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Physical Review A

Efficiency and fidelity of photon-echo quantum memory in an atomic system with longitudinal inhomogeneous broadening

S. A. Moiseev, Арсланов Наркис Мусавирович

Published Aug 5, 2008• 35 citations
Publisher

Abstract

We have performed a theoretical analysis of the photon-echo-based quantum memory realized recently in A. L. Alexander et al., Phys. Rev. Lett. 96, 043602 (2006) in the medium with linear correlation between atomic spatial coordinates and frequency detunings of the inhomogeneously broadened transition. A more general vision on the physical picture of temporal and spatial light-atoms dynamics has been obtained in the analytical solutions, taking into account the atomic phase relaxation, inhomogeneous broadening, and arbitrary parameters of the probe light pulses. We have evaluated preferable experimental conditions for the storage of incoming data light field modes where quantum memory efficiency and fidelity have been found. Physics of high efficiency in the forward geometry of the quantum memory and advantages for the realization of more universal long-lived storage on this basis are clarified.

DOI
10.1103/physreva.78.023803

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We have performed a theoretical analysis of the photon-echo-based quantum memory realized recently in A. L. Alexander et al., Phys. Rev. Lett. 96, 043602 (2006) in the medium with linear correlation between atomic spatial coordinates and frequency detunings of the inhomogeneously broadened transition. A more general vision on the physical picture of temporal and spatial light-atoms dynamics has been obtained in the analytical solutions, taking into account the atomic phase relaxation, inhomogeneous broadening, and arbitrary parameters of the probe light pulses. We have evaluated preferable experimental conditions for the storage of incoming data light field modes where quantum memory efficiency and fidelity have been found. Physics of high efficiency in the forward geometry of the quantum memory and advantages for the realization of more universal long-lived storage on this basis are clarified.
The photon-echo quantum memory is based on a controlled rephasing of the atomic coherence excited by a signal light field in the inhomogeneously broadened resonant line. Here, we demonstrate an active mechanism of the atomic rephasing that provides a perfect retrieval of the stored light field in the photon-echo quantum memory based on the use of arbitrary initial inhomogeneous broadening of the resonant line. We show that the rephasing mechanism can exploit all resonant atoms, thereby maximally increasing an optical depth of the resonant transition, which is one of the critical parameters for the realization of highly efficient quantum memory. We also demonstrate that the rephasing mechanism can be used for various realizations of the photon-echo quantum memory, thereby creating many possibilities for its practical realization.
In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in $\ensuremath{\Lambda}$-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we perform the same analysis for the cavity model. In particular, we show that the retrieval efficiency is equal to C∕(1+C)C∕(1+C)C∕(1+C) independent of the retrieval technique, where CCC is the cooperativity parameter. We also derive the optimal strategy for storage and, in particular, demonstrate that at any detuning one can store, with the optimal efficiency of C∕(1+C)C∕(1+C)C∕(1+C), any smooth input mode satisfying $TC\ensuremath{\gamma}⪢1$ and a certain class of resonant input modes satisfying $TC\ensuremath{\gamma}\ensuremath{\sim}1$, where TTT is the duration of the input mode and $2\ensuremath{\gamma}$ is the transition linewidth. In the two subsequent papers of the series, we present the full analysis of the free-space model and discuss the effects of inhomogeneous broadening on photon storage.
In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)] and in the two preceding papers [Gorshkov et al., this issue, Phys. Rev. A 76, 033804 (2006); 76, 033805 (2006)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in homogeneously broadened $\ensuremath{\Lambda}$-type atomic media, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we generalize this treatment to include inhomogeneous broadening. In particular, we consider the case of Doppler-broadened atoms and assume that there is a negligible difference between the Doppler shifts of the two optical transitions. In this situation, we show that, at high enough optical depth, all atoms contribute coherently to the storage process as if the medium were homogeneously broadened. We also discuss the effects of inhomogeneous broadening in solid state samples. In this context, we discuss the advantages and limitations of reversing the inhomogeneous broadening during the storage time, as well as suggest a way for achieving high efficiencies with a nonreversible inhomogeneous profile.
Here we show that the photon echo equivalent of an NMR gradient echo is completely efficient if the sample is optically thick, the detunings of the atoms vary linearly along the direction of propagation and the storage time is short compared to the decay rate of the atoms. In this process the only light that interacts with the sample of atoms during the storage and retrieval process is the light that is to be stored and then retrieved, their are no auxiliary beams. The stored and recalled light travel in the same direction and their is no need for the phase matching operation that is present in previous quantum memory proposals using controlled inhomogeneous broadening. This greatly simplifies various possible implementations. We present analytical, numerical and experimental results of this scheme. We report experimental efficiencies of up to 15% and suggest simple realizable improvements to significantly increase the efficiency.
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.
We develop the general theoretical approach to an optical quantum memory (QM) based on the three-pulse photon echo (PE) with controlled reversible inhomogeneous broadening. The wavefunction of the retrieved photon echo field is derived explicitly as a function of an arbitrary input data light field taking into account the nonlinear interaction between the quantum light fields and the atomic medium. The result opens a clear possibility for quantum manipulations with arbitrary single- and multi-photon entangled light fields.