A. I. Angström, Ueber die Spectra der einfachen Gase, Annalen der Physik, vol.220, issue.10, pp.300-307, 1871.

A. I. Angström, Ueber die Fraunhofer'schen Linien im Sonnenspectrum, Annalen der Physik, vol.193, issue.10, pp.290-302, 1862.

J. J. Balmer, NotizüberNotiz¨Notizüber die Spectrallinien des Wasserstoffs, Annalen der Physik, vol.261, issue.5, pp.80-87, 1885.

M. Planck, Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum. Verhandlungen der Deutschen physikalischen Gesellschaft, vol.2, p.245, 1900.

E. Rutherford and . Lxxix, The scattering of ? and ? particles by matter and the structure of the atom. The London, Edinburgh, and Dublin Philosophical Magazine, Journal of Science, vol.21, issue.125, pp.669-688, 1911.

N. I. Bohr, On the constitution of atoms and molecules. The London, Edinburgh, and Dublin Philosophical Magazine, Journal of Science, vol.26, issue.151, pp.1-25, 1913.

E. Schrödinger, Quantisierung als Eigenwertproblem, Annalen der Physik, vol.384, issue.4, pp.361-376, 1926.

P. A. Dirac, The quantum theory of the electron, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.117, issue.778, pp.610-624, 1928.

W. E. Lamb and R. C. Retherford, Fine Structure of the Hydrogen Atom by a Microwave Method, Phys. Rev, vol.72, pp.241-243, 1947.

H. A. Bethe, The Electromagnetic Shift of Energy Levels, Phys. Rev, vol.72, pp.339-341, 1947.

C. G. Parthey, A. Matveev, J. Alnis, B. Bernhardt, A. Beyer et al., Daniele 112 Bibliography Rovera, Christophe Salomon, Philippe Laurent, and Theodor W. Hänsch. Improved Measurement of the Hydrogen 1S-2S Transition Frequency, Phys. Rev. Lett, vol.107, p.203001, 2011.

A. Beyer, L. Maisenbacher, A. Matveev, R. Pohl, K. Khabarova et al., The Rydberg constant and proton size from atomic hydrogen, Science, vol.358, issue.6359, pp.79-85, 2017.

S. Héì-ene-fleurbaey, S. Galtier, M. Thomas, L. Bonnaud, and . Julien, François Biraben, François Nez, Michel Abgrall, and Jocelyne Guéna. New measurement of the 1S-3S, 2018.

R. Pohl, A. Antognini, F. Nez, F. D. Amaro, F. Biraben et al., The size of the proton, Nature, p.466, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00697832

Ø. Burrau, Berechnung des Energiewertes des Wasserstoffmolekel-Ions H + 2 im Normalzustand. Naturwissenschaften, vol.15, pp.16-17, 1927.
DOI : 10.1007/bf01504875

, Uber das Wasserstoffmolekülion, Zeitschrift für Physik, vol.61, issue.7, pp.458-480, 1930.

A. Egil and . Hylleraas, ¨ Uber die Elektronenterme des Wasserstoffmoleküls, Zeitschrift für Physik, vol.71, issue.11, pp.739-763, 1931.

G. Jaffé, Zur Theorie des Wasserstoffmolekülions, Zeitschrift für Physik, vol.87, issue.7, pp.535-544, 1934.

J. Karr, L. Hilico, J. C. Koelemeij, and V. I. Korobov, Hydrogen molecular ions for improved determination of fundamental constants, Phys. Rev. A, vol.94, p.50501, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01316849

H. William, G. A. Wing, W. E. Ruff, J. J. Lamb, and . Spezeski, Observation of the Infrared Spectrum of the Hydrogen Molecular Ion HD +, Phys. Rev. Lett, vol.36, pp.1488-1491, 1976.

J. Biesheuvel, J. Ph, L. Karr, K. S. Hilico, W. Eikema et al., Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD +, Nature Communications, vol.7, 2016.

