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We study photon echo generation in disordered media with the help of multiple scattering theory based on diagrammatic approach and numerical simulations. We show that a strong correlation exists between the driving fields at the origin of the echo and the echo beam. Opening the way to a better understanding of non-linear wave propagation in complex materials, this work supports recent experimental results with applications to the measurement of the optical dipole lifetime $T_2$ in powders.

In Er$^{3+}$:Y$_2$SiO$_5$, we demonstrate the selective optical addressing of the $^{89}$Y$^{3+}$ nuclear spins through their superhyperfine coupling with the Er$^{3+}$ electronic spins possessing large Land\'e $g$-factors. We experimentally probe the electron-nuclear spin mixing with photon echo techniques and validate our model. The site-selective optical addressing of the Y$^{3+}$ nuclear spins is designed by adjusting the magnetic field strength and orientation. This constitutes an important step towards the realization of long-lived solid-state qubits optically addressed by telecom photons., Comment: 5 pages, 4 figures, supplementary material (3 pages)

We study the bandwidth and multiplexing capacity of an erbium-doped optical memory for quantum storage purposes. We concentrate on the protocol ROSE (Revival of a Silenced Echo) because it has the largest potential multiplexing capacity. Our analysis is applicable to other protocols that involve strong optical excitation. We show that the memory performance is limited by instantaneous spectral diffusion and we describe how this effect can be minimised to achieve optimal performance.

Interlaced Spin Grating is a scheme for the preparation of spectro-spatial periodic absorption gratings in a inhomogeneously broadened absorption profile. It relies on the optical pumping of atoms in a nearby long-lived ground state sublevel. The scheme takes advantage of the sublevel proximity to build large contrast gratings with unlimited bandwidth and preserved average optical depth. It is particularly suited to Tm-doped crystals in the context of classical and quantum signal processing. In this paper, we study the optical pumping dynamics at play in an Interlaced Spin Grating and describe the corresponding absorption profile shape in an optically thick atomic ensemble. We show that, in Tm:YAG, the diffraction efficiency of such a grating can reach 18.3% in the small angle, and 11.6% in the large angle configuration when the excitation is made of simple pulse pairs, considerably outperforming conventional gratings., Comment: 11 pages, 13 figures in Physical Review A, 2015

We implement the ROSE protocol in an erbium doped solid, compatible with the telecom range. The ROSE scheme is an adaptation of the standard 2-pulse photon echo to make it suitable for a quantum memory. We observe an efficiency of 40% in a forward direction by using specific orientations of the light polarizations, magnetic field and crystal axes.

Based on the similarity of paraxial diffraction and dispersion mathematical descriptions, the temporal imaging of optical pulses combines linear dispersive filters and quadratic phase modulations operating as time lenses. We consider programming a dispersive filter near atomic resonance in rare earth ion doped crystals, which leads to unprecedented high values of dispersive power. This filter is used in an approximate imaging scheme, combining a single time lens and a single dispersive section and operating as a time reversing device, with potential applications in radio-frequency signal processing. This scheme is closely related to three-pulse photon echo with chirped pulses but the connection with temporal imaging and dispersive filtering emphasizes new features., Comment: 21 pages, 11 figures

Coherence rephasing is an essential step in quantum storage protocols that use echo-based strategies. We present a thorough analysis on how two adiabatic rapid passages (ARP) are able to rephase atomic coherences in an inhomogeneously broadened ensemble. We consider both the cases of optical and spin coherences, rephased by optical or radio-frequency (rf) ARPs, respectively. We show how a rephasing sequence consisting of two ARPs in a double-echo scheme is equivalent to the identity operator (any state can be recovered), as long as certain conditions are fulfilled. Our mathematical treatment of the ARPs leads to a very simple geometrical interpretation within the Bloch sphere that permits a visual comprehension of the rephasing process. We also identify the conditions that ensure the rephasing, finding that the phase of the optical or rf ARP fields plays a key role in the capability of the sequence to preserve the phase of the superposition state. This settles a difference between optical and rf ARPs, since field phase control is not readily guaranteed in the former case. We also provide a quantitative comparison between $\pi$-pulse and ARP rephasing efficiencies, showing the superiority of the latter. We experimentally verify the conclusions of our analysis through rf ARP rephasing sequencies performed on the rare-earth ion-doped crystal Tm$^{3+}$:YAG, of interest in quantum memories., Comment: 24 pages, 7 figures

