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Bulletin of the Russian Academy of Sciences Physics

Photon echo area theorem for optically dense media

R. V. Urmancheev, K. I. Gerasimov, Mansur M. Minnegaliev, Sergey A. Moiseev

Published May 1, 2017• 0 citations
Publisher

Abstract

The McCall–Hahn area theorem for a photon echo in an optically dense medium is generalized in light of an absorption line consisting of several spectrally unresolved optical transitions and characterized by symmetrical form. Certain theoretical results are compared to experimental data obtained for a photon echo in a Tm 3+ :Y 3 Al 5 O 12 crystal.

DOI
10.3103/s1062873817050252

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The McCall–Hahn area theorem for a photon echo in an optically dense medium is generalized in light of an absorption line consisting of several spectrally unresolved optical transitions and characterized by symmetrical form. Certain theoretical results are compared to experimental data obtained for a photon echo in a Tm 3+ :Y 3 Al 5 O 12 crystal.
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.
The possibility of using incoherent photon echo in spectroscopy of optically dense impurity media is considered. A theoretical approach to description of this phenomenon is presented. The experimental data on incoherent photon echo in ruby at liquid-helium temperature, with transport of an excitation pulse through a fiber, are reported. The spectral dependence of the echo intensity is studied. The decay curve for an incoherent echo signal is investigated, and the phase relaxation time is found to be 98 ns.
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.
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.