Effective multi-mode photon echo based quantum memory on multi-atomic ensemble in the QED cavity is proposed. Analytical solution is obtained for the quantum memory efficiency that can be equal unity when optimal relations for the cavity and atomic parameters are held. Numerical estimation for realistic atomic and cavity parameters demonstrates the high efficiency of the quantum memory for optically thin resonant atomic system. 42.50.Ct, 42.50.Md Quantum communications and quantum computation require an effective quantum memory (QM) that should possess a multi-mode and high fidelity character [1][2][3][4][5]. Most well-known QM based on electromagnetically induced transparency effect [6] demonstrates an efficient storage and retrieval only for a specific single temporal mode regime [7][8][9]. Photon echo QM [10-14] offers most promising properties for realization of the multi-mode QM [15][16][17]. However, the quantum efficiency of all discussed multi-mode variants of the photon echo QM tends to unity for infinite optical depth αL as [1 − exp(−αL)] 2 , where α and L are resonant absorption coefficient and length of the medium along the light field propagation [18,19]. It imposes a fundamental limit for the QM efficiency so it is necessary to increase either the atomic concentration or the medium length. However, the QM device should be compact and the large increase of the atomic concentration gives rise to atomic decoherence due to the dipole-dipole interactions limiting thereby a storage time. So, using the free space QM scheme is quite problematic for practical devices. Efficient photon echo QM with controlled reverse of inhomogeneous broadening (CRIB) have been studied recently in ideal cavity [20] and in bad cavity [21] where high QM efficiency has been demonstrated only for a specific optimal single mode regime. Here, we propose a general approach for multi-mode photon echo type of QM in QED cavity (single mode resonator). We demonstrate a high efficiency of the QM for the optimized system of atoms and QED cavity at arbitrary temporal shape of the stored field modes. We find a simple analytical solution for QM efficiency and the optimal conditions for matching of the atomic and cavity parameters where the QM efficiency can reach unity even for small optical depth of the medium loaded in the cavity. Basic equations:We analyze resonant multi-atomic system in a single mode QED cavity coupled with signal and bath fields. By following to the cavity mode formalism [22], we use a Tavis-Cumming Hamiltonian [23]Ĥ =Ĥ o +Ĥ 1 , for N atoms, field modes and their interactions taking into account the inhomogeneous and homogeneous broadenings of the atomic frequencies and continuous spectral distribution of the field modes wherêare main energies of atoms (S j z is a z-projection of the spin 1/2 operator), energy of cavity field (â + andâ are arising and decreasing operators), energies of signal (l=1) and bath (l=2) fields (b + l and b l are arising and decreasing operators of the field modesThe first term in (2) compr...

We have proposed a magnon qubit based on coupled configuration of Bose-Einstein condensates (BEC) in two ferromagnetic samples placed closely to each other. We have evaluated the magnon BEC qubit realization in the double BEC scheme where we found a quantum synchronism condition providing an effective Hamiltonian of magnon qubit. It has the form of well-known superconducting Josephson qubit. The possibilities for coherent magnon BEC qubit rotation are analyzed. Implementations of the magnon BEC qubit are considered for small samples and thin ferromagnetic films. Advantages of the proposed macroscopic qubit realization are discussed.

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