, Codata mp/me page

P. J. Mohr, D. B. Newell, and B. N. Taylor, Codata recommended values of the fundamental physical constants, vol.88, p.35009, 2014.

R. S. Van-dyck, D. L. Farnham, S. L. Zafonte, and P. B. Schwinberg, High precision penning trap mass spectroscopy and a new measurement of the protons atomic mass, AIP Conference Proceedings, vol.457, issue.1, pp.101-110, 1999.

S. Sturm, F. Kohler, J. Zatorski, A. Wagner, Z. Harman et al., High-precision 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.

W. H. Wing, G. A. Ruff, W. E. Lamb, and J. J. Spezeski, Observation of the infrared spectrum of the hydrogen molecular ion HD +, Phys. Rev. Lett, vol.36, pp.1488-1491, 1976.

J. C. Koelemeij, B. Roth, A. Wicht, I. Ernsting, and S. Schiller, Vibrational spectroscopy of HD + with 2-ppb accuracy, Phys. Rev. Lett, vol.98, p.173002, 2007.
DOI : 10.1103/physrevlett.98.173002

U. Bressel, A. Borodin, J. Shen, M. Hansen, I. Ernsting et al., Manipulation of individual hyperfine states in cold trapped molecular ions and application to HD + frequency metrology, Phys. Rev. Lett, vol.108, p.183003, 2012.

J. Biesheuvel, J. Karr, L. Hilico, K. S. Eikema, W. Ubachs et al., Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD +, Nat. Commun, vol.7, p.10385, 2016.

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, S. Patra, J. C. Koelemeij, J. Heinrich, N. Sillitoe et al., Hydrogen molecular ions: new schemes for metrology and fundamental physics tests, Journal of Physics: Conference Series, vol.723, issue.1, p.12048, 2016.
DOI : 10.1088/1742-6596/723/1/012048
URL : http://iopscience.iop.org/article/10.1088/1742-6596/723/1/012048/pdf

S. Schiller, I. Kortunov, M. H. Vera, F. Gianturco, and H. Da-silva, Quantum state preparation of homonuclear molecular ions enabled via a cold buffer gas: An ab initio study for the h 2 + and the d 2 + case, Phys. Rev. A, vol.95, p.43411, 2017.

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.
DOI : 10.1103/physreva.94.050501
URL : https://hal.archives-ouvertes.fr/hal-01316849

R. Pohl, A. Antognini, F. Nez, F. D. Amaro, F. Biraben et al., Nature, vol.466, 2010.

A. Antognini, F. Nez, K. Schuhmann, F. D. Amaro, F. Biraben et al.,

J. A. Liu, L. Lopes, C. M. Ludhova, F. Monteiro, T. Mulhauser et al., Proton structure from the measurement of 2s-2p transition frequencies of muonic hydrogen, Science, vol.339, issue.6118, pp.417-420, 2013.

R. Pohl, F. Nez, L. M. Fernandes, F. D. Amaro, F. Biraben et al., Laser spectroscopy of muonic deuterium, Science, vol.353, issue.6300, pp.669-673, 2016.
DOI : 10.1126/science.aaf2468
URL : https://hal.archives-ouvertes.fr/hal-01554340

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.
DOI : 10.1126/science.aah6677
URL : https://science.sciencemag.org/content/sci/358/6359/79.full.pdf

P. Ghosh, Oxford science publications, 1995.

F. Major, V. Gheorghe, and G. Werth, Charged Particle Traps: Physics and Techniques of Charged Particle Field Confinement. Springer Series on Atomic, Optical, and Plasma Physics, 2006.

C. Champenois, Laser Cooling Techniques Applicable to Trapped Ions, ch. Chapter Six, pp.117-145, 2016.

F. Busch and G. H. Dunn, Photodissociation of H + 2 and D + 2 : Experiment, Phys. Rev. A, vol.5, pp.1726-1743, 1972.

Y. Weijun, R. Alheit, and G. Werth, Vibrational population of H + 2 after electroionization of thermal H 2, Zeitschrift für Physik D Atoms, vol.28, pp.87-88, 1993.

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

T. A. , Description and first application of a new technique to measure the gravitational mass of antihydrogen, Nat. Commun, vol.4, 2013.