In low concentration Tm$^{3+}$:YAG, we observe efficient adiabatic rapid passage (ARP) of thulium nuclear spin over flipping times much longer than $T_2$. Efficient ARP with long flipping time has been observed in monoatomic solids for decades and has been analyzed in terms of spin temperature and of the thermodynamic equilibrium of a coupled spin ensemble. In low-concentration impurity-doped crystals the spin temperature concept may be questioned. A single spin model should be preferred since the impurity ions are weakly coupled together but interact with the numerous off-resonant matrix ions that originate the spin-spin relaxation. The experiment takes place in the context of quantum information investigation, involving impurity-doped crystals, spin hyperpolarization by optical pumping, and optical detection of the spin evolution., Comment: 6 pages, 4 figures

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., Comment: 6 pages, 4 figures

We report on light slowing down in a rare earth ion doped crystal by persistent spectral hole burning. The absence of motion of the active ions, the large inhomogeneous broadening, the small homogeneous width and the long lifetime of the hyperfine shelving states make this material convenient for the burning of narrow persistent spectral holes. Since the hole can be burnt long before the arrival of the input signal, there is no need for a strong coupling field, illuminating the sample simultaneously with the input signal, in contrast with procedures such as Electromagnetically Induced Transparency or Coherent Population Oscillations. Analyzing the slowing down process, we point out the role played by off resonance atoms where most of the incoming information is carried over while the pulse is confined within the sample., Comment: 14 pages, 6 figures

We consider in this paper a two-pulse photon echo sequence as a potential quantum light storage protocol. It is widely believed that a two-pulse scheme should lead to very low efficiency and is then not relevant for this specific application. We show experimentally by using a Tm${}^{3+}$:YAG crystal that such a protocol is on contrary very efficient and even too efficient to be considered as a good quantum storage protocol. Our experimental work allows us to point out on one side the real limitations of this scheme and on the other side its benefits which can be a source of inspiration to conceive more promising procedures with rare-earth ion doped crystals.

A thulium-doped crystal is experimentally shown to be an excellent candidate for broadband quantum storage in a solid-state medium. For the first time, nuclear spin coherence is optically excited, detected and characterized in such a crystal. The lifetime of the spin coherence -- the potential storage entity -- is measured by means of Raman echo to be about 300 $\mu$s over a wide range of ground state splittings. This flexibility, attractive for broadband operation, and well fitted to existing quantum sources, results from the simple hyperfine structure, contrasting with Pr- and Eu- doped crystals.

A three-level Lambda system in Tm3+ doped YAG crystal is experimentally investigated in the prospect of quantum information processing. Zeeman effect is used to lift the nuclear spin degeneracy of this ion. In a previous paper [de Seze et al. Phys. Rev. B, 73, 85112 (2006) we measured the gyromagnetic tensor components and concluded that adequate magnetic field orientation could optimize the optical connection of both ground state sublevels to each one of the excited state sublevels, thus generating Lambda systems. Here we report on the direct measurement of the transition probability ratio along the two legs of the Lambda. Measurement techniques combine frequency selective optical pumping with optical nutation or photon echo processes.

Quantum information transfer from light to atom ensembles and vice versa has both basic and practical importance. Among the relevant topics let us mention entanglement and decoherence of macroscopic systems, together with applications to quantum memory for long distance quantum cryptography. Although the first experimental demonstrations have been performed in atomic vapors and clouds, rare earth ion doped crystals are also interesting media for such processes. In this paper we address Tm3+ ions capability to behave as three-level lambda systems, a key ingredient to convert optical excitation into a spontaneous- emission-free spin wave. Indeed Tm3+ falls within reach of light sources that can be stabilized easily to the required degree. In the absence of zero-field hyperfine structure we apply an external magnetic field to lift the nuclear spin degeneracy in Tm3+:YAG. We experimentally determine the gyromagnetic tensor components with the help of spectral hole-burning techniques. Then appropriate orientation of the applied field enables us to optimize the transition probability ratio along the two legs of the lambda. The resulting three-level lambda system should suit quantum information processing requirements.