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AIP conference proceedings

Photon echo area theorem for Gaussian laser beams

R. V. Urmancheev, K. I. Gerasimov, Mansur M. Minnegaliev, S. A. Moiseev, T. Chanelière, Anne Louchet-Chauvet

Published Jan 1, 2018• 0 citations
Publisher

Abstract

We present the results of experimental and theoretical investigation of pulse area theorem for understanding general properties of two pulse (primary) photon echo in the optically deep Tm3+:Y3Al5O12 crystal. Despite discussed limitations the proposed approach allows us to describe the key feature of area theorem dependence introduced by the Gaussian spatial profile of the pulses: the absence of expected downfall to zero at second pulse area θ20 = 2π in the experimental data.

DOI
10.1063/1.5025451

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Two-pulse photon echo area theorem in an optically dense medium

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. However at higher pulse areas, the observations diverge from the analytic solution requiring further theoretical and experimental studies.

Optics Express•Sep 25, 2019•14 citations
We present the results of experimental and theoretical investigation of pulse area theorem for understanding general properties of two pulse (primary) photon echo in the optically deep Tm3+:Y3Al5O12 crystal. Despite discussed limitations the proposed approach allows us to describe the key feature of area theorem dependence introduced by the Gaussian spatial profile of the pulses: the absence of expected downfall to zero at second pulse area θ20 = 2π in the experimental data.
We derive the area theorem for light pulses interacting with an inhomogeneously broadened ensemble of two-level atoms in a single-mode optical waveguide and present its analytical solution for Gaussian-type modes, which demonstrates the significant difference from the formation of $2\ensuremath{\pi}$ pulses by plane waves. We generalize this theorem to the description of photon echo and apply it to the two-pulse (primary) echo and the revival of silenced echo (ROSE) protocol of photon echo quantum memory. We implemented ROSE protocol in a single-mode laser-written waveguide made of an optically thin crystal Tm3+{\mathrm{Tm}}^{3+}Tm3+:Y3Al5O12{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}Y3​Al5​O12​ . The experimental data obtained are satisfactorily explained by the developed theory. Finally, we discuss the obtained experimental results and possible applications of the derived pulse-area approach.
The pulse area theorem is a well-known versatile analytical tool for capturing the general nonlinear nature of light propagation in a two-level medium. Here we derive the pulse area theorem for the photon/spin echo signal generated in a one-side cavity. The obtained analytical solutions for primary and secondary echo pulse areas allow us to describe the nonlinear patterns of the photon/spin echo signals in an atomic ensemble in a cavity. The developed approach and the obtained results constitute an important step in the study of the general properties of the photon/spin echo in optical and microwave cavities expanding applications of the photon echo in coherent spectroscopy, quantum memory, and processing.
The active use of resonators in quantum technologies increases the interest of their application in the creation of optical and microwave quantum memory. The use of photon and spin echoes opens up the possibility of storing a large number of light pulses in one such memory cell. High efficiency of such quantum memory is achieved in an optically dense resonant media, in which the formation of a photon (spin) echo can be accompanied by an increase in the nonlinear interaction of light with atoms causing the appearance of multiple echo signals. In this paper, we develop the pulse area approach to study general nonlinear properties of the primary and multi-pulse echo signals excited in a two-level atomic ensemble located in ring cavities with volumetric and surface modes. Conditions under which one or more echo pulses can be generated are analyzed. The solutions obtained are compared with recent experimental results. We show that the area theorem is one of the simplest and most powerful analytical tools for studying a highly nonlinear and dynamical process of the formation of the sequence of photon/spin echo signals in resonant media inside the resonator.
The authors derive analytical expressions for secondary echoes formed under the two-pulse excitation of the optically dense media developing McCall-Hahn area theorem for echo effects. They find that a series of self-reviving echo signals with a total area of 2$\ensuremath{\pi}$ or 0$\ensuremath{\pi}$ is excited and propagates deep in the media demonstrating strong non-linear nature of light-matter interaction at small changes of second pulse area. The pulse area approach paves the way for precise coherent spectroscopy, the study of different photon echoes and quantum control of light pulses in the optically dense media.