A. Collaboration, Alpha collaboration website

A. Collaboration, Aegis collaboration website

G. Collaboration, Gbar collaboration website

J. Walz and T. W. Hänsch, A proposal to measure antimatter gravity using ultracold antihydrogen atoms, General Relativity and Gravitation, vol.36, pp.561-570, 2004.

L. Schmöger, O. O. Versolato, M. Schwarz, M. Kohnen, A. Windberger et al.,

J. R. Schmidt and . López-urrutia, Coulomb crystallization of highly charged ions, Science, vol.347, issue.6227, pp.1233-1236, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01455746

A. Ostendorf, C. B. Zhang, M. A. Wilson, D. Offenberg, B. Roth et al., Sympathetic cooling of complex molecular ions to millikelvin temperatures, Phys. Rev. Lett, vol.97, p.243005, 2006.

J. Heinrich, A Be + Ion Trap for H + 2 Spectroscopy, 2017.
URL : https://hal.archives-ouvertes.fr/tel-02049379

L. Landau and E. Lifshitz, Mechanics (Third Edition). Oxford: Butterworth-Heinemann, 1976.

F. Bielsa, H + 2 two photons vibrational spectroscopy: 9.166 µm laser source development. Theses, 2007.
URL : https://hal.archives-ouvertes.fr/tel-00199877

J. D. Prestage, G. J. Dick, and L. Maleki, New ion trap for frequency standard applications, Journal of Applied Physics, vol.66, issue.3, p.117, 1989.

A. Reuben, G. Smith, P. Moses, A. Vagov, M. Woods et al., Ion trajectories in exactly determined quadrupole fields, International Journal of Mass Spectrometry and Ion Processes, vol.154, issue.1-2, pp.43-59, 1996.

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.

H. Dehmelt, Radiofrequency spectroscopy of stored ions I: Storage, Advances in Atomic and Molecular Physics, vol.3, pp.53-72, 1968.

E. R. Hudson, Sympathetic cooling of molecular ions with ultracold atoms, EPJ Techniques and Instrumentation, vol.3, p.8, 2016.

M. Cetina, A. T. Grier, and V. Vuleti´cvuleti´c, Micromotion-induced limit to atom-ion sympathetic cooling in paul traps, Phys. Rev. Lett, vol.109, p.253201, 2012.

K. Chen, S. T. Sullivan, and E. R. Hudson, Neutral gas sympathetic cooling of an ion in a paul trap, Phys. Rev. Lett, vol.112, p.143009, 2014.

S. J. Schowalter, A. J. Dunning, K. Chen, P. Puri, C. Schneider et al., Blue-sky bifurcation of ion energies and the limits of neutral-gas sympathetic cooling of trapped ions, Nature Communications, vol.7, p.12448, 2016.

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.

T. Baba and I. Waki, Sympathetic cooling rate of gas-phase ions in a radio-frequency-quadrupole ion trap, Applied Physics B, vol.74, pp.375-382, 2002.

M. Marciante, Dynamique d'ions enpì eges radiofréquences. PhD thesis, Martina Energie, rayonnement et Plasma Aix-Marseille, vol.1, 2011.

Y. S. Nam, E. B. Jones, and R. Blümel, Analytical mean-field scaling theory of radio-frequency heating in a paul trap, Phys. Rev. A, vol.90, p.13402, 2014.

E. L. Pollock and J. P. Hansen, Statistical mechanics of dense ionized matter. II. equilibrium properties and melting transition of the crystallized one-component plasma, Phys. Rev. A, vol.8, pp.3110-3122, 1973.

D. H. Dubin, Theory of structural phase transitions in a trapped Coulomb crystal, Phys. Rev. Lett, vol.71, pp.2753-2756, 1993.

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.

M. Drewsen, C. Brodersen, L. Hornekaer, J. S. Hangst, and J. P. Schifffer, Large ion crystals in a linear paul trap, Phys. Rev. Lett, vol.81, pp.2878-2881, 1998.

L. Hornekaer and M. Drewsen, Formation process of large ion Coulomb crystals in linear paul traps, Phys. Rev. A, vol.66, p.13412, 2002.

