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arXiv:1606.00736 · Physical Review A

Simultaneous slow and fast light involving the Faraday effect

B. Macke, Bernard Ségard

Published Oct 3, 2016• 7 citations
arXivHTMLPDF

Abstract

We theoretically study the linear transmission of linearly polarized light pulses in an ensemble of cold atoms submitted to a static magnetic field parallel to the direction of propagation. The carrier frequency of the incident pulses coincides with a resonance frequency of the atoms. The transmitted light, the electric field of which is transversal, is examined in the polarizations parallel and perpendicular to that of the incident pulses. We give explicit analytic expressions for the transfer functions of the system for both polarizations and for the corresponding group delays. We demonstrate that slow light can be observed in a polarization, whereas fast light is simultaneously observed in the perpendicular polarization. Moreover, we point out that, due to the polarization postselection, the system is not necessarily minimum phase shift. Slow light can then be obtained in situations where an irrelevant application of the Kramers-Kronig relations could lead one to expect fast light. When the incident light is step modulated, we finally show that, in suitable conditions, the system enables one to separate optical precursor and main field.

DOI
10.1103/physreva.94.043801

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We theoretically study the linear transmission of linearly polarized light pulses in an ensemble of cold atoms submitted to a static magnetic field parallel to the direction of propagation. The carrier frequency of the incident pulses coincides with a resonance frequency of the atoms. The transmitted light, the electric field of which is transversal, is examined in the polarizations parallel and perpendicular to that of the incident pulses. We give explicit analytic expressions for the transfer functions of the system for both polarizations and for the corresponding group delays. We demonstrate that slow light can be observed in a polarization, whereas fast light is simultaneously observed in the perpendicular polarization. Moreover, we point out that, due to the polarization postselection, the system is not necessarily minimum phase shift. Slow light can then be obtained in situations where an irrelevant application of the Kramers-Kronig relations could lead one to expect fast light. When the incident light is step modulated, we finally show that, in suitable conditions, the system enables one to separate optical precursor and main field.
We study the propagation of light pulses in an absorbing medium when the frequency of their carrier coincides with a zero of the refractive index dispersion. Although slow light and, a fortiori, fast light are not expected in such conditions, we show that both can be obtained by selecting particular phase components of the transmitted field. Analytical expressions of the resulting signals are obtained by a procedure of periodic continuation of the incident pulse, and a proof of principle of the predicted phenomena is performed by means of a very simple electrical network; the transfer function of which mimics that of the medium.
We theoretically study the stacked optical transients generated from a series of square pulses passing through a cold atomic ensemble. Using the hybrid analysis and fast Fourier transform, we identify the stacked coherent transients [Europhys. Lett. 4, 47 (1987)] as optical precursors. With slow-light and electromagnetically induced transparency, we obtain nearly 700% transmitted intensity at the transient spikes resulting from the interference between the delayed main field and the stacked optical precursors.
We systematically studied slow light (SL) and stored light in the presence of a static magnetic field, either parallel to or transverse to the direction of light propagation. The theoretical calculations are in good agreement with the measured data, and paves the way for determining the information of optical density, coupling Rabi frequency, and ground state population distribution of a system. We also observed an unexpected double-peak profile in the output of SL and the retrieved signal of stored light under a large transverse magnetic field. Our work provides a better understanding in the studies of SL and storage of light.
We propose a "channelization" architecture to achieve wide-band electromagnetically induced transparency (EIT) and ultra-slow light propagation in atomic Rb-87 vapors. EIT and slow light are achieved by shining a strong, resonant "pump" laser on the atomic medium, which allows slow and unattenuated propagation of a weaker "signal" beam, but only when a two-photon resonance condition is satisfied. Our wideband architecture is accomplished by dispersing a wideband signal spatially, transverse to the propagation direction, prior to entering the atomic cell. When particular Zeeman sub-levels are used in the EIT system, then one can introduce a magnetic field with a linear gradient such that the two-photon resonance condition is satisfied for each individual frequency component. Because slow light is a group velocity effect, utilizing differential phase shifts across the spectrum of a light pulse, one must then introduce a slight mismatch from perfect resonance to induce a delay. We present a model which accounts for diffusion of the atoms in the varying magnetic field as well as interaction with levels outside the ideal three-level system on which EIT is based. We find the maximum delay-bandwidth product decreases with bandwidth, and that delay-bandwidth product 1 should be achievable with bandwidth 50 MHz (5 ns delay). This is a large improvement over the 1 MHz bandwidths in conventional slow light systems and could be of use in signal processing applications.
We propose to control light trapping in a large ensemble of cold atoms by an external, static magnetic field. For an appropriate choice of frequency and polarization of the exciting pulse, the field is expected to speed up the fluorescence of a dilute atomic system. In a dense ensemble, the field does not affect the early-time superradiant signal but amplifies intensity oscillations at intermediate times and induces a very slow, nonexponential long-time decay. The slowing down of fluorescence is due to the excitation of spatially localized collective atomic states that appear only under a strong magnetic field and have exponentially long lifetimes. Our results therefore pave a way towards experimental observation of the disorder-induced localization of light in cold atomic systems.
We demonstrate the generation of slow and fast light (SFL) in a linear and passive three-beam interferometer. Such propagation regimes occur for narrowband pulses with center frequency close to the transmission minima. A model that fully describes SFL effects in this system is developed and an analytical approximate expression for the group delay at the minima is derived. We demonstrate that slow light is not possible if the length difference between adjacent branches of the interferometer is a constant. If a small length detuning ($\ensuremath{\xi}$) in one of the branches is introduced, slow light at one of the two minima can be obtained as long as $\ensuremath{\xi}$ exceeds a critical value. Simultaneously, tunneling, superluminal, or normal regime is sustained at the other minimum, depending on the system's length. A proof-of-model experiment is performed in the radiofrequency range using coaxial cables and $1\ifmmode\times\else\texttimes\fi{}3$ power splitters. The possible realization and performance of such a system in the optical range is also discussed. This system is proposed as a simple alternative to active systems and photonic band-gap structures for sustaining both slow and fast light.