. .. Introduction-d-'une-déviationdéviationà-la-loi-de-la-gravitation, 55 2.5.1 Cas d'un interféromètre avec un seul isotope du rubidium, p.58

A. Derevianko, B. Obreshkov, and V. A. Dzuba, Mapping Out Atom-Wall Interaction with Atomic Clocks, Physical Review Letters, vol.103, issue.13, p.133201, 2009.
DOI : 10.1103/PhysRevLett.103.133201
URL : http://arxiv.org/abs/0905.4780

G. Barton, Frequency shifts near an interface: inadequacy of two-level atomic models, Journal of Physics B: Atomic and Molecular Physics, vol.7, issue.16, p.2134, 1974.
DOI : 10.1088/0022-3700/7/16/012

E. A. Power and S. Zineau, Coulomb Gauge in Non-Relativistic Quantum Electro-Dynamics and the Shape of Spectral Lines, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.251, issue.999, p.427, 1959.
DOI : 10.1098/rsta.1959.0008

G. Compagno, R. Passante, and F. Persico, Atom-Field Interactions and Dressed Atoms, 1995.
DOI : 10.1017/CBO9780511599774

N. W. Ashcroft and N. D. Mermin, Solid State Physics, 1976.

Q. Niu, X. Zhao, G. A. Georgakis, and M. G. Raizen, Atomic Landau-Zener Tunneling and Wannier-Stark Ladders in Optical Potentials, Physical Review Letters, vol.76, issue.24, p.4504, 1996.
DOI : 10.1103/PhysRevLett.76.4504

G. Peters and J. H. Wilkinson, Eigenvalues of Ax = ??Bx with band symmetric A and B, The Computer Journal, vol.12, issue.4, p.398, 1969.
DOI : 10.1093/comjnl/12.4.398

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 1992.

A. G. Abrashkevich, D. G. Abrashkevich, M. S. Kaschiev, and I. V. Puzynin, Finite-element solution of the coupled-channel Schr??dinger equation using high-order accuracy approximations, Computer Physics Communications, vol.85, issue.1, p.40, 1995.
DOI : 10.1016/0010-4655(94)00106-C

N. Sukumar and J. E. Pask, Classical and enriched finite element formulations for Bloch-periodic boundary conditions, International Journal for Numerical Methods in Engineering, vol.54, issue.11, p.1121, 2009.
DOI : 10.1002/nme.2457
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.147.8635

P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics, American Journal of Physics, vol.62, issue.12, 1994.
DOI : 10.1119/1.17618

H. B. Casimir and D. Polder, The Influence of Retardation on the London-van der Waals Forces, Physical Review, vol.73, issue.4, p.360, 1948.
DOI : 10.1103/PhysRev.73.360

C. I. Sukenik, M. G. Boshier, D. Cho, V. Sandoghdar, and E. A. Hinds, Measurement of the Casimir-Polder force, Physical Review Letters, vol.70, issue.5, p.560, 1993.
DOI : 10.1103/PhysRevLett.70.560

A. Landragin, J. Y. Courtois, G. Labeyrie, N. Vansteenkiste, C. I. Westbrook et al., Measurement of the van der Waals Force in an Atomic Mirror, Physical Review Letters, vol.77, issue.8, p.1464, 1996.
DOI : 10.1103/PhysRevLett.77.1464

F. Shimizu, Specular Reflection of Very Slow Metastable Neon Atoms from a Solid Surface, Physical Review Letters, vol.86, issue.6, p.987, 2001.
DOI : 10.1103/PhysRevLett.86.987

V. Druzhinina and M. Dekieviet, Experimental Observation of Quantum Reflection far from Threshold, Physical Review Letters, vol.91, issue.19, p.193202, 2003.
DOI : 10.1103/PhysRevLett.91.193202

T. A. Pasquini, M. Saba, G. Jo, Y. Shin, W. Ketterle et al., Low Velocity Quantum Reflection of Bose-Einstein Condensates, Physical Review Letters, vol.97, issue.9, p.93201, 2006.
DOI : 10.1103/PhysRevLett.97.093201

M. Antezza, L. P. Pitaevskii, and S. Stringari, Effect of the Casimir-Polder force on the collective oscillations of a trapped Bose-Einstein condensate, Physical Review A, vol.70, issue.5, p.53619, 2004.
DOI : 10.1103/PhysRevA.70.053619

D. M. Harber, J. M. Obrecht, J. M. Mcguirk, and E. A. Cornell, Measurement of the Casimir-Polder force through center-of-mass oscillations of a Bose-Einstein condensate, Physical Review A, vol.72, issue.3, p.33610, 2005.
DOI : 10.1103/PhysRevA.72.033610

M. Antezza, L. P. Pitaevskii, S. Stringari, and V. B. Svetovoy, Casimir-Lifshitz Force Out of Thermal Equilibrium and Asymptotic Nonadditivity, Physical Review Letters, vol.97, issue.22, p.223203, 2006.
DOI : 10.1103/PhysRevLett.97.223203
URL : http://arxiv.org/abs/cond-mat/0607205

A. Lambrecht, P. A. Neto, and S. Reynaud, The Casimir effect within scattering theory, New Journal of Physics, vol.8, issue.10, p.243, 2006.
DOI : 10.1088/1367-2630/8/10/243
URL : https://hal.archives-ouvertes.fr/hal-00112885