J. P. Schiffer, M. Drewsen, J. S. Hangst, and L. Hornekr, Temperature, ordering, and equilibrium with time-dependent confining forces, Proceedings of the National Academy of Sciences, vol.97, issue.20, pp.10697-10700, 2000.

L. Turner, Collective effects on equilibria of trapped charged plasmas, Physics of Fluids, vol.30, issue.10, pp.3196-3203, 1958.

S. T. Pratt, Excited-state molecular photoionization dynamics, Reports on Progress in Physics, vol.58, issue.8, p.821, 1995.

S. Anderson, G. Kubiak, and R. Zare, Resonance-enhanced multiphoton ionization of molecular hydrogen via the E,F 1 ? + g state: Photoelectron energy and angular distributions, Chemical Physics Letters, vol.105, pp.22-27, 1984.

M. A. Ohalloran, 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.

W. E. Perreault, N. Mukherjee, and R. N. Zare, Angular and internal state distributions of H + 2 generated by (2 + 1) resonance enhanced multiphoton ionization of H 2 using time-of-flight mass spectrometry, The Journal of Chemical Physics, vol.144, issue.21, p.214201, 2016.

X. Urbain, B. Fabre, E. M. Staicu-casagrande, N. De-ruette, V. M. Andrianarijaona et al., Intense-laser-field ionization of molecular hydrogen in the tunneling regime and its effect on the vibrational excitation of H + 2, Phys. Rev. Lett, vol.92, p.163004, 2004.

J. E. Pollard, D. J. Trevor, Y. T. Lee, and D. A. Shirley, Rotational relaxation in supersonic beams of hydrogen by high resolution photoelectron spectroscopy, The Journal of Chemical Physics, vol.77, issue.10, pp.4818-4825, 1982.

V. Tran, Towards high precision spectroscopy of hydrogen molecular Ions H + 2 and HD + : theory and experiment, 2013.

X. Tong, D. Wild, and S. Willitsch, Collisional and radiative effects in the state-selective preparation of translationally cold molecular ions in ion traps, Phys. Rev. A, vol.83, p.23415, 2011.

M. G. Kokish, V. Rajagopal, J. P. Marler, and B. C. Odom, Note: High density pulsed molecular beam for cold ion chemistry, Review of Scientific Instruments, vol.85, issue.8, p.86111, 2014.

N. Ramsey, Molecular Beams, 1986.

, NIST H 2 page

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

X. Urbain, Private Communication

D. Halwidl, Development of an Effusive Molecular Beam Apparatus, vol.06, p.2016

D. Miller, Free jet sources, Atomic and Molecular Beam Methods (G. Scoles, pp.14-53, 1988.

W. E. Perreault, N. Mukherjee, and R. N. Zare, Angular and internal state distributions of H + 2 generated by (2+1) resonance enhanced multiphoton ionization of H 2 using time-of-flight mass spectrometry, The Journal of Chemical Physics, vol.144, issue.21, p.214201, 2016.

S. Kilic, Leprobì eme coulombienàcoulombienà trois corps : ´ etats liés, résonances et interaction avec lalumì ere vers la spectroscopie vibrationnelle dans H + 2, 2005.

G. Dunn, Jila report, 1968.

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.

D. A. Church and H. G. Dehmelt, Radiative cooling of an electrodynamically contained proton gas, Journal of Applied Physics, vol.40, issue.9, pp.3421-3424, 1969.

P. Allmendinger, J. Deiglmayr, and F. Merkt, Experimental study of the ion-molecule reaction H + 2 + H 2 ? H + 3 + H at low collision energies, Journal of Physics: Conference Series, vol.635, issue.11, p.112132, 2015.

C. W. Eaker and G. C. Schatz, A surface hopping quasiclassical trajectory study of the H + 2 +H 2 and (H 2 +D + 2 ) systems, Chemical Physics Letters, vol.127, issue.4, pp.343-346, 1986.

M. Baer and C. Y. Ng, A three-dimensional quantum mechanical study of the H 2 + H + 2 system: Calculation of reactive and charge transfer cross sections, The Journal of Chemical Physics, vol.93, issue.11, pp.7787-7799, 1990.

