Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1904.10492 · Physical Review Research

Photon echoes in optically dense media

Sergey A. Moiseev, Mahmood Sabooni, Ravil V. Urmancheev

Published Jan 24, 2020• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevresearch.2.012026

Related papers

Photon echo area theorem for optically dense media

R. V. Urmancheev, K. I. Gerasimov, Mansur M. Minnegaliev +1 more

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.

Bulletin of the Russian Academy of Sciences Physics•May 1, 2017•0 citations

Primary photon echo in optically dense media

Oleg Kh Khasanov, T. V. Smirnova, Olga M. Fedotova

The primary photon echo signal excited by two non-collinear pulses in optically dense media with extreme inhomogeneous broadening is investigated theoretically and numerically. Non-linear evolution of both echo exciting pulses and echo response during propagation is taken into account. Red frequency shift of the primary photon echo is predicted. The influence of pulse transformation on the echo time delay is analyzed.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 14, 2000•0 citations

Photon echo in a ring cavity: pulse area approach

Sergey A. Moiseev, R. V. Urmancheev

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.

Journal of the Optical Society of America B•Mar 7, 2025•1 citation

Angular echo spectroscopy of optically dense media

Olga M. Fedotova, Oleg Kh Khasanov, T. V. Smirnova

The peculiarities of the photon echo excitation by two non- collinear pulses in optically dense media with extreme inhomogeneous broadening are investigated theoretically and numerically. Non-linear pulse evolution during propagation is taken into account. Red frequency shift of the primary photon echo signal is predicted. The influence of pulse transformation on the echo time delay is analyzed.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 29, 1999•0 citations

Photon/spin echo in a Fabry–Perot cavity

S. A. Moiseev, R. V. Urmancheev

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.

Optics Letters•Jul 5, 2022•9 citations

Evolution of the stimulated photon echo in optically dense media

Oleg Kh Khasanov, T. V. Smirnova

A numerical investigation is reported of the characteristics of the stimulated photon echo (SPE) excited by a sequence of 2 n ( n ≥ 2) paired pulses in an extended medium. The evolution of these pulses during propagation is taken into account. The SPE is shown to have a threshold governed by the total initial area of the excitation pulses. Stable SPE amplification is observed when this total area exceeds the threshold value, which is π. The optimal conditions for the SPE are identical for optically thin and dense media. This is a cumulative effect. The existence of a threshold affects also the cumulative effect: the nature of the dependence of the SPE amplitude on the number of the excitation pulse pairs varies with their total initial area. The cumulative effect is observed also when the pulse areas are no longer small. The linear part of the dependence of the SPE signal on n becomes narrower when the dimensions of a sample are increased, which is a consequence of the nonlinear nature of the evolution of pulse pairs in extended media.

Quantum Electronics•May 31, 1996•0 citations
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\ensuremathπ\ensuremath{\pi}\ensuremathπ or 0\ensuremathπ\ensuremath{\pi}\ensuremathπ 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 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 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.
A numerical investigation is reported of the characteristics of the stimulated photon echo (SPE) excited by a sequence of 2 n ( n ≥ 2) paired pulses in an extended medium. The evolution of these pulses during propagation is taken into account. The SPE is shown to have a threshold governed by the total initial area of the excitation pulses. Stable SPE amplification is observed when this total area exceeds the threshold value, which is π. The optimal conditions for the SPE are identical for optically thin and dense media. This is a cumulative effect. The existence of a threshold affects also the cumulative effect: the nature of the dependence of the SPE amplitude on the number of the excitation pulse pairs varies with their total initial area. The cumulative effect is observed also when the pulse areas are no longer small. The linear part of the dependence of the SPE signal on n becomes narrower when the dimensions of a sample are increased, which is a consequence of the nonlinear nature of the evolution of pulse pairs in extended media.