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New Journal of Physics

Slow light in inhomogeneous and transverse fields

Leon Karpa, Martin Weitz

Published Apr 30, 2008• 9 citations
Publisher

Abstract

For all known massive particles, the value of the magnetic dipole moment is different from zero. In contrast, photons in vacuum have no magnetic moment. Here, we describe experimental studies that show that light, when transmitted through a dense atomic medium under the conditions of electromagnetically induced transparency (EIT), can behave as if it has acquired a magnetic dipole moment. In the area of solid-state physics, such effective particle properties (e.g. effective masses) are well known. In our experiments, slow light passing through a rubidium gas cell is deflected when exposed to a magnetic field gradient. The beam deflection is proportional to the propagation time through the cell and can be understood by assuming that dark-state polaritons have a nonzero effective magnetic moment aligned collinearly to the optical propagation axis. In more recent experiments, we have studied different dark-state configurations. We observe EIT, slow group velocities and stored light in a transverse magnetic field configuration, where the moving magnetic dipole is directed orthogonal to the optical propagation axis. The latter can be used for further studies of the quasiparticle properties of dark-state polaritons.

DOI
10.1088/1367-2630/10/4/045015

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For all known massive particles, the value of the magnetic dipole moment is different from zero. In contrast, photons in vacuum have no magnetic moment. Here, we describe experimental studies that show that light, when transmitted through a dense atomic medium under the conditions of electromagnetically induced transparency (EIT), can behave as if it has acquired a magnetic dipole moment. In the area of solid-state physics, such effective particle properties (e.g. effective masses) are well known. In our experiments, slow light passing through a rubidium gas cell is deflected when exposed to a magnetic field gradient. The beam deflection is proportional to the propagation time through the cell and can be understood by assuming that dark-state polaritons have a nonzero effective magnetic moment aligned collinearly to the optical propagation axis. In more recent experiments, we have studied different dark-state configurations. We observe EIT, slow group velocities and stored light in a transverse magnetic field configuration, where the moving magnetic dipole is directed orthogonal to the optical propagation axis. The latter can be used for further studies of the quasiparticle properties of dark-state polaritons.
Electromagnetically induced transparency allows for light transmission through dense atomic media by means of quantum interference of absorption amplitudes. Media exhibiting electromagnetically induced transparency have interesting properties, such as very slow group velocities. Associated with the slow light propagation are quasiparticles, so-called dark polaritons, which are mixtures of a photonic and an atomic contribution. Here, we demonstrate that these excitations behave as particles with a nonzero magnetic moment, which is in clear contrast to the properties of a free photon. It is found that circularily polarized light passing through a rubidium gas cell under the conditions of electromagnetically induced transparency is deflected by a small magnetic field gradient. The deflection angle is proportional to the propagation time of an optical pulse through the cell. The observed beam deflection can be understood by assuming that dark state polaritons have an effective magnetic moment. This is attributed to the spin wave contribution that develops upon entry of light into the medium. Our experiment can be described in terms of a Stern-Gerlach experiment for the dark polaritons.
Polaritons are the collective excitations of many atoms dressed by resonant photons, which can be used to explain the slow light propagation with the mechanism of electromagnetically induced transparency. As quasiparticles, these collective excitations possess the typical feature of the matter particles, which can be reflected and deflected by the inhomogeneous medium in its spatial motion with some velocity. In this paper we develop a quantum theory to systematically describe the spatial motion of polaritons in inhomogeneous magnetic and optical fields. This theoretical approach treats these quasiparticles through an effective Schr\"odinger equation with anisotropic dispersion that the longitudinal motion is similar to an ultrarelativistic motion of a ``slow light velocity'' while the transverse motion is of nonrelativity with certain effective mass. We find that, after passing through the EIT medium, the light ray bends due to the spatial-dependent profile of external field. This phenomenon explicitly demonstrates the exotic corpuscular and anisotropic property of polaritons.
