V. We, S. Bergeret, J. C. Cuevas, A. C. Doherty, A. L. Yeyati et al., Yuli Nazarov and Vitaly Shumeiko for enlightening discussions . We gratefully acknowledge help from other members of the Quantronics group. Work partially financed by ANR through projects ANR-09

P. W. Anderson and J. M. Rowell, Probable Observation of the Josephson Superconducting Tunneling Effect, Physical Review Letters, vol.10, issue.6, p.230, 1963.
DOI : 10.1103/PhysRevLett.10.230

A. A. Golubov, M. Y. Kupriyanov, and E. , The current-phase relation in Josephson junctions, Reviews of Modern Physics, vol.76, issue.2, p.411, 2004.
DOI : 10.1103/RevModPhys.76.411

A. Furusaki and M. Tsukada, Dc Josephson effect and Andreev reflection, Solid State Communications, vol.78, issue.4, p.299, 1991.
DOI : 10.1016/0038-1098(91)90201-6

P. F. Bagwell, Suppression of the Josephson current through a narrow, mesoscopic, semiconductor channel by a single impurity, Physical Review B, vol.46, issue.19, p.12573, 1992.
DOI : 10.1103/PhysRevB.46.12573

C. W. Beenakker, Quantum transport in semiconductor-superconductor microjunctions, Physical Review B, vol.46, issue.19, p.12841, 1992.
DOI : 10.1103/PhysRevB.46.12841

M. L. Della-rocca, M. Chauvin, B. Huard, H. Pothier, D. Esteve et al., Measurement of the Current-Phase Relation of Superconducting Atomic Contacts, Physical Review Letters, vol.99, issue.12, p.127005, 2007.
DOI : 10.1103/PhysRevLett.99.127005

URL : https://hal.archives-ouvertes.fr/hal-00186792

L. Bretheau, Ç. Ö. Girit, H. Pothier, D. Esteve, and C. Urbina, Exciting Andreev pairs in a superconducting atomic contact, Nature, vol.336, issue.7458, p.312, 2013.
DOI : 10.1038/nature12315

URL : https://hal.archives-ouvertes.fr/hal-00823378

M. A. Desposito and A. L. Yeyati, Controlled dephasing of Andreev states in superconducting quantum point contacts, Physical Review B, vol.64, issue.14, p.140511, 2001.
DOI : 10.1103/PhysRevB.64.140511

A. Zazunov, V. S. Shumeiko, E. N. Bratus, J. Lantz, and G. Wendin, Andreev Level Qubit, Physical Review Letters, vol.90, issue.8, p.87003, 2003.
DOI : 10.1103/PhysRevLett.90.087003

A. Zazunov, V. S. Shumeiko, G. Wendin, and E. N. Bratus, Dynamics and phonon-induced decoherence of Andreev level qubit, Physical Review B, vol.71, issue.21, p.214505, 2005.
DOI : 10.1103/PhysRevB.71.214505

F. S. Bergeret, P. Virtanen, T. T. Heikkilä, and J. C. Cuevas, Theory of Microwave-Assisted Supercurrent in Quantum Point Contacts, Physical Review Letters, vol.105, issue.11, p.117001, 2010.
DOI : 10.1103/PhysRevLett.105.117001

G. Romero, I. Lizuain, V. S. Shumeiko, E. Solano, and F. S. Bergeret, Circuit quantum electrodynamics with a superconducting quantum point contact, Physical Review B, vol.85, issue.18, p.180506, 2012.
DOI : 10.1103/PhysRevB.85.180506

F. Kos, S. E. Nigg, and L. I. Glazman, Frequency-dependent admittance of a short superconducting weak link, Physical Review B, vol.87, issue.17, p.174521, 2013.
DOI : 10.1103/PhysRevB.87.174521

M. H. Devoret, D. Esteve, H. Grabert, G. Ingold, H. Pothier et al., Effect of the electromagnetic environment on the Coulomb blockade in ultrasmall tunnel junctions, Physical Review Letters, vol.64, issue.15, p.1824, 1990.
DOI : 10.1103/PhysRevLett.64.1824

B. W. Shore and P. L. Knight, The Jaynes-Cummings Model, Journal of Modern Optics, vol.764, issue.7, p.1195, 1993.
DOI : 10.1103/PhysRevA.21.1624

N. M. Chtchelkatchev and Y. V. Nazarov, Andreev Quantum Dots for Spin Manipulation, Physical Review Letters, vol.90, issue.22, p.226806, 2003.
DOI : 10.1103/PhysRevLett.90.226806

M. Zgirski, L. Bretheau, Q. Le-masne, H. Pothier, D. Esteve et al., Evidence for Long-Lived Quasiparticles Trapped in Superconducting Point Contacts, Physical Review Letters, vol.106, issue.25, p.257003, 2011.
DOI : 10.1103/PhysRevLett.106.257003

URL : https://hal.archives-ouvertes.fr/hal-00595339

D. G. Olivares, Dynamics of quasiparticle trapping in Andreev levels, Physical Review B, vol.89, issue.10, p.104504, 2014.
DOI : 10.1103/PhysRevB.89.104504

URL : https://hal.archives-ouvertes.fr/cea-01384760

V. Gramich, B. Kubala, S. Rohrer, and J. Ankerhold, From Coulomb-Blockade to Nonlinear Quantum Dynamics in a Superconducting Circuit with a Resonator, Physical Review Letters, vol.111, issue.24, p.247002, 2013.
DOI : 10.1103/PhysRevLett.111.247002

L. Bretheau, Localized Excitations in Superconducting Atomic Contacts: Probing the Andreev doublet, Ecole Polytechnique, 2013.
URL : https://hal.archives-ouvertes.fr/pastel-00862029