R. Messina, D. A. Dalvit, P. A. Neto, A. Lambrecht, and S. Reynaud, Dispersive interactions between atoms and nonplanar surfaces, Physical Review A, vol.80, issue.2, p.22119, 2009.
DOI : 10.1103/PhysRevA.80.022119
URL : http://arxiv.org/abs/0902.3235

J. M. Wylie and J. E. Sipe, Quantum electrodynamics near an interface, Physical Review A, vol.30, issue.3, p.1185, 1984.
DOI : 10.1103/PhysRevA.30.1185

S. Y. Buhmann, D. Welsch, and T. Kampf, Ground-state van der Waals forces in planar multilayer magnetodielectrics, Physical Review A, vol.72, issue.3, p.32112, 2005.
DOI : 10.1103/PhysRevA.72.032112
URL : http://arxiv.org/abs/quant-ph/0502183

K. M. Case, Singular Potentials, Physical Review, vol.80, issue.5, p.797, 1950.
DOI : 10.1103/PhysRev.80.797

W. M. Frank, D. J. Land, and R. M. Spector, Singular Potentials, Reviews of Modern Physics, vol.43, issue.1, p.36, 1971.
DOI : 10.1103/RevModPhys.43.36

P. A. Neto, A. Lambrecht, and S. Reynaud, Casimir energy between a plane and a sphere in electromagnetic vacuum, Physical Review A, vol.78, issue.1, p.12115, 2008.
DOI : 10.1103/PhysRevA.78.012115
URL : https://hal.archives-ouvertes.fr/hal-00266744

A. Canaguier-durand, P. A. Neto, I. Cavero-pelaez, A. Lambrecht, and S. Reynaud, Casimir Interaction between Plane and Spherical Metallic Surfaces, Physical Review Letters, vol.102, issue.23, p.230404, 2009.
DOI : 10.1103/PhysRevLett.102.230404
URL : https://hal.archives-ouvertes.fr/hal-00354768

A. Canaguier-durand, A. Gérardin, R. Gué-r-o-u-t, P. A. Neto, V. V. Nesvizhevsky et al., Casimir interaction between a dielectric nanosphere and a metallic plane, Physical Review A, vol.83, issue.3, p.32508, 2011.
DOI : 10.1103/PhysRevA.83.032508
URL : https://hal.archives-ouvertes.fr/hal-00560372

G. Compagno, R. Passante, and F. Persico, Virtual Field and Internal Structure of Half-Dressed Extended Particles, Europhysics Letters (EPL), vol.7, issue.5, p.399, 1988.
DOI : 10.1209/0295-5075/7/5/004

A. Derevianko, W. R. Johnson, M. S. Safronova, and J. F. Babb, High-Precision Calculations of Dispersion Coefficients, Static Dipole Polarizabilities, and Atom-Wall Interaction Constants for Alkali-Metal Atoms, Physical Review Letters, vol.82, issue.18, p.3589, 1999.
DOI : 10.1103/PhysRevLett.82.3589

J. C. Slater, Atomic Radii in Crystals, The Journal of Chemical Physics, vol.41, issue.10, p.3199, 1964.
DOI : 10.1063/1.1725697

E. Clementi, D. L. Raimondi, and W. P. Reinhardt, Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons, The Journal of Chemical Physics, vol.47, issue.4, p.1300, 1967.
DOI : 10.1063/1.1712084

A. A. Geraci, S. B. Papp, and J. Kitching, Short-Range Force Detection Using Optically Cooled Levitated Microspheres, Physical Review Letters, vol.105, issue.10, p.101101, 2010.
DOI : 10.1103/PhysRevLett.105.101101
URL : http://arxiv.org/abs/1006.0261

N. W. Ashcroft and N. D. Mermin, Solid State Physics, 1976.

G. H. Wannier, Wave Functions and Effective Hamiltonian for Bloch Electrons in an Electric Field, Physical Review, vol.117, issue.2, p.432, 1960.
DOI : 10.1103/PhysRev.117.432

M. Gluck, A. R. Kolovsky, H. J. Korsch, and N. Moiseyev, Calculation of Wannier-Bloch and Wannier-Stark states, The European Physical Journal D - Atomic, Molecular and Optical Physics, vol.4, issue.3, p.239, 1998.
DOI : 10.1007/s100530050205

P. Lemonde and P. Wolf, Optical lattice clock with atoms confined in a shallow trap, Physical Review A, vol.72, issue.3, p.33409, 2005.
DOI : 10.1103/PhysRevA.72.033409

P. Wolf, P. Lemonde, A. Lambrecht, S. Bize, A. Landragin et al., From optical lattice clocks to the measurement of forces in the Casimir regime, Physical Review A, vol.75, issue.6, p.63608, 2007.
DOI : 10.1103/PhysRevA.75.063608
URL : https://hal.archives-ouvertes.fr/hal-00088469

R. Messina, S. Pelisson, M. Angonin, and P. Wolf, Atomic states in optical traps near a planar surface, Physical Review A, vol.83, issue.5, p.52111, 2011.
DOI : 10.1103/PhysRevA.83.052111
URL : http://arxiv.org/abs/1103.1581

Q. Beaufils, G. Tackmann, B. Pelle, S. Pelisson, P. Wolf et al., Laser Controlled Tunneling in a Vertical Optical Lattice, Physical Review Letters, vol.106, issue.21, p.213002, 2011.
DOI : 10.1103/PhysRevLett.106.213002
URL : https://hal.archives-ouvertes.fr/hal-00568873

