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 propose a quantum memory based on the precreated long-lived macroscopic quantum coherence. It is shown that the proposed approach provides new physical properties and methods for retrieval of the signal light fields and improvement of the basic parameters of quantum memory. We demonstrate how the precreated coherence can enable quantum storage with low quantum noise and programmable and on demand retrieval of signal light fields in atomic ensembles with natural inhomogeneous broadening. The feasibility of implementing this proposal in various crystals doped with rare earth ions, as well as in atomic gases with a Raman transition indicates, a new way for the development of optical quantum memory.

The results of laser site selective and Zeeman spectroscopy studies of ZnWO4 single crystal doped with Er3+ ions are reported. Three types of Er3+ sites have been discovered. The energies of the levels of the (4)I(15/)2 and I-4(13/2) multiplets and the g-factors of several states were determined for three orientations of the crystal relative to the magnetic field. The possible structure of three types of sites and further research techniques are discussed.

We present the optical and magneto-optical spectroscopy and electron paramagnetic resonance (EPR) investigations of CaMoO4 single crystals doped with the erbium ions. Telecom-wavelength resonance transition inhomogeneous line width of Er3+ is relatively narrow for oxide crystals which makes this material promising for quantum technologies applications. The hyperfine structure in optical spectra of 167Er3+ isotope is well resolved. Energies and symmetries of wavefunctions of 39 energy levels of Er3+ ions in the crystal-field (CF) of S4 symmetry and g-factors of some CF Kramers doublets were measured and successfully simulated on the basis of CF calculations. The obtained set of CF parameters was used for modeling the hyperfine structure profiles observed in the optical absorption spectra.

Microwave quantum memory promises advanced capabilities for noisy intermediate-scale superconducting quantum computers. Existing approaches to microwave quantum memory lack complete combination of high efficiency, long storage time, noiselessness and multi-qubit capacity. Here we report an efficient microwave broadband multimode quantum memory. The memory stores two spectral modes of single photon level microwave radiation in on-chip system of eight coplanar superconducting resonators. Single mode storage shows a power efficiency of up to $60\pm 3\%$ at single photon energy and more than $73\pm 3\%$ at higher intensity. The demonstrated efficiency is an order of magnitude larger than the previously reported multimode microwave quantum memory. The noiseless character of the storage is confirmed by coherent state quantum process tomography. The demonstrated results pave the way to further increase in efficiency and hence building a practical multimode microwave memory for superconducting quantum circuits.

We derive the area theorem for light pulses interacting with 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 $2π$ 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. For the first time, we implemented ROSE protocol in a single-mode laser-written waveguide made of an optically thin crystal $Tm^{3+}:Y_3Al_5O_{12}$. 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.

The results of investigations of Er3+ ions at an optical transition with a telecommunication wavelength (λ~1530 nm) in a YPO4 crystal by using photon echo and high-resolution laser spectroscopy in magnetic fields up to 4 T are presented. The maximum coherence time (T2) was 113 μs in a magnetic field of 4 T when it is oriented along the optical axis c of the crystal. The main sources of decoherence are discussed.

An optical quantum memory protocol has been implemented on the basis of the revival of silenced echo at the telecommunication wavelength for signal light fields with a small number of photons. To this end, a long-lived (>1 s) absorption line has been initialized and the orthogonal geometry of the propagation of the signal and rephasing fields has been chosen. An efficiency of revival of (17 ± 1)% has been reached for the orthogonal polarization components of a signal pulse at a storage time of 60 μs. The input pulse contains ~38 photons on average, the revived echo signal includes ~6 photons, and the signal-to-noise ratio is 1.3.

