R. P. Feynman, Simulating physics with computers, International Journal of Theoretical Physics, vol.21, issue.6-7, pp.6-7467, 1982.
DOI : 10.1007/BF02650179

G. E. Moore, Cramming More Components Onto Integrated Circuits, Proceedings of the IEEE, vol.86, issue.1, pp.82-85, 1998.
DOI : 10.1109/JPROC.1998.658762

P. W. Shor, Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer, SIAM Journal on Computing, vol.26, issue.5, pp.1484-1509, 1997.
DOI : 10.1137/S0097539795293172

E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature, vol.409, issue.6816, pp.46-52, 2001.
DOI : 10.1038/35051009

F. Bussières, N. Sangouard, M. Afzelius, H. De-riedmatten, C. Simon et al., Prospective applications of optical quantum memories, Journal of Modern Optics, vol.4, issue.08, pp.1519-1537
DOI : 10.1103/PhysRevLett.104.203603

H. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication, Physical Review Letters, vol.81, issue.26, pp.5932-5935, 1998.
DOI : 10.1103/PhysRevLett.81.5932

O. A. Collins, S. D. Jenkins, A. Kuzmich, and T. A. Kennedy, Multiplexed Memory-Insensitive Quantum Repeaters, Physical Review Letters, vol.98, issue.6, p.60502, 2007.
DOI : 10.1103/PhysRevLett.98.060502

N. Sangouard, C. Simon, H. De-riedmatten, and N. Gisin, Quantum repeaters based on atomic ensembles and linear optics, Reviews of Modern Physics, vol.83, issue.1, pp.33-80, 2011.
DOI : 10.1103/RevModPhys.83.33

J. Nunn, N. K. Langford, W. S. Kolthammer, T. F. Champion, M. R. Sprague et al., Enhancing Multiphoton Rates with Quantum Memories, Physical Review Letters, vol.110, issue.13, pp.133601-2013
DOI : 10.1103/PhysRevLett.110.133601

C. Simon, M. Afzelius, J. Appel, A. B. De-la-giroday, S. J. Dewhurst et al., Quantum memories, The European Physical Journal D, vol.80, issue.1, pp.1-22, 2010.
DOI : 10.1140/epjd/e2010-00103-y

T. Golubeva, Y. Golubev, O. Mishina, A. Bramati, J. Laurat et al., High-speed spatially multimode atomic memory, Physical Review A, vol.83, issue.5, p.53810, 2011.
DOI : 10.1103/PhysRevA.83.053810

URL : http://arxiv.org/abs/1012.5016

C. Simon, H. De-riedmatten, and M. Afzelius, Temporally multiplexed quantum repeaters with atomic gases, Physical Review A, vol.82, issue.1, p.10304, 2010.
DOI : 10.1103/PhysRevA.82.010304

C. Simon, H. De-riedmatten, M. Afzelius, N. Sangouard, H. Zbinden et al., Quantum Repeaters with Photon Pair Sources and Multimode Memories, Physical Review Letters, vol.98, issue.19, 2007.
DOI : 10.1103/PhysRevLett.98.190503

N. Sinclair, E. Saglamyurek, H. Mallahzadeh, J. A. Slater, M. George et al., Spectral Multiplexing for Scalable Quantum Photonics using an Atomic Frequency Comb Quantum Memory and Feed-Forward Control, Physical Review Letters, vol.113, issue.5, pp.53603-2014
DOI : 10.1103/PhysRevLett.113.053603

A. I. Lvovsky, B. C. Sanders, and W. Tittel, Optical quantum memory, Nature Photonics, vol.95, issue.12, pp.706-714, 2009.
DOI : 10.1038/nphoton.2009.231

M. Afzelius, C. Simon, H. De-riedmatten, and N. Gisin, Multimode quantum memory based on atomic frequency combs, Physical Review A, vol.79, issue.5, p.52329, 2009.
DOI : 10.1103/PhysRevA.79.052329

