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Laser Physics

Dark-state polaritons in a degenerate two-level system

Angelo Maggitti, Milan Radonjić, B. M. Jelenković

Published Sep 17, 2013• 2 citations
Publisher

Abstract

We investigate the formation of dark-state polaritons in an ensemble of degenerate two-level atoms admitting electromagnetically induced transparency. Using a generalization of microscopic equation-of-motion technique, multiple collective polariton modes are identified depending on the polarizations of two coupling fields. For each mode, the polariton dispersion relation and composition are obtained in a closed form out of a matrix eigenvalue problem for arbitrary control field strengths. We illustrate the algorithm by considering the F g = 2 → F e = 1 transition of the D 1 line in 87 Rb atomic vapor. In addition, an application of dark-state polaritons to the frequency and/or polarization conversion, using D 1 and D 2 transitions in cold Rb atoms, is given.

DOI
10.1088/1054-660x/23/10/105202

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We investigate the formation of dark-state polaritons in an ensemble of degenerate two-level atoms admitting electromagnetically induced transparency. Using a generalization of microscopic equation-of-motion technique, multiple collective polariton modes are identified depending on the polarizations of two coupling fields. For each mode, the polariton dispersion relation and composition are obtained in a closed form out of a matrix eigenvalue problem for arbitrary control field strengths. We illustrate the algorithm by considering the F g = 2 → F e = 1 transition of the D 1 line in 87 Rb atomic vapor. In addition, an application of dark-state polaritons to the frequency and/or polarization conversion, using D 1 and D 2 transitions in cold Rb atoms, is given.
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We derive the properties of polaritons in single-$\ensuremath{\Lambda}$ and double-$\ensuremath{\Lambda}$ media using a microscopic equation-of-motion technique. In each case, the polaritonic dispersion relation and composition arise from a matrix eigenvalue problem for arbitrary control field strengths. We show that the double-$\ensuremath{\Lambda}$ medium can be used to up- or down-convert single photons while preserving quantum coherence. The existence of a dark-state polariton protects this single-photon four-wave mixing effect against incoherent decay of the excited atomic states. The efficiency of this conversion is limited mainly by the sample size and the lifetime of the metastable state.
We identify form-stable coupled excitations of light and matter ("dark-state polaritons") associated with the propagation of quantum fields in electromagnetically induced transparency. The properties of dark-state polaritons such as the group velocity are determined by the mixing angle between light and matter components and can be controlled by an external coherent field as the pulse propagates. In particular, light pulses can be decelerated and "trapped" in which case their shape and quantum state are mapped onto metastable collective states of matter. Possible applications of this reversible coherent-control technique are discussed.
Dark-state polaritons in a five-level MMM-type atomic ensemble are proposed in the electromagnetically induced transparency. Under conditions of the low excitation limit and adiabatic following, the quantum field can be mapped onto the atomic polarization states, forming the shape preserving quantum states of polaritons. Two channels for robust quantum memory are provided, which enables the potential applications in quantum-information processing.
An ideal and reversible transfer technique for the quantum state between light and metastable collective states of matter is presented and analyzed in detail. The method is based on the control of photon propagation in coherently driven three-level atomic media, in which the group velocity is adiabatically reduced to zero. Form-stable coupled excitations of light and matter (``dark-state polaritons'') associated with the propagation of quantum fields in electromagnetically induced transparency are identified, their basic properties discussed and their application for quantum memories for light analyzed.
We present a general scheme to determine the loss-free adiabatic eigensolutions (dark-state polaritons) of the interaction of multiple probe laser beams with a coherently driven atomic ensemble under conditions of electromagnetically induced transparency. To this end we generalize the Morris-Shore transformation to linearized Heisenberg-Langevin equations describing the coupled light-matter system in the weak excitation limit. For the simple lambda-type coupling scheme the generalized Morris-Shore transformation reproduces the dark-state polariton solutions of slow light. Here we treat a closed-loop dual-VVV scheme wherein two counterpropagating control fields generate a quasistationary pattern of two counterpropagating probe fields---so-called stationary light. We show that contrary to previous predictions, there exists a single unique dark-state polariton; it obeys a simple propagation equation.