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Optics Letters

Effects of hyperfine structures on an optical stimulated echo memory device

Masaharu Mitsunaga, Ken-ichi Kubodera, H. Kanbe

Published May 1, 1986• 16 citations
Publisher

Abstract

An optical three-pulse stimulated echo signal is analyzed theoretically and numerically for three pulses of arbitrary shape in a medium having hyperfine structures in the ground and excited states. The feasibility of its use as an optical fast-memory device is emphasized. Numerical analysis shows that the fidelity of the memory is reasonably good as long as the storage time T is short compared with the excited-state lifetime T1. However, the echo suffers severe modulation because of the hyperfine structures when T exceeds T1.

DOI
10.1364/ol.11.000339

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An optical three-pulse stimulated echo signal is analyzed theoretically and numerically for three pulses of arbitrary shape in a medium having hyperfine structures in the ground and excited states. The feasibility of its use as an optical fast-memory device is emphasized. Numerical analysis shows that the fidelity of the memory is reasonably good as long as the storage time T is short compared with the excited-state lifetime T1. However, the echo suffers severe modulation because of the hyperfine structures when T exceeds T1.
We present the results of analytical and numerical calculations of the amplitude and temporal shape of photon echoes produced in optically thick absorbing media. In particular, we are interested in echo output signals that mimic the temporal shape of one of the input pulses (the data pulse). Echo recall efficiencies of temporally structured data pulses exceeding unity can be obtained in optically thick media while preserving the information content of the data pulse. We find that the relationship between the maximum echo efficiency and the Beer's length at which that maximum is attained is nearly linear. This linear relation holds well beyond the optimal absorption length predicted by linear theory for both two-pulse photon echoes and three-pulse stimulated photon echoes. These results have significance in the development of optical coherent transient memory and processing systems, where previous calculations predicted recall efficiencies of only a few percent.
The three-pulse photon echo is a well-known technique to store intense light pulses in an inhomogeneously broadened atomic ensemble. This protocol is attractive because it is relatively simple and it is well suited for the storage of multiple temporal modes. Furthermore, it offers very long storage times, greater than the phase relaxation time. Here, we consider the three-pulse photon echo in both two- and three-level systems as a potential technique for the storage of light at the single-photon level. By explicit calculations, we show that the ratio between the echo signal corresponding to a single-photon input and the noise is smaller than one. This severely limits the achievable fidelity of the quantum state storage, making the three-pulse photon echo unsuitable for single-photon quantum memory.
When the intensity of photon echo in a two-level system is measured as a function of delay time of the two input pulses, one obtains a simple exponential decay with the characteristic phase relaxation time. When the two levels contain hyperfine structures, the interference among the hyperfine levels gives rise to modulation of the decay envelope. The Fourier transform of the modulation pattern reveals the hyperfine structure of the rare-earth ions. The hyperfine structure, and therefore the modulation pattern, are both sensitively affected by the crystal environment of the ionic site. We extend photon-echo modulation spectroscopy to three-pulse, stimulated photon-echo modulation, and we find that the stimulated echo modulation patterns are quite distinct from the two-pulse, photon-echo case and are affected by a different set of atomic and crystal interaction parameters. The modulation is measured, in several photon-echo transitions of praseodymium ions in lanthanum trifluoride and yttrium aluminum garnet crystals, as functions of delay times between first and second pulses and between first and third pulses. Comparison of the experimental results with density-matrix calculations allows us to determine hyperfine parameters that are not easily observed with two-pulse echo modulation.
The possibility of increase of the information storage time in optical memory devices based on the long-lived photon echo in rare-earth ion doped crystals provided that the latter are nanometer ones is analyzed. Taking into account that in such materials the information storage time is determined by the population lifetimes of hyperfine sublevels of a ground electron state it is possible to increase it due to the modification of phonon density of states in nanocrystals as compared to bulk crystals.
We investigated the preservation of information encoded into the relative phase and amplitudes of optical pulses during storage and retrieval in an optical memory based on stimulated photon echo. By interfering photon echoes produced in a single-mode Ti:Er:LiNbO(3) waveguide, we found that decoherence in the medium translates only as loss and not as degradation of information. We measured a visibility for interfering echoes close to 100%. These results may have important implications for future long-distance quantum communication protocols.