S. Patra, J. Karr, L. Hilico, V. Germann, J. Korobov et al., Proton-electron mass ratio from HD + revisited, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.51, issue.2, p.24003, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01703663

M. Beyer, N. Hölsch, J. A. Agner, J. Deiglmayr, H. Schmutz et al., Metrology of high-n Rydberg states of molecular hydrogen with ??/? = 2 × 10 ?10 accuracy, Phys. Rev. A, vol.97, p.12501, 2018.

V. I. Korobov, L. Hilico, and J. Karr, Fundamental Transitions and Ionization Energies of the Hydrogen Molecular Ions with Few ppt Uncertainty, Phys. Rev. Lett, vol.118, p.233001, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01554919

J. Karr, , 2018.

S. Sturm, F. Köhler, J. Zatorski, A. Wagner, Z. Harman et al., Highprecision measurement of the atomic mass of the electron, Nature, vol.506, pp.467-470, 2014.

F. Heiße, F. Köhler-langes, S. Rau, J. Hou, S. Junck et al., High-Precision Measurement of the Proton's Atomic Mass, Phys. Rev. Lett, vol.119, p.33001, 2017.

V. L. Ryjkov, X. Zhao, and H. A. Schuessler, Simulations of the rf heating rates in a linear quadrupole ion trap, Phys. Rev. A, vol.71, p.33414, 2005.

R. D. Knight and M. H. Prior, Laser scanning measurement of the density distribution of confined 6 Li + ions, Journal of Applied Physics, vol.50, issue.5, pp.3044-3049, 1979.

P. Pérez, D. Banerjee, F. Biraben, D. Brook-roberge, M. Charlton et al.,

L. Hervieux, A. Hilico, P. Husson, S. Indelicato, and J. Jonsell,

K. Karr, N. Khabarova, N. Kolachevsky, A. Kuroda, A. M. Lambrecht et al., The GBAR antimatter gravity experiment, Hyperfine Interactions, vol.233, issue.1, pp.21-27, 2015.

N. Sillitoe, Production of state-selected H + 2 ions and numerical simulations of sympathetic cooling in RF traps, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01896819

R. P. Feynman, Simulating Physics with Computers, International Journal of Theoretical Physics, vol.21, issue.6, pp.467-488, 1982.

M. Johanning, F. Andrés, C. Varón, and . Wunderlich, Quantum simulations with cold trapped ions, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.42, issue.15, p.154009, 2009.

B. Szymanski, R. Dubessy, B. Dubost, S. Guibal, J. Likforman et al., Large two dimensional Coulomb crystals in a radio frequency surface ion trap, Applied Physics Letters, vol.100, issue.17, p.171110, 2012.

P. Richerme, Two-dimensional ion crystals in radiofrequency traps for quantum simulation, Phys. Rev. A, vol.94, p.32320, 2016.

W. Paul, H. P. Reinhard, and U. Von-zahn, Das elektrische Massenfilter als Massenspektrometer und Isotopentrenner, Zeitschrift für Physik, vol.152, issue.2, pp.143-182, 1958.
DOI : 10.1007/bf01327353

W. Paul, Electromagnetic traps for charged and neutral particles, Rev. Mod. Phys, vol.62, issue.3, pp.531-540, 1990.
DOI : 10.1103/revmodphys.62.531
URL : http://www.nobelprize.org/nobel_prizes/physics/laureates/1989/paul-lecture.pdf

G. Jacob, K. Groot-berning, S. Wolf, S. Ulm, L. Couturier et al., Single particle microscopy with nanometer resolution, 2014.

S. Wolf, J. Wechs, J. Von-zanthier, and F. Schmidt-kaler, Visibility of young's interference fringes: Scattered light from small ion crystals, Phys. Rev. Lett, vol.116, p.183002, 2016.
DOI : 10.1103/physrevlett.116.183002
URL : http://arxiv.org/pdf/1511.08697

S. Wolf and F. Schmidt-kaler, , 2017.

L. Hilico, J. Karr, A. Douillet, P. Indelicato, S. Wolf et al., Preparing single ultra-cold antihydrogen atoms for free-fall in GBAR, International Journal of Modern Physics: Conference Series, vol.30, p.1460269, 2014.