G. Tackmann, B. Pelle, A. Hilico, Q. Beaufils, F. Pereira et al., Raman-laser spectroscopy of Wannier-Stark states, Physical Review A, vol.84, issue.6, p.63422, 2011.
DOI : 10.1103/PhysRevA.84.063422
URL : https://hal.archives-ouvertes.fr/hal-00629340

S. Pelisson, R. Messina, M. Angonin, and P. Wolf, Dynamical aspects of atom interferometry in an optical lattice in proximity to a surface, Physical Review A, vol.86, issue.1, p.13614, 2012.
DOI : 10.1103/PhysRevA.86.013614

J. Agler and R. Froese, Existence of Stark ladder resonances, Communications in Mathematical Physics, vol.181, issue.2, p.161, 1985.
DOI : 10.1007/BF01212445

J. E. Avron, Model Calculation of Stark Ladder Resonances, Physical Review Letters, vol.37, issue.23, p.1568, 1976.
DOI : 10.1103/PhysRevLett.37.1568

F. Bentosela, V. Grecchi, and F. Zironi, Approximate ladder of resonances in a semi-infinite crystal, Journal of Physics C: Solid State Physics, vol.15, issue.35, p.7119, 1982.
DOI : 10.1088/0022-3719/15/35/010

V. Grecchi, M. Maioli, and A. Sacchetti, Wannier ladders and perturbation theory, Journal of Physics A: Mathematical and General, vol.26, issue.7, p.379, 1993.
DOI : 10.1088/0305-4470/26/7/006

V. Grecchi and A. Sacchetti, Lifetime of the Wannier-Stark Resonances and Perturbation Theory, Communications in Mathematical Physics, vol.185, issue.2, p.359, 1997.
DOI : 10.1007/s002200050094

V. Buslaev and A. Grigis, Imaginary parts of Stark???Wannier resonances, Journal of Mathematical Physics, vol.39, issue.5, p.2520, 1998.
DOI : 10.1063/1.532406

]. S. Glutsch and F. Bechstedt, Interaction of Wannier-Stark ladders and electrical breakdown in superlattices, Physical Review B, vol.60, issue.24, p.16584, 1999.
DOI : 10.1103/PhysRevB.60.16584

E. Balslev and J. M. Combes, Spectral properties of many-body Schr??dinger operators with dilatation-analytic interactions, Communications in Mathematical Physics, vol.12, issue.5, p.280, 1971.
DOI : 10.1007/BF01877511

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 1992.

E. Power and S. Zienau, Coulomb Gauge in Non-Relativistic Quantum Electro-Dynamics and the Shape of Spectral Lines, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.251, issue.999, p.427, 1959.
DOI : 10.1098/rsta.1959.0008

N. Moiseyev, Non-Hermitian Quantum mechanics, 2011.
DOI : 10.1017/CBO9780511976186

M. Takamoto, F. Hong, R. Higashi, and H. Katori, An optical lattice clock, Nature, vol.19, issue.7040, p.321, 2005.
DOI : 10.1016/S0030-4018(97)00669-X

P. Cladé, Determination of the Fine Structure Constant Based on Bloch Oscillations of Ultracold Atoms in a Vertical Optical Lattice, Physical Review Letters, vol.96, issue.3, p.33001, 2006.
DOI : 10.1103/PhysRevLett.96.033001

H. J. Briegel, Quantum computing with neutral atoms, Journal of Modern Optics, vol.1, issue.2-3, p.415, 2000.
DOI : 10.1103/RevModPhys.68.733
URL : http://arxiv.org/abs/quant-ph/9904010

D. Schrader, Neutral Atom Quantum Register, Physical Review Letters, vol.93, issue.15, p.150501, 2004.
DOI : 10.1103/PhysRevLett.93.150501
URL : http://arxiv.org/abs/quant-ph/0409037

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, Quantum Logic Gates in Optical Lattices, Physical Review Letters, vol.82, issue.5, p.1060, 1999.
DOI : 10.1103/PhysRevLett.82.1060
URL : http://arxiv.org/abs/quant-ph/9806021

L. Förster, Microwave Control of Atomic Motion in Optical Lattices, Physical Review Letters, vol.103, issue.23, p.233001, 2009.
DOI : 10.1103/PhysRevLett.103.233001

M. B. Dahan, Bloch Oscillations of Atoms in an Optical Potential, Physical Review Letters, vol.76, issue.24, p.4508, 1996.
DOI : 10.1103/PhysRevLett.76.4508

S. R. Wilkinson, Observation of Atomic Wannier-Stark Ladders in an Accelerating Optical Potential, Physical Review Letters, vol.76, issue.24, p.4512, 1996.
DOI : 10.1103/PhysRevLett.76.4512

V. V. Ivanov, Coherent Delocalization of Atomic Wave Packets in Driven Lattice Potentials, Physical Review Letters, vol.100, issue.4, p.43602, 2008.
DOI : 10.1103/PhysRevLett.100.043602

G. Roati, Atom Interferometry with Trapped Fermi Gases, Physical Review Letters, vol.92, issue.23, p.230402, 2004.
DOI : 10.1103/PhysRevLett.92.230402
URL : http://arxiv.org/abs/cond-mat/0402328

P. Cladé, A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave, Europhysics Letters (EPL), vol.71, issue.5, p.730, 2005.
DOI : 10.1209/epl/i2005-10163-6

