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arXiv:quant-ph/0307223 · Physical Review A

Electromagnetically induced transparency and storing of a pair of pulses of light

Andrzej Raczyński, Jarosław Zaremba, S. Zielińska-Kaniasty

Published Apr 1, 2004• 61 citations
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Abstract

Electromagnetically induced transparency and light storing are discussed in the case of an atomic medium in a double $\ensuremath{\Lambda}$ configuration. A polariton description of both phenomena is systematically introduced. Analytic expressions are given which allow one to predict the shapes and phases of both the transmitted pulses and the stored and released ones as well as the atomic coherence in the storage stage. A comparison of the numerical solutions of the Maxwell-Bloch equations with the results due to the polariton model proves a strong predictive power of the latter.

DOI
10.1103/physreva.69.043801

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Electromagnetically induced transparency and light storing are discussed in the case of an atomic medium in a double \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration. A polariton description of both phenomena is systematically introduced. Analytic expressions are given which allow one to predict the shapes and phases of both the transmitted pulses and the stored and released ones as well as the atomic coherence in the storage stage. A comparison of the numerical solutions of the Maxwell-Bloch equations with the results due to the polariton model proves a strong predictive power of the latter.
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Light propagation and storing in a medium of atoms in the tripod configuration driven by two control pulses are investigated theoretically in terms of two polaritons and numerically. It is shown that a magnetic field switched on at the pulse storage stage changes the phase relations between the atomic coherences due to the stored pulse, which leads to an essential modification of the released pulse. Quantitative relations concerning the released pulse and the coherences are given. A general situation when the two control fields are not proportional at the pulse release stage is also examined. It is shown that in both cases a single dark state polariton is not sufficient to account for the pulse evolution, which is connected with the fact that a part of the signal remains in the medium after the release stage.
By solving the self-consistent system of Maxwell and density-matrix equations in the case where the time of relaxations to the ground state is much shorter than the pulse duration we derive an analytical solution for the probe pulse propagation. We obtain an excellent consistency of our analytical solution with direct numerical integration. We investigate the asymptotic behavior of analytical solution and show that under certain conditions it passes to the well-known dark-state polariton propagation regime. We analyzed the dynamics of propagation and, in particular, explain the fact that in the well-known experiments only fractions of pulses were stored.
We consider storage and retrieval of light based on electromagnetically induced transparency in an atomic medium using nonadiabatic switching of a control field. We derive various conditions for writing (and reading) the light information to (and from) the atomic coherence. We obtain an analytical solution for the retrieval of the stored pulse that is in excellent agreement with the full numerical results. We identify the origin of distortion at the output and derive a condition to correct the distortions by manipulating the retrieval process.
We study the influence of a lossless material medium on the coherent storage and quantum-state transfer of a quantized probe light in an ensemble of $\ensuremath{\Lambda}$-type atoms. The medium is modeled as uniformly distributed two-level atoms with the same energy level spacing, coupling to a probe light. This coupled system can be simplified to a collection of two-mode polaritons which couple to one transition of the $\ensuremath{\Lambda}$-type atoms. We show that, when the other transition of $\ensuremath{\Lambda}$-type atoms is controlled by a classical light, electromagnetically induced transparency can also occur for the polaritons. In this case the coherent storage and quantum transfer for photon states are achievable through novel dark states with respect to the polaritons. By calculating the corresponding dispersion relation, we find that the ensemble of three-level atoms with $\ensuremath{\Lambda}$-type transitions may serve as quantum memory for it slows or even stops light propagation through the mechanism of electromagnetically induced transparency.
We consider adiabatic propagation of a pair of quantized light pulses in a coherently prepared atomic medium with the tripod level configuration. We find that under conditions of electromagnetically induced transparency, two distinct polariton modes are simultaneously formed in the medium. These polaritons, represented by certain coherent superpositions of the quantized fields, have different group velocities; the fast one propagates at essentially the speed of light, while the group velocity of the slow polariton can be dynamically reduced to zero. The state mapping between the electromagnetic field and atomic ensemble is also demonstrated.