B. Lauritzen, J. Miná?-r, H. De-riedmatten, M. Afzelius, and N. Gisin, Approaches for a quantum memory at telecommunication wavelengths, Physical Review A, vol.83, issue.1
DOI : 10.1103/PhysRevA.83.012318

E. Saglamyurek, J. Jin, V. B. Verma, M. D. Shaw, F. Marsili et al., Quantum storage of entangled telecom-wavelength photons in an erbium-doped optical fibre, Nature Photonics, vol.52, issue.2, pp.83-87
DOI : 10.1038/nphoton.2013.13

B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. Kröll et al., Quantum memory for nonstationary light fields based on controlled reversible inhomogeneous broadening, Physical Review A, vol.73, issue.2, p.20302, 2006.
DOI : 10.1103/PhysRevA.73.020302

A. L. Alexander, J. J. Longdell, M. J. Sellars, and N. B. Manson, Photon Echoes Produced by Switching Electric Fields, Physical Review Letters, vol.96, issue.4, p.43602, 2006.
DOI : 10.1103/PhysRevLett.96.043602

G. Hétet, J. J. Longdell, A. L. Alexander, P. K. Lam, and M. J. Sellars, Electro-Optic Quantum Memory for Light Using Two-Level Atoms, Physical Review Letters, vol.100, issue.2
DOI : 10.1103/PhysRevLett.100.023601

B. Lauritzen, J. Miná?-r,-de-riedmatten, H. , M. Afzelius, N. Sangouard et al., Telecommunication-Wavelength Solid-State Memory at the Single Photon Level, Physical Review Letters, vol.104, issue.8, p.80502, 2010.
DOI : 10.1103/PhysRevLett.104.080502

V. Damon, M. Bonarota, A. Louchet-chauvet, T. Chanelière, and J. Gouët, Revival of silenced echo and quantum memory for light, New Journal of Physics, vol.13, issue.9, pp.93031-93041, 2011.
DOI : 10.1088/1367-2630/13/9/093031

M. Bonarota, J. Dajczgewand, A. Louchet-chauvet, J. Gouët, and T. Chanelière, Photon echo with a few photons in two-level atoms, Laser Physics, vol.24, issue.9, pp.94003-94014, 2014.
DOI : 10.1088/1054-660X/24/9/094003

G. Liu and B. Jacquier, Spectroscopic Properties of Rare Earths in Optical Materials, 2005.

A. J. Freeman and R. E. Watson, Theoretical Investigation of Some Magnetic and Spectroscopic Properties of Rare-Earth Ions, Physical Review, vol.127, issue.6, pp.2058-2075, 1962.
DOI : 10.1103/PhysRev.127.2058

G. H. Dieke and H. M. Crosswhite, The Spectra of the Doubly and Triply Ionized Rare Earths, Applied Optics, vol.2, issue.7, pp.675-686, 1963.
DOI : 10.1364/AO.2.000675

R. J. Mears, L. Reekie, I. M. Jauncey, and D. N. Payne, Low-noise erbium-doped fibre amplifier operating at 1.54??m, Electronics Letters, vol.23, issue.19, pp.1026-1028, 1987.
DOI : 10.1049/el:19870719

E. Desurvire, D. Bayart, B. Desthieux, and S. Bigo, Erbium-Doped Fiber Amplifiers, Device and System Developments, 2002.

R. Moncorge, Rare earth materials in optical storage and data processing applications, Spectroscopic Properties of Rare Earths in Optical Materials by G. Liu and B. Jacquier, 2005.

Y. Sun, T. Böttger, C. W. Thiel, and R. L. Cone, Magnetic g tensors for the 4

G. Liu, Electronic Energy Level Structure, Spectroscopic Properties of Rare Earths in Optical Materials by
DOI : 10.1007/3-540-28209-2_1

H. K. Kramers, Théorie générale de la rotation paramagnétique dans les cristaux, Proceedings Koninklijke Akademie van Wetenschappen, pp.959-972, 1930.