F. G. Major, V. N. Gheorghe, and G. Werth, Charged Particle Traps, 2005.

L. D. Landau, E. M. Lifshitz, and . Mechanics, , 1976.

D. R. Denison, Operating Parameters of a Quadrupole in a Grounded Cylindrical Housing, The Journal of Vacuum Science and Technology, vol.8, issue.1, pp.266-269, 1971.

J. Pedregosa, C. Champenois, M. Houssin, and M. Knoop, Anharmonic contributions in real RF linear quadrupole traps, International Journal of Mass Spectroscopy, vol.290, issue.2-3, pp.100-105, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00444728

J. Biesheuvel, Probing QED and fundamental constants through vibrational spectroscopy of HD +, 2016.

L. Hilico, . Billy, D. Grémaud, and . Delande, Polarizabilities, light shifts and two-photon transition probabilities between J = 0 states of the H + 2 and D + 2 molecular ions, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.34, issue.3, p.491, 2001.

J. Karr, F. Bielsa, A. Douillet, J. P. Gutierrez, V. I. Korobov et al., Vibrational spectroscopy of H 2 + : Hyperfine structure of twophoton transitions, Phys. Rev. A, vol.77, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00287607

H. Kogelnik and T. Li, Laser Beams and Resonators, Applied Optics, vol.5, issue.10, pp.1550-1567, 1966.

J. D. Siverns, L. R. Simkins, S. Weidt, and W. K. Hensinger, On the application of radio frequency voltages to ion traps via helical resonators, Appl Phys B, vol.107, issue.4, pp.921-934, 2012.

H. Schnitzler, Development of an Experiment for Trapping, Cooling, and Spectroscopy of Molecular Hydrogen Ions, 2001.

S. Wolf, D. Studer, K. Wendt, and F. Schmidt-kaler, Efficient and robust photo-ionization loading of beryllium ions, 2017.

, Gas Correction Factors for Bayard-Alpert Ionization Gauges

. Applicationnotes/ig1bagasapp,

M. Wong, Review of papers regarding vacuum system and materials

P. Lebedew, UntersuchungenüberUntersuchungen¨Untersuchungenüber die Druckkräfte des Lichtes, Annalen der Physik, vol.311, issue.11, pp.433-458, 1901.

A. Kastler, Quelques suggestions concernant la production optique et la détection optique d'une inégalité de population des niveaux de quantifigation spatiale des atomes. Applicationà Application`Applicationà l'expérience de Stern et Gerlach etàet`età la résonance magnétique, J. Phys. Radium, vol.11, issue.6, pp.255-265, 1950.

D. J. Wineland, R. E. Drullinger, and F. L. Walls, RadiationPressure Cooling of Bound Resonant Absorbers, Phys. Rev. Lett, vol.40, pp.1639-1642, 1978.

W. Nörtershäuser, C. Geppert, A. Krieger, K. Pachucki, M. Puchalski et al., Precision Test of Many-Body QED in the Be + 2p Fine Structure Doublet Using Short-Lived Isotopes, Phys. Rev. Lett, vol.115, p.33002, 2015.

C. Cohen-tannoudji, Atomic motion in laser light, Fundamental Systems in Quantum Optics, 1990.

R. C. Hilborn, Einstein coefficients, cross sections, f values, dipole moments, and all that, 2002.

F. M. Cozijn, J. Biesheuvel, A. S. Flores, W. Ubachs, G. Blume et al., Koelemeij. Laser cooling of beryllium ions using a frequency-doubled 626 nm diode laser, Opt. Lett, vol.38, issue.13, pp.2370-2372, 2013.

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano et al., Resolved-Sideband Raman Cooling of a Bound Atom to the 3D Zero-Point Energy, Phys. Rev. Lett, vol.75, pp.4011-4014, 1995.