J. E. Pollard, L. K. Johnson, D. A. Lichtin, and R. B. Cohen, Stateselected reactive scattering. i. H + 2 +H 2 ? H + 3 +H, The Journal of Chemical Physics, vol.95, issue.7, pp.4877-4893, 1991.

J. T. Broad and W. P. Reinhardt, One-and two-electron photoejection from H ? : A multichannel J-matrix calculation, Phys. Rev. A, vol.14, pp.2159-2173, 1976.

S. J. Smith and D. S. Burch, Photodetachment cross section of the negative hydrogen ion, Phys. Rev. Lett, vol.2, pp.165-166, 1959.

C. D. Schlaff, A. Krauze, A. Belard, J. J. O'connell, and K. A. Camphausen, Bringing the heavy: carbon ion therapy in the radiobiological and clinical context, Radiation Oncology, vol.9, p.88, 2014.

. Miyamoto, Fundamentals of plasma physics and controlled fusion, 2000.

B. Cagnac and J. Pebay-péroula, Physique atomique: introductionàintroductionà la physique quantique et structure de l'´ edifice atomique. Applications de la mécanique quantique, 1982.

H. Kogelnik and T. Li, Laser beams and resonators, Appl. Opt, vol.5, pp.1550-1567, 1966.
DOI : 10.1109/proc.1966.5119

N. Sillitoe and L. Hilico, Numerical Simulations Of Ion Cloud Dynamics, ch. Chapter Eight, pp.161-177, 2016.
DOI : 10.1142/9781786340139_0008

L. Verlet, Computer "experiments" on classical fluids. I. thermodynamical properties of lennard-jones molecules, Phys. Rev, vol.159, pp.98-103, 1967.

W. Huang and B. Leimkuhler, The adaptive verlet method, SIAM J. Sci. Comput, vol.18, pp.239-256, 1997.

E. Hairer, Variable time step integration with symplectic methods, Applied Numerical Mathematics, vol.25, issue.2, pp.219-227, 1997.
DOI : 10.1016/s0168-9274(97)00061-5

N. Sillitoe, J. Karr, J. Heinrich, T. Louvradoux, A. Douillet et al., ¯ H + Sympathetic Cooling Simulations with a Variable Time
DOI : 10.7566/jpscp.18.011014
URL : https://journals.jps.jp/doi/pdf/10.7566/JPSCP.18.011014

I. Rouse and S. Willitsch, Superstatistical velocity distributions of cold trapped ions in molecular-dynamics simulations, Phys. Rev. A, vol.92, p.53420, 2015.

L. Nyland, M. Harris, and J. Prins, Fast N-Body Simulation with CUDA, GPU Gems, vol.3, 2007.

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.
DOI : 10.1142/s2010194514602695
URL : http://arxiv.org/pdf/1402.1695

K. Chen, S. T. Sullivan, W. G. Rellergert, and E. R. Hudson, Measurement of the Coulomb logarithm in a radio-frequency paul trap, Phys. Rev. Lett, vol.110, p.173003, 2013.

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.

G. Zwicknagel, C. Toepffer, and P. Reinhard, Stopping of heavy ions in plasmas at strong coupling, Physics Reports, vol.309, issue.3, pp.117-208, 1999.

S. B. Lippman, J. Lajoie, B. E. Moo, and . Primer, , 2012.

B. Stroustrup, The C++ Programming Language, 2013.

. Nvidia, CUDA Udacity course

S. Cook, CUDA Programming: A Developer's Guide to Parallel Computing with GPUs, 2013.

J. Makino and T. Saitoh, Astrophysics with grape, Progress of Theoretical and Experimental Physics, vol.2012, issue.1, 2012.
DOI : 10.1093/ptep/pts029
URL : https://academic.oup.com/ptep/article-pdf/2012/1/01A303/11590598/pts029.pdf

T. Fukushige and A. Kawai, Hierarchical tree algorithm for collisional N-body simulations on grape, Publications of the Astronomical Society of Japan, 2016.
DOI : 10.1093/pasj/psw018
URL : https://academic.oup.com/pasj/article-pdf/68/3/30/6847547/psw018.pdf