M. J. Klein, On a Degeneracy Theorem of Kramers, American Journal of Physics, vol.20, issue.2, pp.65-71, 1952.
DOI : 10.1119/1.1933118

C. Li, C. Wyon, and R. Moncorge, Spectroscopic properties and fluorescence dynamics of Er/sup 3+/ and Yb/sup 3+/ in Y/sub 2/SiO/sub 5/, IEEE Journal of Quantum Electronics, vol.28, issue.4, pp.1209-1221, 1992.
DOI : 10.1109/3.135248

R. M. Macfarlane and R. M. Shelby, Coherent transient and holeburning spectroscopy of rare earth ions In Spectroscopy of solids containing rare earth ions by, 1987.

A. Abragam and B. Bleaney, Electronic Paramagnetic Resonance of Transition Ions, p.20, 1970.

T. Böttger, Y. Sun, C. W. Thiel, and R. L. Cone, :Y 2 SiO 5 at 1.5 ??m for optical processing, memory, and laser frequency stabilization applications, Advanced Optical Data Storage, pp.51-61, 2003.
DOI : 10.1117/12.474784

R. M. Macfarlane, T. L. Harris, Y. Sun, R. L. Cone, and R. W. , Measurement of photon echoes in Er:Y_2SiO_5 at 15????????m with a diode laser and an amplifier, Optics Letters, vol.22, issue.12, pp.871-873, 1997.
DOI : 10.1364/OL.22.000871

T. Böttger, C. W. Thiel, Y. Sun, and R. L. Cone, concentration, Physical Review B, vol.73, issue.7, pp.75101-75124, 2006.
DOI : 10.1103/PhysRevB.73.075101

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms, p.25, 1987.

R. M. Macfarlane, Inhomogeneous broadening of spectral lines in doped insulators, Journal of Luminescence, vol.45, issue.1-6, pp.1-5, 1990.
DOI : 10.1016/0022-2313(90)90089-T

W. B. Mims, K. Nassau, and J. D. Mcgee, Spectral Diffusion in Electron Resonance Lines, Physical Review, vol.123, issue.6, pp.2059-2069, 1961.
DOI : 10.1103/PhysRev.123.2059

J. R. Klauder and P. W. Anderson, Spectral Diffusion Decay in Spin Resonance Experiments, Physical Review, vol.125, issue.3, pp.912-932, 1962.
DOI : 10.1103/PhysRev.125.912

A. M. Stoneham, Shapes of Inhomogeneously Broadened Resonance Lines in Solids, Reviews of Modern Physics, vol.41, issue.1, pp.82-108, 1969.
DOI : 10.1103/RevModPhys.41.82

W. B. Mims, Electron spin echoes In Electron paramagnetic resonance by S. Geschwind, chapter 4, 1972.

G. K. Liu and R. L. Cone, compounds as observed in photon-echo experiments, Physical Review B, vol.41, issue.10, pp.6193-6200, 1990.
DOI : 10.1103/PhysRevB.41.6193

G. K. Liu, R. L. Cone, M. F. Joubert, B. Jacquier, and J. L. Skinner, Energy transfer and instantaneous spectral diffusion processes in Tb 3+ compounds as probed in photon echo experiments, Journal of Luminescence, vol.45, issue.102, pp.1-6, 1990.

A. S. Van-de-nes, J. J. Braat, and S. F. Pereira, High-density optical data storage, Rep. Prog. Phys, vol.69, issue.8, p.2323, 2006.