D. S. Weiss, B. C. Young, and S. Chu, Precision measurement of ?/m Cs based on photon recoil using laser-cooled atoms and atomic interferometry, Applied Physics B Lasers and Optics, vol.72, issue.3, p.217, 1994.
DOI : 10.1007/BF01081393

P. Lemonde and P. Wolf, Optical lattice clock with atoms confined in a shallow trap, Physical Review A, vol.72, issue.3, p.33409, 2005.
DOI : 10.1103/PhysRevA.72.033409

S. Kuhr, Analysis of dephasing mechanisms in a standing-wave dipole trap, Physical Review A, vol.72, issue.2, p.23406, 2005.
DOI : 10.1103/PhysRevA.72.023406

M. F. Andersen, A. Kaplan, and N. Davidson, Echo Spectroscopy and Quantum Stability of Trapped Atoms, Physical Review Letters, vol.90, issue.2, p.23001, 2003.
DOI : 10.1103/PhysRevLett.90.023001

A. Derevianko, ???Doubly Magic??? Conditions in Magic-Wavelength Trapping of Ultracold Alkali-Metal Atoms, Physical Review Letters, vol.105, issue.3, p.33002, 2010.
DOI : 10.1103/PhysRevLett.105.033002

A. Kaplan, M. F. Andersen, and N. Davidson, Suppression of inhomogeneous broadening in rf spectroscopy of optically trapped atoms, Physical Review A, vol.66, issue.4, p.45401, 2002.
DOI : 10.1103/PhysRevA.66.045401

P. Wolf, From optical lattice clocks to the measurement of forces in the Casimir regime, Physical Review A, vol.75, issue.6, p.63608, 2007.
DOI : 10.1103/PhysRevA.75.063608
URL : https://hal.archives-ouvertes.fr/hal-00088469

N. Poli, Precision Measurement of Gravity with Cold Atoms in an Optical Lattice and Comparison with a Classical Gravimeter, Physical Review Letters, vol.106, issue.3, p.38501, 2011.
DOI : 10.1103/PhysRevLett.106.038501

M. Karski, Imprinting patterns of neutral atoms in an optical lattice using magnetic resonance techniques, New Journal of Physics, vol.12, issue.6, p.65027, 2010.
DOI : 10.1088/1367-2630/12/6/065027

L. Yi, Clock Transition, Physical Review Letters, vol.106, issue.7, p.73005, 2011.
DOI : 10.1103/PhysRevLett.106.073005

P. Lemonde and P. Wolf, Optical lattice clock with atoms confined in a shallow trap, Physical Review A, vol.72, issue.3, p.33409, 2005.
DOI : 10.1103/PhysRevA.72.033409

R. Messina, S. Pelisson, M. Angonin, and P. Wolf, Atomic states in optical traps near a planar surface, Physical Review A, vol.83, issue.5, p.52111, 2011.
DOI : 10.1103/PhysRevA.83.052111

H. B. Casimir and D. Polder, The Influence of Retardation on the London-van der Waals Forces, Physical Review, vol.73, issue.4, p.360, 1948.
DOI : 10.1103/PhysRev.73.360

N. W. Ashcroft and N. D. Mermin, Solid State Physics, 1976.

Q. Beaufils, G. Tackmann, X. Wang, B. Pelle, S. Pelisson et al., Laser Controlled Tunneling in a Vertical Optical Lattice, Physical Review Letters, vol.106, issue.21, p.213002, 2011.
DOI : 10.1103/PhysRevLett.106.213002
URL : https://hal.archives-ouvertes.fr/hal-00568873

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 1992.

P. Lemonde and P. Wolf, Optical lattice clock with atoms confined in a shallow trap, Physical Review A, vol.72, issue.3, p.33409, 2005.
DOI : 10.1103/PhysRevA.72.033409

L. D. Broglie, Waves and Quanta, Nature, vol.112, issue.2815, 1923.
DOI : 10.1038/112540a0

C. Davisson and L. H. Germer, Diffraction of Electrons by a Crystal of Nickel, Physical Review, vol.30, issue.6, p.705, 1927.
DOI : 10.1103/PhysRev.30.705

O. R. Frisch, H. Von-halban, J. Jr, and . Koch, Some Experiments on the Magnetic Properties of Free Neutrons, Physical Review, vol.53, issue.9, p.719, 1938.
DOI : 10.1103/PhysRev.53.719

L. Marton and E. Interferometer, Electron Interferometer, Physical Review, vol.85, issue.6, p.1057, 1952.
DOI : 10.1103/PhysRev.85.1057

H. Rauch, W. Treimer, and U. Bonse, Test of a single crystal neutron interferometer, Physics Letters A, vol.47, issue.5, p.369, 1974.
DOI : 10.1016/0375-9601(74)90132-7

O. Carnal and J. Mlynek, Young???s double-slit experiment with atoms: A simple atom interferometer, Physical Review Letters, vol.66, issue.21, p.2689, 1991.
DOI : 10.1103/PhysRevLett.66.2689

D. W. Keith, C. R. Ekstrom, Q. A. Turchette, and D. A. Pritchard, An interferometer for atoms, Physical Review Letters, vol.66, issue.21, p.2693, 1991.
DOI : 10.1103/PhysRevLett.66.2693

M. S. Chapman, C. R. Ekstrom, T. D. Hammond, R. A. Rubienstein, J. Schmiedmayer et al., Molecules, Physical Review Letters, vol.74, issue.24, p.4783, 1995.
DOI : 10.1103/PhysRevLett.74.4783

M. Arndt, O. Nairz, J. Petschinka, and A. Zeilinger, High contrast interference with C 40 and C 70, Compt. Rend. Acad.Sci. SerieIV, vol.2, issue.4, p.581, 2001.

