapor medium. The most striking result is the conversion of electromagnetically induced transparency (EIT) into electromagnetically induced absorption (EIA) as we start switching from weak probe regime to strong probe regime. The dependence of this conversion on residual Doppler averaging due to wavelength mismatch is also shown by choosing the coupling transition as a Rydberg transition.
A comparison between forward and diffusely scattered light propagating in a coherently prepared ultracold 87Rb atomic vapor is presented. This research is part of the ongoing effort to characterize the processes, such as diffusion, that contribute to coherence loss in atomic media under conditions of electromagnetically induced transparency, for applications in realistic systems. Toward this end, a magneto optical trap (MOT) of 87Rb has been built, and the atomic vapor sample characterized in terms of atomic density, shape and size, temperature, and optical depth. Next, two co-propagating beams were sent through the sample, to establish an electromagnetically induced transparency in a Λ-type system. In these measurements the two laser fields are not phase-locked, so ground state coherence will be affected by the lasers' phase fluctuations. Observation of the forward and diffusely scattered light were made for different conditions of probe pulse length, control field intensity, and probe field frequency detuning. Storage and retrieval of slow light pulses was achieved for the forward scattering (transmission) channel, but was not observed unambiguously in the diffusely scattered (fluorescence) channel.
The propagation of probe radiation pulses in ultracold atomic ensembles is studied theoretically under conditions of electromagnetically induced transparency. The pulse 'stopping' process is considered which takes place upon nonadiabatic switching off and subsequent switching on the control field. We analysed the formation of an inverted recovered probe radiation pulse, i.e. the pulse propagating in the direction opposite to the propagation direction before the pulse stopping. Based on this analysis, a scheme is proposed for lidar probing atomic or molecular clouds in which the probe pulse penetrates into a cloud over the specified depth, while information on the cloud state is obtained from the parameters of the inverted pulse. Calculations are performed for an ensemble of 87 Rb atoms.