W. Tittel, M. Afzelius, T. Chanelière, R. L. Cone, S. Kröll et al., Photon-echo quantum memory in solid state systems, Laser & Photonics Reviews, vol.456, issue.41, pp.244-267, 2010.
DOI : 10.1002/lpor.200810056

K. Hammerer, A. S. Sørensen, and E. S. Polzik, Quantum interface between light and atomic ensembles, Reviews of Modern Physics, vol.82, issue.2, pp.1041-1093, 2010.
DOI : 10.1103/RevModPhys.82.1041

M. O. Scully and S. Zubairy, Quantum Optics, 1997.

F. Bloch, Nuclear Induction, Physical Review, vol.70, issue.7-8, pp.460-474, 1946.
DOI : 10.1103/PhysRev.70.460

R. P. Feynman, F. L. Vernon, and R. W. Hellwarth, Geometrical Representation of the Schr??dinger Equation for Solving Maser Problems, Journal of Applied Physics, vol.28, issue.1, pp.49-52, 1957.
DOI : 10.1063/1.1722572

H. Torrey, Transient Nutations in Nuclear Magnetic Resonance, Physical Review, vol.76, issue.8, pp.1059-1068, 1949.
DOI : 10.1103/PhysRev.76.1059

E. L. Hahn, Spin Echoes, Physical Review, vol.80, issue.4, pp.580-594, 1950.
DOI : 10.1103/PhysRev.80.580

N. A. Kurnit, I. D. Abella, and S. R. Hartmann, Observation of a Photon Echo, Physical Review Letters, vol.13, issue.19, pp.567-568, 1964.
DOI : 10.1103/PhysRevLett.13.567

I. D. Abella, N. A. Kurnit, and S. R. Hartmann, Photon Echoes, Physical Review, vol.141, issue.1, pp.391-406, 1966.
DOI : 10.1103/PhysRev.141.391

E. Hahn, Nuclear Induction Due to Free Larmor Precession, Physical Review, vol.77, issue.2, pp.297-298, 1950.
DOI : 10.1103/PhysRev.77.297.2

R. Brewer and R. Shoemaker, Optical Free Induction Decay, Physical Review A, vol.6, issue.6, 1972.
DOI : 10.1103/PhysRevA.6.2001

L. Mandel and E. Wolf, Optical coherence and quantum optics. chapter 7, 1995.

J. Ruggiero, T. Chanelière, and J. Gouët, Coherent response to optical excitation in a strongly absorbing rare-earth ion-doped crystal, Journal of the Optical Society of America B, vol.27, issue.1
DOI : 10.1364/JOSAB.27.000032

M. Bonarota, Optimisation de la programmation d'un cristal dopé aux ions de terres rares, opérant comme processeur analogique d'analyse spectrale RF, ou de stockage d'information quantique, p.50, 2012.

S. O. Elyutin, S. M. Zakharov, and E. A. Manykin, Theory of the photon-echo formation, Sov. Phys. JETP, vol.49, p.421, 1979.

N. W. Carlson, W. R. Babbitt, T. W. Mossberg, L. J. Rothberg, and A. G. Yodh, Storage and time reversal of light pulses using photon echoes, Optics Letters, vol.8, issue.9
DOI : 10.1364/OL.8.000483

J. Ruggiero, J. Gouët, C. Simon, and T. Chanelière, Why the two-pulse photon echo is not a good quantum memory protocol, Physical Review A, vol.79, issue.5, p.53851, 2009.
DOI : 10.1103/PhysRevA.79.053851

W. K. Wootters and W. H. Zurek, A single quantum cannot be cloned, Nature, vol.15, issue.5886, pp.802-803, 1982.
DOI : 10.1038/299802a0

N. Sangouard, C. Simon, J. Miná?, M. Afzelius, T. Chanelière et al., Impossibility of faithfully storing single photons with the three-pulse photon echo, Physical Review A, vol.81, issue.6, p.62333, 2010.
DOI : 10.1103/PhysRevA.81.062333

N. Sangouard, C. Simon, M. Afzelius, and N. Gisin, Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening, Physical Review A, vol.75, issue.3
DOI : 10.1103/PhysRevA.75.032327