L. P. Kapitza and P. A. Dirac, The reflection of electrons from standing light waves, Proc. Cambridge, p.297, 1933.
DOI : 10.1017/S0305004100011105

S. Altshuler, L. M. Frantz, and S. Braunstein, Reflection of Atoms from Standing Light Waves, Physical Review Letters, vol.17, issue.5, p.231, 1966.
DOI : 10.1103/PhysRevLett.17.231

P. E. Moskowitz, P. L. Gould, S. R. Atlas, and D. Pritchard, Diffraction of an Atomic Beam by Standing-Wave Radiation, Physical Review Letters, vol.51, issue.5, p.370, 1983.
DOI : 10.1103/PhysRevLett.51.370

E. M. Rasel, M. K. Oberthaler, H. Batelaan, J. Schmiedmayer, and A. Zeilinger, Atom Wave Interferometry with Diffraction Gratings of Light, Physical Review Letters, vol.75, issue.14, p.2633, 1995.
DOI : 10.1103/PhysRevLett.75.2633

D. M. Giltner, R. W. Mcgowan, and S. A. Lee, Atom Interferometer Based on Bragg Scattering from Standing Light Waves, Physical Review Letters, vol.75, issue.14, p.2638, 1995.
DOI : 10.1103/PhysRevLett.75.2638

S. B. Cahn, A. Kumarakrishnan, U. Shim, and T. Sleator, Time-Domain de Broglie Wave Interferometry, Physical Review Letters, vol.79, issue.5, p.784, 1997.
DOI : 10.1103/PhysRevLett.79.784

I. Rabi, J. R. Zacharias, S. Millman, and P. Kusch, A New Method of Measuring Nuclear Magnetic Moment, Physical Review, vol.53, issue.4, p.318, 1938.
DOI : 10.1103/PhysRev.53.318

N. F. Ramsey, A New Molecular Beam Resonance Method, Physical Review, vol.76, issue.7, p.996, 1949.
DOI : 10.1103/PhysRev.76.996

C. Bordé, Atomic interferometry with internal state labelling, Physics Letters A, vol.140, issue.1-2, 1989.
DOI : 10.1016/0375-9601(89)90537-9

F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. Bordé, Optical Ramsey spectroscopy in a rotating frame: Sagnac effect in a matter-wave interferometer, Physical Review Letters, vol.67, issue.2, p.177, 1991.
DOI : 10.1103/PhysRevLett.67.177

M. Kasevich, D. Weiss, A. Riis, K. Moler, S. Kasapi et al., Atomic velocity selection using stimulated Raman transitions, Physical Review Letters, vol.66, issue.18, p.2297, 1991.
DOI : 10.1103/PhysRevLett.66.2297

L. Landau and E. Lifchitz, Physique théorique tome 3 -Mécanique Quantique, 1966.

R. P. Feynman, Space-Time Approach to Non-Relativistic Quantum Mechanics, Reviews of Modern Physics, vol.20, issue.2, p.367, 1948.
DOI : 10.1103/RevModPhys.20.367

P. Storey and C. Cohen-tannoudji, The Feynman path integral approach to atomic interferometry. A??tutorial, Journal de Physique II, vol.4, issue.11, 1994.
DOI : 10.1051/jp2:1994103
URL : https://hal.archives-ouvertes.fr/jpa-00248106

L. Landau and E. Lifchitz, Physique théorique tome 1 -Mécanique, 1964.

Q. Bodart, S. Merlet, N. Malossi, F. P. Santos, P. Bouyer et al., A cold atom pyramidal gravimeter with a single laser beam, Applied Physics Letters, vol.96, issue.13, p.134101, 2010.
DOI : 10.1063/1.3373917
URL : https://hal.archives-ouvertes.fr/hal-00462216

J. Kitching, S. Knappe, and E. A. Donley, Atomic Sensors – A Review, IEEE Sensors Journal, vol.11, issue.9, p.1749, 2011.
DOI : 10.1109/JSEN.2011.2157679

P. Gill, When should we change the definition of the second?, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.34, issue.10, p.4109, 2011.
DOI : 10.1364/OL.34.001573

C. W. Chou, D. B. Hume, J. C. Koelemeij, D. J. Wineland, and T. Rosenband, Frequency comparison of two high accuracy Al+ optical clocks, J. Opt. Soc. Am. B, vol.22, p.1819, 2005.