A. C. Wilson, C. Ospelkaus, A. P. Vandevender, J. A. Mlynek, K. R. Brown et al., A 750-mW, continuous-wave, solid-state laser source at 313 nm for cooling and manipulating trapped 9 Be + ions, Applied Physics B, vol.105, pp.741-748, 2011.

H. Lo, J. Alonso, D. Kienzler, B. C. Keitch, L. E. De-clercq et al., All-solid-state continuous-wave laser systems for ionization, cooling and quantum state manipulation of beryllium ions, Applied Physics B, vol.114, issue.1, 2014.

S. Vasilyev, A. Nevsky, I. Ernsting, M. Hansen, J. Shen et al., Compact all-solid-state continuous-wave singlefrequency UV source with frequency stabilization for laser cooling of Be + ions, Applied Physics B, vol.103, issue.1, 2011.

H. Ball, M. W. Lee, S. D. Gensemer, and M. J. Biercuk, A highpower 626 nm diode laser system for Beryllium ion trapping, Review of Scientific Instruments, vol.84, issue.6, p.63107, 2013.

X. Baillard, A. Gauguet, S. Bize, P. Lemonde, . Ph et al., Interference-filterstabilized external-cavity diode lasers, Optics Communications, vol.266, issue.2, pp.609-613, 2006.

G. Blume, O. Nedow, D. Feise, J. Pohl, and K. Paschke, Monolithic 626 nm single-mode AlGaInP DBR diode laser. Opt, vol.21, pp.21677-21684, 2013.

R. and C. Jones, A New Calculus for the Treatment of Optical SystemsI. Description and Discussion of the Calculus, J. Opt. Soc. Am, vol.31, issue.7, pp.488-493, 1941.

J. C. Koelemeij, W. Hogervorst, and W. Vassen, High-power frequency stabilized laser for laser cooling of metastable helium at 389 nm, Review of Scientific Instruments, vol.76, issue.3, p.33104, 2005.

S. Hannig, J. Mielke, J. A. Fenske, M. Misera, N. Beev et al., A highly stable monolithic enhancement cavity for SHG generation in the UV, vol.09, p.2017

T. W. Hänsch and B. Couillaud, Laser Frequency Stabilization by Polarization Spectroscopy of a Reflecting Reference Cavity, Optics Communications, vol.35, pp.441-444, 1980.

G. D. Boyd and D. A. Kleinman, Parametric Interaction of Focused Gaussian Light Beams, Journal of Applied Physics, vol.39, issue.8, pp.3597-3639, 1968.

A. Ashkin, G. Boyd, and J. Dziedzic, Resonant optical second harmonic generation and mixing, IEEE Journal of Quantum Electronics, vol.2, issue.6, pp.109-124, 1966.

E. S. Polzik and H. J. Kimble, Frequency doubling with KNbO 3 in an external cavity, Opt. Lett, vol.16, issue.18, pp.1400-1402, 1991.

J. Karr, A. Douillet, and L. Hilico, Photodissociation of trapped H + 2 ions for REMPD spectroscopy, Applied Physics B, vol.107, issue.4, pp.1043-1052, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00966115

S. T. Pratt, P. M. Dehmer, and J. L. Dehmer, Photoionization of excited molecular states. H 2 C 1 ? u, Chemical Physics Letters, vol.105, issue.1, pp.28-33, 1984.

T. Vu-quang, Towards high precision spectroscopy of hydrogen molecular ions H + 2 and HD + : Theory and Experiment, 2013.

M. A. O'halloran, S. T. Pratt, P. M. Dehmer, and J. L. Dehmer, Photoionization dynamics of H 2 C 1 ? u : Vibrational and rotational branching ratios, The Journal of Chemical Physics, vol.87, issue.6, pp.3288-3298, 1987.

F. Bielsa, Spectroscopie vibrationellè a deux photons de l'Ion H + 2 : Développement d'une source laseràlaserà 9, vol.166, 2007.