A. Abragam, Principles of Nuclear Magnetism, 1961.

M. M. Loy, Observation of Population Inversion by Optical Adiabatic Rapid Passage, Physical Review Letters, vol.32, issue.15, pp.814-817, 1974.
DOI : 10.1103/PhysRevLett.32.814

M. F. Pascual-winter, R. Tongning, T. Chanelière, and J. Gouët, Securing coherence rephasing with a pair of adiabatic rapid passages, New Journal of Physics, vol.15, issue.5, pp.55024-2013
DOI : 10.1088/1367-2630/15/5/055024

M. S. Silver, R. I. Joseph, and D. I. Hoult, Selective spin inversion in nuclear magnetic resonance and coherent optics through an exact solution of the Bloch-Riccati equation, Physical Review A, vol.31, issue.4, pp.2753-2755, 1985.
DOI : 10.1103/PhysRevA.31.2753

I. Zafarullah, M. Tian, T. Chang, and W. R. Babbitt, Preparation of inverted medium and processing in the inverted medium, Proceedings of the Ninth International Meeting on Hole Burning, Single Molecule, and Related Spectroscopies: Science and Applications Hole Burning, Single Molecule, and Related Spectroscopies: Science and Applications, pp.158-163, 2007.
DOI : 10.1016/j.jlumin.2007.02.019

L. Rippe, M. Nilsson, S. Kröll, R. Klieber, and D. Suter, Experimental demonstration of efficient and selective population transfer and qubit distillation in a rare-earth-metal-ion-doped crystal, Physical Review A, vol.71, issue.6, pp.62328-67, 2005.
DOI : 10.1103/PhysRevA.71.062328

H. M. Gibbs, Incoherent Resonance Fluorescence from a Rb Atomic Beam Excited by a Short Coherent Optical Pulse, Physical Review A, vol.8, issue.1, pp.446-455, 1973.
DOI : 10.1103/PhysRevA.8.446

J. Dajczgewand, J. Gouët, A. Louchet-chauvet, and T. Chanelière, Large efficiency at telecom wavelength for optical quantum memories, Optics Letters, vol.39, issue.9
DOI : 10.1364/OL.39.002711

F. R. Graf, A. Renn, G. Zumofen, and U. P. Wild, Photon-echo attenuation by dynamical processes in rare-earth-ion-doped crystals, Physical Review B, vol.58, issue.9, pp.5462-5478, 1998.
DOI : 10.1103/PhysRevB.58.5462

J. Huang, J. M. Zhang, A. Lezama, and T. W. Mossberg, Excess dephasing in photon-echo experiments arising from excitation-induced electronic level shifts, Physical Review Letters, vol.63, issue.1, pp.78-81, 1989.
DOI : 10.1103/PhysRevLett.63.78

J. Dajczgewand, R. Ahlefeldt, T. Böttger, A. Louchet-chauvet, J. Gouët et al., Optical memory bandwidth and multiplexing capacity in the erbium telecommunication window, New Journal of Physics, vol.17, issue.2, pp.23031-2015
DOI : 10.1088/1367-2630/17/2/023031

M. Mitsunaga, T. Takagahara, R. Yano, and N. Uesugi, Excitation-induced frequency shift probed by stimulated photon echoes, Physical Review Letters, vol.68, issue.21, pp.3216-3219, 1992.
DOI : 10.1103/PhysRevLett.68.3216

C. W. Thiel, R. M. Macfarlane, Y. Sun, T. Böttger, N. Sinclair et al., Measuring and analyzing excitation-induced decoherence in rare-earth-doped optical materials, Laser Physics, vol.24, issue.10, pp.106002-2014
DOI : 10.1088/1054-660X/24/10/106002

F. De-seze, F. Dahes, V. Crozatier, I. Lorgeré, F. Bretenaker et al., Coherent driving of Tm3+:YAG ions using a complex hyperbolic secant optical field, The European Physical Journal D, vol.9, issue.3, pp.343-355, 2005.
DOI : 10.1140/epjd/e2005-00086-8