We study a washboard potential in a light-driven ensemble of three-level atoms induced by the externally applied magnetic fields under electromagnetically induced transparency (EIT). We find that a dark-state polariton, which is formed by an atomic ensemble dressed by the photon can display a typical quantum interference effect (i.e., the quasiparticle Bloch oscillation). The dark-state polariton is subjected to a washboard configuration potential with a spatially uniform force and a periodic potential provided by the linearly and periodically external magnetic fields, respectively. Due to the slower group velocity of the photons in the EIT medium, the period of Bloch oscillation can achieve a millisecond order of magnitude. Also, in our protocol, the Bloch oscillation of the dark-state polariton is feasibly modulated through the applied control and magnetic fields.
We study the coherent propagation of light whose dynamics is governed by the effective Schr\"odinger equation derived in a magneto-optically manipulated atomic ensemble with a four-level tripod configuration for electromagnetically induced transparency (EIT). The small transverse deflection of an optical beam, which is ultrasensitive to the EIT effect, could be drastically amplified via a weak measurement with an appropriate preselection and postselection of the polarization state. The physical mechanism is explained as the effect of wave-packet reshaping, which results in an enlarged group velocity in the transverse direction.
In this work quantum coherence effects in dense rubidium atomic vapour are investigated. Prepared in a laser driven atomic system, coherent effects, like the well-known electromagnetically induced transparency, have a remarkable ability to significantly alter optical properties of the used medium. Electromagnetically induced transparency and related phenomena like slow and stored light can be explained in terms of dark state polaritons, representing quasiparticles consisting of light and matter components. In this thesis, experiments aiming to the concept of quasiparticles are described. Furthermore, in this thesis the concept of resonance retrieval of a stored coherence is investigated, a concept that might prove useful in metrology. In this thesis, the focus is set on the experimental study of the particle-like nature of dark state polaritons. Therefore, a radiofrequency spectroscopy is performed on stationary and moving polaritons with an internal level structure. To this end, an experimental setup is described that allows for the existence of two state dark polaritons in a tripod level scheme. The internal level structure of these polaritons is then probed by a radiofrequency field and a transfer of population between two dark states is observed. The measured population transfer, though with a limited contrast, strongly indicates that dark state polaritons can be considered as quasiparticles with an internal level structure. Since the dark state polaritons exhibit features of an effective magnetic dipole moment, the existence of the Aharonov-Casher phase effect for these quasiparticles is investigated experimentally. It is predicted by a known Aharonov-Casher effect that taking two particles with a finite magnetic dipole moment around a line of charge causes an accumulated phase difference between them. In this work, a detection system with a phase sensitivity of 10-5 rad is described, which sets the upper boundary on the experimentally detectable Aharonov-Casher phase for the hot rubidium gas system. In the last part of this thesis experiments on storage and resonant retrieval of an atomic coherence are described. To this end, an RF field creates an atomic coherence which is stored and subsequently read out with an optical field. The retrieved field is shown to be frequency locked to the optical field. The difference frequency is, within the limits of experimental sensitivity, at the atomic resonance frequency independently on the amplitude and frequency variations of the radiofrequency excitation field.
We present a semiclassical theory for light deflection by a coherent $\ensuremath{\Lambda}$-type three-level atomic medium in an inhomogeneous magnetic field or an inhomogeneous control laser. When the atomic energy levels (or the Rabi coupling by the control laser) are position-dependent due to the Zeeman effect caused by the inhomogeneous magnetic field (or due to inhomogeneity of the control field profile), the spatial dependence of the refraction index of the atomic medium will result in an observable deflection of slow signal light when the electromagnetically induced transparency cancels medium absorption. Our theoretical approach based on Fermat's principle in geometrical optics not only provides a consistent explanation for the most recent experiment in a straightforward way, but also predicts the two-photon detuning dependent behaviors and larger deflection angles by three orders of magnitude for the slow signal light deflection by the atomic media in an inhomogeneous off-resonant control laser field.