M. Chwalla, J. Benhelm, K. Kim, G. Kirchmain, T. Monz et al., Clock Transition, Physical Review Letters, vol.102, issue.2, p.23002, 2009.
DOI : 10.1103/PhysRevLett.102.023002

R. L. Targat, X. Baillard, M. Fouché, A. Brusch, O. Tcherbakoff et al., Atoms, Physical Review Letters, vol.97, issue.13, p.130801, 2006.
DOI : 10.1103/PhysRevLett.97.130801
URL : https://hal.archives-ouvertes.fr/hal-00136647

N. D. Lemke, A. D. Ludlow, Z. W. Barber, T. M. Fortier, S. A. Diddams et al., Optical Lattice Clock, Spin-1/2 optical lattice clock, p.63001, 2009.
DOI : 10.1103/PhysRevLett.103.063001

G. Grynberg and C. Robilliard, Cold atoms in dissipative optical lattices, Physics Reports, vol.355, issue.5-6, p.335, 2001.
DOI : 10.1016/S0370-1573(01)00017-5

R. Grimm, M. Weidemüller, and Y. Ovchinnikov, Optical Dipole Traps for Neutral Atoms, Adv. At. Mol. Opt. Phys, vol.42, p.95, 2000.
DOI : 10.1016/S1049-250X(08)60186-X

S. Chu, J. E. Bjorkholm, A. Ashkin, and A. Cable, Experimental Observation of Optically Trapped Atoms, Physical Review Letters, vol.57, issue.3, p.314, 1986.
DOI : 10.1103/PhysRevLett.57.314

J. Vigué, Possibility of applying laser-cooling techniques to the observation of collective quantum effects, Physical Review A, vol.34, issue.5, p.4476, 1986.
DOI : 10.1103/PhysRevA.34.4476

M. Glück, A. Kolovsky, and H. J. Korsch, Wannier???Stark resonances in optical and semiconductor superlattices, Physics Reports, vol.366, issue.3, 2002.
DOI : 10.1016/S0370-1573(02)00142-4

H. B. Casimir, On the attraction between two perfectly conducting plates, Proc. K. Ned. Akad. Wet, vol.51, p.793, 1948.

P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics, American Journal of Physics, vol.62, issue.12, 1994.
DOI : 10.1119/1.17618

M. Abramowitz and I. Stegun, Handbook of mathematical fiunctions, 1964.

H. B. Casimir and D. Polder, The Influence of Retardation on the London-van der Waals Forces, Physical Review, vol.73, issue.4, p.360, 1948.
DOI : 10.1103/PhysRev.73.360

S. Y. Buhmann, L. Knöll, D. Welsch, and H. T. Dung, Casimir-Polder forces: A nonperturbative approach, Physical Review A, vol.70, issue.5, p.52117, 2004.
DOI : 10.1103/PhysRevA.70.052117
URL : http://arxiv.org/abs/quant-ph/0403128

E. Power and T. Thirunamachandran, The Multipolar Hamiltonian in Radiation Theory, Proc. R. Soc. Lond. A 372, p.265, 1980.
DOI : 10.1098/rspa.1980.0112

D. P. Craig and E. A. Power, The asymptotic Casimir-Polder potential from second-order perturbation theory and its generalization for anisotropic polarizabilities, International Journal of Quantum Chemistry, vol.46, issue.6, p.903, 1969.
DOI : 10.1002/qua.560030613

L. Spruch, Long-Range (Casimir) Interactions, Science, vol.272, issue.5267, p.1452, 1996.
DOI : 10.1126/science.272.5267.1452

E. A. Power and T. Thirunamachandran, Casimir-Polder potential as an interaction between induced dipoles, Physical Review A, vol.48, issue.6, p.4761, 1993.
DOI : 10.1103/PhysRevA.48.4761

S. Weinberg, The Quantum Theory of Fields I, 1995.

H. Yukawa, On the interaction of elementary particles, Proc. Phys, p.48, 1935.

R. V. Eötvös, D. Pekár, and E. Fekete, Beitr??ge zum Gesetze der Proportionalit??t von Tr??gheit und Gravit??t, Beiträge zum Gesetze der Proportionalität von Trägheit und Gravität, p.11, 1922.
DOI : 10.1002/andp.19223730903

I. Ciufolini, E. Pavlis, F. Chieppa, E. Fernandes-vieira, and J. Pérez-mercader, Test of General Relativity and Measurement of the Lense-Thirring Effect with Two Earth Satellites, Test of General Relativity and Measurement of the Lense-Thirring Effect with Two Earth Satellites, p.2100, 1998.
DOI : 10.1126/science.279.5359.2100

J. G. Williams, S. G. Turyshev, and D. H. Boggs, LUNAR LASER RANGING TESTS OF THE EQUIVALENCE PRINCIPLE WITH THE EARTH AND MOON, International Journal of Modern Physics D, vol.18, issue.07, p.50, 2005.
DOI : 10.1142/S021827180901500X

N. I. Kolosnitsyn and V. N. Melnikov, Test of the Inverse Square Law Through Precession of Orbits, General Relativity and Gravitation, vol.36, issue.7, p.1619, 2004.
DOI : 10.1023/B:GERG.0000032154.73097.5b

D. H. Eckhardt, C. Jekeli, A. R. Lazarewicz, A. J. Romaides, and R. W. Sands, Tower Gravity Experiment: Evidence for Non-Newtonian Gravity, Physical Review Letters, vol.60, issue.25, p.2567, 1988.
DOI : 10.1103/PhysRevLett.60.2567

E. Fischbach and C. L. Talmadge, The search for Non-Newtonian gravity, 1999.
DOI : 10.1007/978-1-4612-1438-0

A. S. Konopliv, S. W. Asmar, W. M. Folkner, O. Karatekin, D. C. Nunes et al., Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters, Marshighresolutiongravity fields from MRO, Mars seasonal gravity, and other dynamical parameters, p.401, 2011.
DOI : 10.1016/j.icarus.2010.10.004