F. Bielsa, A. Douillet, T. Valenzuela, J. Karr, and L. Hilico, Narrow-line phase-locked quantum cascade laser in the 9.2 µm range, Optics Letters, vol.32, issue.12, pp.1641-1643, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00129020

E. Wigner, On the interaction of electrons in metals, Phys. Rev, vol.46, pp.1002-1011, 1934.

F. Diedrich, E. Peik, J. M. Chen, W. Quint, and H. Walther, Observation of a Phase Transition of Stored Laser-Cooled Ions, Phys. Rev. Lett, vol.59, pp.2931-2934, 1987.

D. J. Wineland, J. C. Bergquist, W. M. Itano, J. J. Bollinger, and C. H. Manney, Atomic-Ion Coulomb Clusters in an Ion Trap, Phys. Rev. Lett, vol.59, pp.2935-2938, 1987.

J. P. Schiffer, M. Drewsen, J. S. Hangst, and L. Hornekaer, Temperature, ordering, and equilibrium with time-dependent confining forces, Proceedings of the National Academy of Sciences of the United States of America, vol.97, pp.10697-10700, 2000.

G. Birkl, S. Kassner, and H. Walther, Multiple-shell structures of laser-cooled 24

, Mg + ions in a quadrupole storage ring, Nature, vol.357, pp.310-313, 1992.

I. Waki, S. Kassner, G. Birkl, and H. Walther, Observation of ordered structures of laser-cooled ions in a quadrupole storage ring, Phys. Rev. Lett, vol.68, 1992.

M. Block, H. Drakoudis, . Leuthner, G. Seibert, M. Werth et al., Crystalline ion structures in a Paul trap, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.33, issue.11, p.375, 2000.

M. Drewsen, C. Brodersen, L. Hornekaer, and J. S. Hangst, Large Ion Crystals in a Linear Paul Trap, Phys. Rev. Lett, vol.81, pp.2878-2881, 1992.

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Minimization of ion micromotion in a Paul trap, Journal of Applied Physics, vol.83, issue.10, pp.5025-5033, 1998.

D. Li-jun, C. Ting, S. Hong-fang, C. Shao-long, L. Hai-xia et al., Compensating for excess micromotion of ion crystals, Chinese Physics B, vol.24, issue.8, p.83702, 2015.

P. Bowe, L. Hornekaer, C. Brodersen, M. Drewsen, J. S. Hangst et al., Sympathetic Crystallization of Trapped Ions, Phys. Rev. Lett, vol.82, pp.2071-2074, 1999.

C. B. Zhang, D. Offenberg, B. Roth, M. A. Wilson, and S. Schiller, Molecular-dynamics simulations of cold single-species and multispecies ion ensembles in a linear Paul trap, Phys. Rev. A, vol.76, p.12719, 2007.

M. R. Kamsap, J. Pedregosa-gutierrez, C. Champenois, D. Guyomarc'h, M. Houssin et al., Fast and efficient transport of large ion clouds, Phys. Rev. A, vol.92, p.43416, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01154665

R. E. Drullinger, D. J. Wineland, and J. C. Bergquist, Highresolution optical spectra of laser cooled ions, Applied physics, vol.22, issue.4, pp.365-368, 1980.

D. J. Larson, J. C. Bergquist, J. J. Bollinger, W. M. Itano, and D. J. Wineland, Sympathetic cooling of trapped ions: A laser-cooled two-species nonneutral ion plasma, Phys. Rev. Lett, vol.57, pp.70-73, 1986.

T. Baba and I. Waki, Cooling and Mass-Analysis of Molecules Using Laser-Cooled Atoms, Japanese Journal of Applied Physics, vol.35, issue.9A, p.1134, 1996.

Y. Moriwaki, M. Tachikawa, Y. Maeno, and T. Shimizu, Collision Cooling of Ions Stored in Quadrupole Radio-Frequency Trap, Japanese Journal of Applied Physics, vol.31, issue.11B, p.1640, 1992.

S. Schiller and C. Lämmerzahl, Molecular dynamics simulation of sympathetic crystallization of molecular ions, Phys. Rev. A, vol.68, p.53406, 2003.