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arXiv:2301.10294

Photon echo in ring cavity: pulse area approach

Moiseev, Sergey A., R. V. Urmancheev

Published Jan 24, 2023• 0 citations
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Abstract

Pulse area approach has been established as a versatile analytical tool for studying the resonant interaction between the light and the resonant atomic ensemble. In recent years photon and spin echoes in cavity assisted schemes become increasingly interesting. In this article we develop the photon echo pulse area approach to describe primary and multi-pulse echo generation in the atomic ensemble placed in the ring cavity. We show that the pulse area approach predicts relative echo magnitudes and whether the system is operating in a single- or a multi-pulse generation regime. We also analyze the conditions needed for the realization of these generation regimes. This work develops the pulse area theorem approach for analytical study of photon/spin echoes in optical and microwave cavities and echo based protocols of quantum memory.

DOI
10.48550/arxiv.2301.10294

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Pulse area approach has been established as a versatile analytical tool for studying the resonant interaction between the light and the resonant atomic ensemble. In recent years photon and spin echoes in cavity assisted schemes become increasingly interesting. In this article we develop the photon echo pulse area approach to describe primary and multi-pulse echo generation in the atomic ensemble placed in the ring cavity. We show that the pulse area approach predicts relative echo magnitudes and whether the system is operating in a single- or a multi-pulse generation regime. We also analyze the conditions needed for the realization of these generation regimes. This work develops the pulse area theorem approach for analytical study of photon/spin echoes in optical and microwave cavities and echo based protocols of quantum memory.
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.
Based on new obtained analytical results, the main properties of photon echo quantum memory protocols are analysed and discussed together with recently achieved experimental results. The main attention is paid to studying the influence of spectral dispersion and nonlinear interaction of light pulses with resonant atoms. The distinctive features of the effect of spectral dispersion on the quantum storage of broadband signal pulses in the studied echo protocols are identified and discussed. Using photon echo area theorem, closed analytical solutions for echo protocols of quantum memory are obtained, describing the storage of weak and intense signal pulses, allowing us to find the conditions for the implementation of high efficiency in the echo protocols under strong nonlinear interaction of signal and control pulses with atoms. The key existing practical problems and the ways to solve them in realistic experimental conditions are outlined. We also briefly discuss the potential of using the considered photon echo quantum memory protocols in a quantum repeater.
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.
In investigations of predicted new types of photon echoes — an echo from a homogeneous ensemble of atoms and an echo of a single light pulse — have established that the magnitude and form of these new types of photon echoes are completely determined by the type of optical transition and by the “area” and polarization of the exciting light pulses (and the form can be controlled by varying the magnetic field). It is also established that the echo amplitude decreases for both small (compared to 1) and large light-pulse areas, and the optimal areas for which the maximum echo is obtained have been found. Investigations show that such photon echoes can also appear under conditions when an ordinary photon echo is absent (in atomic or molecular gases at high pressure, in the far-IR region of the spectrum, from cooled trapped atoms or ions, and so on).
We have analyzed an efficient integration of the multi-qubit echo quantum memory into the quantum computer scheme on the atomic resonant ensembles in quantum electrodynamics cavity. Here, one atomic ensemble with controllable inhomogeneous broadening is used for the quantum memory node and other atomic ensembles characterized by the homogeneous broadening of the resonant line are used as processing nodes. We have found optimal conditions for efficient integration of multi-qubit quantum memory modified for this analyzed physical scheme and we have determined a specified shape of the self temporal modes providing a perfect reversible transfer of the photon qubits between the quantum memory node and arbitrary processing nodes. The obtained results open the way for realization of full-scale solid state quantum computing based on using the efficient multi-qubit quantum memory.