J. K. Hoskins, R. D. Newman, R. Spero, and J. Schultz, Experimental tests of the gravitational inverse-square law for mass separations from 2 to 105 cm, Physical Review D, vol.32, issue.12, p.3084, 1985.
DOI : 10.1103/PhysRevD.32.3084

J. C. Long, H. W. Chan, A. B. Churnside, E. A. Gulbis, M. C. Varney et al., Upper limits to submillimetre-range forces from extra space-time dimensions, Nature, vol.7, issue.6926, p.922, 2003.
DOI : 10.1016/S0370-2693(99)01421-5

C. D. Hoyle, D. J. Kapner, B. Heckel, E. G. Adelberger, J. H. Gundlach et al., Submillimeter tests of the gravitational inverse-square law, Physical Review D, vol.70, issue.4, p.42004, 2004.
DOI : 10.1103/PhysRevD.70.042004

H. E. Hoyle and . Swanson, Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale, Phys. Rev. Lett, vol.98, p.21101, 2007.

S. J. Smullin, A. A. Geraci, D. M. Weld, J. Chiaverini, S. Holmes et al., Constraints on Yukawa-type deviations from Newtonian gravity at 20 microns, Constraints on Yukawa-type deviations from Newtonian gravity at 20 microns, p.122001, 2005.
DOI : 10.1103/PhysRevD.72.122001

S. K. Lamoreaux, Demonstration of the Casimir Force in the 0, Phys. Rev. Lett, vol.6, issue.78, p.5, 1997.

R. S. Decca, D. López, E. Fischbach, G. L. Klimchitskaya, D. E. Krause et al., Constraining New Forces in the Casimir Regime Using the Isoelectronic Technique, Physical Review Letters, vol.94, issue.24, p.240401, 2005.
DOI : 10.1103/PhysRevLett.94.240401

R. S. Decca, D. López, E. Fischbach, G. L. Klimchitskaya, D. E. Krause et al., Tests of new physics from precise measurements of the Casimir pressure between two gold-coated plates, Physical Review D, vol.75, issue.7, p.77101, 2007.
DOI : 10.1103/PhysRevD.75.077101

S. Dimopoulos and A. A. Geraci, Probing submicron forces by interferometry of Bose-Einstein condensed atoms, Physical Review D, vol.68, issue.12, p.124201, 2003.
DOI : 10.1103/PhysRevD.68.124021

G. Wannier, Wave Functions and Effective Hamiltonian for Bloch Electrons in an Electric Field, Physical Review, vol.117, issue.2, p.432, 1960.
DOI : 10.1103/PhysRev.117.432

M. Glück, A. R. Kolovsky, H. J. Korsch, and N. Moiseyev, Calculation of Wannier- Bloch and Wannier-Stark states, Eur, J. Phys. D, vol.4, p.239, 1998.

J. B. Krieger and G. J. Iafrate, Time evolution of Bloch electrons in a homogeneous electric field, Physical Review B, vol.33, issue.8, p.5494, 1986.
DOI : 10.1103/PhysRevB.33.5494

C. Zener, A Theory of the Electrical Breakdown of Solid Dielectrics, Proc. R. Soc. Lond. A 145, p.523, 1934.
DOI : 10.1098/rspa.1934.0116

G. Peters and J. H. Wilkinson, Eigenvalues of Ax = ?Bx with band symmetric A and B, Comp, J, vol.12, p.398, 1969.

R. Messina, Casimir-Polder force between atom and surface : geometrical and dynamical effects, 2010.

A. Lambrecht, P. M. Neto, and S. Reynaud, The Casimir effect within scattering theory, New Journal of Physics, vol.8, issue.10, p.243, 2006.
DOI : 10.1088/1367-2630/8/10/243
URL : https://hal.archives-ouvertes.fr/hal-00112885

R. Messina, D. A. Dalvit, P. A. Neto, A. Lambrecht, and S. Reynaud, Dispersive interactions between atoms and nonplanar surfaces, Dispersive interactions between atoms and nonplanar surfaces, p.22119, 2009.
DOI : 10.1103/PhysRevA.80.022119
URL : http://arxiv.org/abs/0902.3235

J. M. Wylie and J. E. Sipe, Quantum electrodynamics near an interface, Physical Review A, vol.30, issue.3, p.1185, 1984.
DOI : 10.1103/PhysRevA.30.1185

S. Y. Buhmann, D. Welsch, and T. Kampf, Ground-state van der Waals forces in planar multilayer magnetodielectrics, Ground-state van der Waals forces in planar multilayer magnetodielectrics, p.32112, 2005.
DOI : 10.1103/PhysRevA.72.032112

K. M. Case, Singular Potentials, Physical Review, vol.80, issue.5, p.797, 1950.
DOI : 10.1103/PhysRev.80.797

W. M. Frank, D. J. Land, and R. M. Spector, Singular Potentials, Singular potentials, p.36, 1971.
DOI : 10.1103/RevModPhys.43.36

A. Canaguier-durand, A. Gérardin, R. Guérout, P. A. Neto, V. Nesvizhevsky et al., Casimir interaction between a dielectric nanosphere and a metallic plane, Physical Review A, vol.83, issue.3, p.32508, 2011.
DOI : 10.1103/PhysRevA.83.032508
URL : https://hal.archives-ouvertes.fr/hal-00560372

J. C. Slater, Atomic Radii in Crystals, The Journal of Chemical Physics, vol.41, issue.10, p.3199, 1964.
DOI : 10.1063/1.1725697