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 ${\mathrm{Tm}}^{3+}$:${\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ . 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 this work, optical spectroscopy of thulium ions in a single-mode optical waveguide fabricated in a Tm3+:Y3Al5O12 crystal using the femtosecond laser printing method was carried out and an optical quantum memory protocol was demonstrated in a revival of silenced echo scheme. An analysis of the experimental data indicates the presence of instantaneous spectral diffusion at a thulium ion concentration of less than 0.01%, a weak effect of imperfections in the formed waveguide on the lifetime of the optical memory, and indicates the possibility of achieving a high efficiency of input signal recovery in the implemented waveguide scheme of the protocol.

Optical quantum memory is one of the basic elements of quantum information systems. However, the possibilities of its application in such systems sometimes can hardly be estimated by existing methods for its characterization. In this work, the tomography of quantum memory has been implemented as a quantum process in a logical basis . It has been shown that the implemented quantum memory scheme for polarization photon qubits with a high accuracy corresponds to the identity transformation and is promising for application in quantum communication and quantum computing.

quantum memory protocol has been implemented on the basis of the revival of silenced echo (ROSE) in the 167 Er 3+ :Y 2 SiO 5 crystal at the telecommunication wavelength for input light fields with a small number of photons. An efficiency of storage of 44% has been reached at a storage time of 40 μs. The input pulse contains ~340 photons on average, the reconstructed echo signal includes ~150 photons, and the signal-to-noise ratio is 4. It has been shown that the main source of noise is the spontaneous emission of atoms remaining in the excited state because the parameters of two rephasing pulses are imperfect. Methods of increasing the signal-to-noise ratio for the implementation of the efficient quantum memory for single-photon fields have been discussed.

В настоящей работе был реализован протокол оптической квантовой памяти в схеме восстановления сигнала подавленного эха в одномодовой волноводной структуре, сформированной кристалле Tm3+:Y3Al5O12, актуальной для создания интегральной квантовой памяти в кристаллах, активированных редкоземельными ионами.

A quantum memory protocol has been implemented on the basis of the revival of silenced echo (ROSE) in the 167Er3+:Y2SiO5 crystal at the telecommunication wavelength for input light fields with a small number of photons. An efficiency of storage of 44% has been reached at a storage time of 40 μs. The input pulse contains ~340 photons on average, the reconstructed echo signal includes ~150 photons, and the signal-to-noise ratio is 4. It has been shown that the main source of noise is the spontaneous emission of atoms remaining in the excited state because the parameters of two rephasing pulses are imperfect. Methods of increasing the signal-to-noise ratio for the implementation of the efficient quantum memory for single-photon fields have been discussed.

В настоящей работе был реализован протокол оптической квантовой памяти в схеме восстановления сигнала подавленного эха в одномодовой волноводной структуре, сформированной кристалле Tm3+:Y3Al5O12, актуальной для создания интегральной квантовой памяти в кристаллах, активированных редкоземельными ионами.

We report an observation of the linear Stark effect in a ${\mathrm{Tm}}^{3+}:{\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ crystal with the distribution of the Stark coefficient over the ion ensemble. We associate this effect with local lattice distortions near the positions of ${\mathrm{Tm}}^{3+}$ ions. Using this effect, the addressable storage of a series of weak light pulses in a cavity-assisted scheme of the revival of silenced echo quantum memory protocol is implemented. In this memory scheme, we also demonstrate storage of a light pulse on the few photon level. The application of an optical resonator makes it possible to increase the memory efficiency in this crystal and to reduce the minimal number of photons in the input signal pulse to 5.6 for the signal-to-noise ratio of 1 in the retrieved echo pulse. The results are in good agreement with the theoretical analysis. The possible ways of the further improvement of the implemented memory scheme are also discussed.

Экспериментально реализован ROSE-протокол сохранения малофотонных световых полей (со средним числом фотонов 5,5 в импульсе) в кристалле Tm3+: Y3Al5O12, помещенном в оптический резонатор Фабри - Перо при восстановлении сигнального импульса, содержащего ~1 фотон при соотношении сигнал/ шум ~ 1. Обсуждаются способы подавления шума в использованной схеме памяти.