R. M. Macfarlane, Optical Stark spectroscopy of solids, Journal of Luminescence, vol.125, issue.1-2, pp.156-174, 2007.
DOI : 10.1016/j.jlumin.2006.08.012

S. R. Hastings-simon, M. U. Staudt, M. Afzelius, P. Baldi, D. Jaccard et al., Controlled Stark shifts in Er3+-doped crystalline and amorphous waveguides for quantum state storage, Optics Communications, vol.266, issue.2, pp.716-719, 2006.
DOI : 10.1016/j.optcom.2006.05.003

M. P. Hedges, High performance solid state quantum memory, 2011.

V. Crozatier, G. Gorju, F. Bretenaker, J. Gouët, I. Lorgeré et al., Experimental observation of spectral diffusion in an optically pumped crystal, Journal of Luminescence, vol.127, issue.1, pp.65-70, 2007.
DOI : 10.1016/j.jlumin.2007.02.010

S. B. Altner, G. Zumofen, U. P. Wild, and M. Mitsunaga, Photon-echo attenuation in rare-earth-ion-doped crystals, Physical Review B, vol.54, issue.24, pp.17493-17507, 1996.
DOI : 10.1103/PhysRevB.54.17493

Y. S. Bai and R. Kachru, Nonequilibrium resonant-phonon-induced excess photon-echo dephasing, Physical Review B, vol.46, issue.21, pp.13735-13738, 1992.
DOI : 10.1103/PhysRevB.46.13735

K. P. Kretsch, C. Belton, S. Lipson, W. J. Blau, F. Z. Henari et al., Amplified spontaneous emission and optical gain spectra from stilbenoid and phenylene vinylene derivative model compounds, Journal of Applied Physics, vol.86, issue.11, pp.6155-6159, 1999.
DOI : 10.1063/1.371668

L. W. Casperson and A. Yariv, Spectral narrowing in high-gain lasers, IEEE Journal of Quantum Electronics, vol.8, issue.2, pp.80-85, 1972.
DOI : 10.1109/JQE.1972.1076944

A. Costela, O. García, L. Cerdán, I. García-moreno, and R. Sastre, Amplified spontaneous emission and optical gain measurements from pyrromethene 567 ????? doped polymer waveguides and quasi-waveguides, Optics Express, vol.16, issue.10, pp.7023-7036, 2008.
DOI : 10.1364/OE.16.007023

M. D. Mcgehee, R. Gupta, S. Veenstra, E. K. Miller, M. A. Díaz-garcía et al., Amplified spontaneous emission from photopumped films of a conjugated polymer, Physical Review B, vol.58, issue.11, pp.7035-7039, 1998.
DOI : 10.1103/PhysRevB.58.7035

F. Auzel, G. Baldacchini, L. Laversenne, and G. Boulon, Radiation trapping and self-quenching analysis in Yb3+, Er3+, and Ho3+ doped Y2O3, Proceedings of the Fifth French-Israeli Workshop on Optical Properties of Inorganic Materials, pp.103-109, 2003.
DOI : 10.1016/S0925-3467(03)00112-5

R. Brede, E. Heumann, J. Koetke, T. Danger, G. Huber et al., Green up???conversion laser emission in Er???doped crystals at room temperature, Applied Physics Letters, vol.63, issue.15
DOI : 10.1063/1.110581

C. W. Thiel, W. R. Babbitt, and R. L. Cone, Optical decoherence studies of yttrium oxyorthosilicate Y 2 SiO 5 codoped with Er 3+ and Eu 3+ for optical signal processing and quantum information applications at 1.5 microns

K. W. Jang and R. S. Meltzer, in disordered crystalline systems, Physical Review B, vol.52, issue.9, pp.6431-6439, 1995.
DOI : 10.1103/PhysRevB.52.6431

A. Amisse, Efficient quantum memory in the telecommunication wavelength range