R. Messina, S. Pelisson, M. C. Angonin, and P. Wolf, Atomic states in optical traps near a planar surface, Physical Review A, vol.83, issue.5, p.52111, 2011.
DOI : 10.1103/PhysRevA.83.052111

C. Zener, Non-Adiabatic Crossing of Energy Levels, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.137, issue.833, p.696, 1932.
DOI : 10.1098/rspa.1932.0165

L. D. Landau, Zur Theorie der Enregieübertragung II, Phys, Z. Sowjetunion, vol.2, p.46, 1932.

Y. Gefen, E. Ben-jacob, and A. O. Caldeira, Zener transitions in dissipative driven systems, Physical Review B, vol.36, issue.5, p.2770, 1987.
DOI : 10.1103/PhysRevB.36.2770

D. Iliescu, S. Fishman, and E. Ben-jacob, Quasienergy spectroscopy in mesoscopic systems, Physical Review B, vol.46, issue.22, p.14675, 1992.
DOI : 10.1103/PhysRevB.46.14675

N. Moiseyev, Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling, Physics Reports, vol.302, issue.5-6, p.211, 1998.
DOI : 10.1016/S0370-1573(98)00002-7

A. I. Baz-' and Y. B. , Zel'dovich, and A. M. Perelomov, Scattering, reactions and decay in non-relativistic quantum mechanics, 1969.

B. R. Junker, Recent Computational Developments in the use of Complex Scaling in Resonance Phenomena, Adv. At. Mol. Phys, vol.18, p.207, 1982.
DOI : 10.1016/S0065-2199(08)60242-0

J. Aguilar and J. M. Combes, A class of analytic perturbations for one-body Schr??dinger Hamiltonians, Communications in Mathematical Physics, vol.10, issue.5, p.269, 1971.
DOI : 10.1007/BF01877510

B. Simon, Quadratic form techniques and the Balslev-Combes theorem, Communications in Mathematical Physics, vol.73, issue.1, 1972.
DOI : 10.1007/BF01649654

B. Simon, Resonances in n-Body Quantum Systems With Dilatation Analytic Potentials and the Foundations of Time-Dependent Perturbation Theory, The Annals of Mathematics, vol.97, issue.2, p.247, 1973.
DOI : 10.2307/1970847

W. Hunziker, Distortion analyticity and molecular resonance curves, Ann. Inst. Henri Poincaré, vol.45, p.339, 1986.

N. Moiseyev and L. S. Cederbaum, Resonance solutions of the nonlinear Schr??dinger equation: Tunneling lifetime and fragmentation of trapped condensates, Physical Review A, vol.72, issue.3, p.33605, 2005.
DOI : 10.1103/PhysRevA.72.033605

W. P. Reinhardt, Complex Coordinates in the Theory of Atomic and Molecular Structure and Dynamics, Annual Review of Physical Chemistry, vol.33, issue.1, p.223, 1982.
DOI : 10.1146/annurev.pc.33.100182.001255

N. Moiseyev, Non-hermitian quantum mechanics, 2011.
DOI : 10.1017/CBO9780511976186

N. Moiseyev, P. R. Certain, and F. Weinhold, Resonance properties of complex-rotated hamiltonians, Molecular Physics, vol.7, issue.6, p.1613, 1978.
DOI : 10.1080/00268977800102631

E. Brändas and P. Froelich, Continuum orbitals, complex scaling problem, and the extended virial theorem, Physical Review A, vol.16, issue.6, p.2207, 1977.
DOI : 10.1103/PhysRevA.16.2207

N. Moiseyev, Resonance states by the generalized complex variational method, Molecular Physics, vol.14, issue.3, p.3, 1982.
DOI : 10.1080/00268978200100422

H. Barkay and N. Moiseyev, Complex density probability in non-Hermitian quantum mechanics: Interpretation and a formula for resonant tunneling probability amplitude, Physical Review A, vol.64, issue.4, p.44702, 2001.
DOI : 10.1103/PhysRevA.64.044702

N. Moiseyev and P. R. , Perturbation approach to the complex-rotation method, Molecular Physics, vol.1, issue.5, p.1621, 1979.
DOI : 10.1080/00268977900101161

S. Graffi, V. Grecchi, and H. J. Silverstone, Resonances and convergence of perturbation theory for N-body atomic systems in external AC-electric field, Ann. Inst. Henri Poincaré, vol.42, p.215, 1985.

A. U. Hazi and H. S. Taylor, Stabilization Method of Calculating Resonance Energies: Model Problem, Physical Review A, vol.1, issue.4, 1970.
DOI : 10.1103/PhysRevA.1.1109

B. R. Junker, The complex stabilization method: Application to atomic resonances, International Journal of Quantum Chemistry, vol.5, issue.S14, p.53, 1980.
DOI : 10.1002/qua.560180808

S. Pelisson, R. Messina, M. C. Angonin, and P. Wolf, Lifetimes of atoms trapped in an optical lattice in proximity of a surface, submitted to, Phys. Rev. A, 2013.

G. Tackmann, B. Pelle, A. Hilico, Q. Beaufils, and F. P. Santos, Raman-laser spectroscopy of Wannier-Stark states, Physical Review A, vol.84, issue.6, p.63422, 2011.
DOI : 10.1103/PhysRevA.84.063422
URL : https://hal.archives-ouvertes.fr/hal-00629340