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Physical Review A

Slowing down of a guided light field along a nanofiber in a cold atomic gas

Fam Le Kien, K. Hakuta

Published Jan 22, 2009• 30 citations
Publisher

Abstract

We develop a systematic formalism to study the propagation of a guided probe light field along a nanofiber embedded in a cold atomic gas. We derive a general axial propagation equation for the amplitude of the photon flux of the guided light, which allows us to take into account the complexity of the guided-field vector structure and the evanescent-wave nature of the guided-field transverse profile. We use our formalism to explore the possibility of slowing down of the guided light via the process of electromagnetically induced transparency. We show that, despite the effects of the spatially varying detuning, caused by the van der Waals potential, and the spatially varying atom-field coupling, caused by the evanescent-wave nature of the guided mode in the transverse plane, the group velocity of the guided light can be substantially reduced due to the steep dispersion of the atomic gas in the condition of electromagnetically induced transparency.

DOI
10.1103/physreva.79.013818

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Physical Review A•Apr 15, 2009•28 citations
We develop a systematic formalism to study the propagation of a guided probe light field along a nanofiber embedded in a cold atomic gas. We derive a general axial propagation equation for the amplitude of the photon flux of the guided light, which allows us to take into account the complexity of the guided-field vector structure and the evanescent-wave nature of the guided-field transverse profile. We use our formalism to explore the possibility of slowing down of the guided light via the process of electromagnetically induced transparency. We show that, despite the effects of the spatially varying detuning, caused by the van der Waals potential, and the spatially varying atom-field coupling, caused by the evanescent-wave nature of the guided mode in the transverse plane, the group velocity of the guided light can be substantially reduced due to the steep dispersion of the atomic gas in the condition of electromagnetically induced transparency.
Tapered optical fibers with a nanofiber waist are versatile tools for interfacing light and matter. In this context, laser-cooled atoms trapped in the evanescent field surrounding the optical nanofiber are of particular interest: They exhibit both long ground-state coherence times and efficient coupling to fiber-guided fields. Here, we demonstrate electromagnetically induced transparency, slow light, and the storage of fiber-guided optical pulses in an ensemble of cold atoms trapped in a nanofiber-based optical lattice. We measure a slow-down of light pulses to group velocities of 50 m/s. Moreover, we store optical pulses at the single photon level and retrieve them on demand in the fiber after 2 microseconds with an overall efficiency of (3.0 +/- 0.4) %. Our results show that nanofiber-based interfaces for cold atoms have great potential for the realization of building blocks for future optical quantum information networks.
Abstract Slow light with electromagnetically induced transparency (EIT) in the core of optical fibre containing three-level atoms is investigated. The guided modes are treated in the weakly guiding approximation which renders the analysis into a manageable form. The transparency window and permittivity profile of the core due to the strong pump field in the EIT scheme is calculated. For a specific permittivity profile of the core due to EIT, the propagation constant of the weak signal field and spatial shape of fundamental guided mode are calculated by solving the vector wave equation using the finite difference method. It is found that the transparency window and slow light field can be controlled via the optical fibre parameters. The reduced group velocity of slow light in this configuration is useful for many technological applications such as optical memories, effective control of single photon fields, optical buffers and delay lines.
We study the propagation of guided light along an array of three-level atoms in the vicinity of an optical nanofiber under the condition of electromagnetically induced transparency. We examine two schemes of atomic levels and field polarizations where the guided probe field is quasilinearly polarized along the major or minor principal axis, which is parallel or perpendicular, respectively, to the radial direction of the atomic position. Our numerical calculations indicate that 200 cesium atoms in a linear array with a length of 100 $\ensuremath{\mu}\mathrm{m}$ at a distance of 200 nm from the surface of a nanofiber with a radius of 250 nm can slow down the speed of guided probe light by a factor of about $3.5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ (the corresponding group delay is about 1.17 $\ensuremath{\mu}\mathrm{s})$. In the neighborhood of the Bragg resonance, a significant fraction of the guided probe light can be reflected back with a negative group delay. The reflectivity and the group delay of the reflected field do not depend on the propagation direction of the probe field. However, when the input guided light is quasilinearly polarized along the major principal axis, the transmittivity and the group delay of the transmitted field substantially depend on the propagation direction of the probe field. Under the Bragg resonance condition, an array of atoms prepared in an appropriate internal state can transmit guided light polarized along the major principal in one specific direction even in the limit of infinitely large atom numbers. The directionality of transmission of guided light through the array of atoms is a consequence of the existence of a longitudinal component of the guided light field as well as the ellipticity of both the field polarization and the atomic dipole vector.
Slow light with electromagnetically induced transparency (EIT) in the core of cylindrical waveguide (CW) for an optical fiber system containing three-level atoms is investigated. The CW modes are treated in the weakly guiding approximation which renders the analysis into manageable form. The transparency window and permittivity profile of the waveguide due to the strong pump field in the EIT scheme is calculated. For a specific permittivity profile of the waveguide due to EIT, the propagation constant of the weak signal field and spatial shape of fundamental guided mode are calculated by solving the vector wave equation using the finite difference method. It is found that the transparency window and slow light field can be controlled via the CW parameters. The reduced group velocity of slow light in this configuration is useful for many technological applications such as optical memories, effective control of single photon fields, optical buffer and delay line.
Due to the finite transverse distribution of the control field and cold atoms, there can exist a set of guiding modes for ultraslow signal field propagating in an atomic medium with electromagnetically induced transparency. For cold four-level atoms, these guiding modes can be manipulated by varying the laser fields and atomic distribution. By carefully designing the distribution of the induced refractive index, we show that it is possible to realize single mode operation for slow light propagation which may have practical applications.
We study intracavity electromagnetically induced transparency in atoms around a nanofiber with a pair of Bragg grating mirrors. We calculate the transmission of the composite cavity-fiber-atom system and the time development of the guided probe light field. We derive analytical approximate expressions for the output probe field and its group delay. We show that the group delay of the guided light substantially depends on the input pulse length, the mirror reflectivity, the atomic number density, and the coupling field intensity. We demonstrate that the group delay of the guided light can be significantly enhanced by the presence of the fiber-Bragg-grating cavity even when the finesse of the cavity is moderate.