Strongly Enhanced Inelastic Collisions in a Bose-Einstein Condensate near Feshbach Resonances, Physical Review Letters, vol.82, issue.12, p.2422 ,
DOI : 10.1103/PhysRevLett.82.2422
Evidence for Efimov quantum states in an ultracold gas of caesium atoms, Nature, vol.47, issue.7082, p.315, 2006. ,
DOI : 10.1038/nature04626
17 For N spin-1 / 2 fermions, the spin configuration can be chosen as ? N ? ? N ? where the first N ? factors of the tensorial product are the spin-up state and the N ? = N ? N ? remaining factors are the spin-down state. In this case, the wave function r 1 ,...,r N is antisymmetric for the permutation of the positions of the N ? first particles and also antisymmetric for the permutation of the last N ? particles. 18 In the context of cold atoms, hyperspherical coordinates were used, e.g, Phys. Rev. A Phys. Rev. Lett.D.S. Petrov, Phys. Rev. A Phys. Rev. A, vol.71, issue.584, 1998. ,
Solvable Models in Quantum Mechanics, 1988. ,
Proceedings of the International School of Physics " Enrico Fermi, Course CLXIV, 2006. ,
26 L. Pricoupenko and Y. Castin, Phys. Rev. Lett. J. Phys. A Phys. Rev. Lett, vol.99, issue.91, 2003. ,
29 O. Juillet, Ultra-cold Fermi Gases 3. 31 L. Tarruell et al.,i nUltra-cold Fermi Gases 3, 2004. ,
47 For details, see F. Werner, e-print arXiv:0803, Phys. Rev. A Europhys. Lett. Rev. Mod. Phys, vol.70, issue.463, 1999. ,
56 In low dimensions there is a caveat: the thermalization time may diverge with the system size, see A. Polkovnikov and V. Gritsev, Phys. Rev. Lett. Nat. Phys, vol.92, issue.4, 2008. ,
60 If the expansion dynamics is known theoretically, then other, Lectures on quantum statistics Gordon & Breach, pp.2179-2226, 1967. ,
Superfluid Fermi Gases with Large Scattering Length, Physical Review Letters, vol.91, issue.5, p.50401, 2003. ,
DOI : 10.1103/PhysRevLett.91.050401
URL : http://arxiv.org/abs/physics/0303094
Strongly Enhanced Inelastic Collisions in a Bose-Einstein Condensate near Feshbach Resonances, Physical Review Letters, vol.82, issue.12, p.2422, 1999. ,
DOI : 10.1103/PhysRevLett.82.2422
Evidence for Efimov quantum states in an ultracold gas of caesium atoms, Nature, vol.47, issue.7082, p.315, 2006. ,
DOI : 10.1038/nature04626
Universality in few-body systems with large scattering length, Physics Reports, vol.428, issue.5-6, p.259, 2006. ,
DOI : 10.1016/j.physrep.2006.03.001
Dilute Bose-Einstein Condensate with Large Scattering Length, Physical Review Letters, vol.88, issue.4, p.40401, 2002. ,
DOI : 10.1103/PhysRevLett.88.040401
URL : http://arxiv.org/abs/cond-mat/0108380
Universal Behavior of the Energy of Trapped Few-Boson Systems with Large Scattering Length, Physical Review Letters, vol.89, issue.25, p.250401, 2002. ,
DOI : 10.1103/PhysRevLett.89.250401
Production of three-body Efimov molecules in an optical lattice, Physical Review A, vol.72, issue.2, p.22714, 2005. ,
DOI : 10.1103/PhysRevA.72.022714
Observation of a Strongly Interacting Degenerate Fermi Gas of Atoms, Science, vol.298, issue.5601, p.2179, 2002. ,
DOI : 10.1126/science.1079107
Fermi Gas, Physical Review Letters, vol.91, issue.2, p.20402, 2003. ,
DOI : 10.1103/PhysRevLett.91.020402
URL : https://hal.archives-ouvertes.fr/hal-00001552
Observation of Bose-Einstein Condensation of Molecules, Physical Review Letters, vol.91, issue.25, p.250401, 2003. ,
DOI : 10.1103/PhysRevLett.91.250401
Observation of Resonance Condensation of Fermionic Atom Pairs, Physical Review Letters, vol.92, issue.4, pp.40403-120403, 2004. ,
DOI : 10.1103/PhysRevLett.92.040403
Observation of the Pairing Gap in a Strongly Interacting Fermi Gas, Science, vol.305, issue.5687, p.1128, 2004. ,
DOI : 10.1126/science.1100818
Laser Probing of Atomic Cooper Pairs, Physical Review Letters, vol.85, issue.3, p.487, 2000. ,
DOI : 10.1103/PhysRevLett.85.487
P e d r i ,S .S t r i n g a r i ,P h y s .R e v .L e t t, p.250402, 2002. ,
Fermi Gases in Slowly Rotating Traps: Superfluid versus Collisional Hydrodynamics, Physical Review Letters, vol.91, issue.7, p.70401, 2003. ,
DOI : 10.1103/PhysRevLett.91.070401
Vortex Arrays in a Rotating Superfluid Fermi Gas, Physical Review Letters, vol.93, issue.20, p.200406, 2004. ,
DOI : 10.1103/PhysRevLett.93.200406
Microscopic Structure of a Vortex Line in a Dilute Superfluid Fermi Gas, Physical Review Letters, vol.90, issue.21, p.210402, 2003. ,
DOI : 10.1103/PhysRevLett.90.210402
Instability of the nonvortex state toward a quantized vortex in a Bose-Einstein condensate under external rotation, Physical Review A, vol.60, issue.4, p.3313, 1999. ,
DOI : 10.1103/PhysRevA.60.3313
Shape deformations and angular-momentum transfer in trapped Bose-Einstein condensates, Physical Review A, vol.63, issue.1, p.11601, 2000. ,
DOI : 10.1103/PhysRevA.63.011601
P h y s .R e v .L e t t, p.806, 2000. ,
Dynamic Instability of a Rotating Bose-Einstein Condensate, Physical Review Letters, vol.87, issue.19, p.190402, 2001. ,
DOI : 10.1103/PhysRevLett.87.190402
URL : https://hal.archives-ouvertes.fr/hal-00002093
Stationary States of a Rotating Bose-Einstein Condensate: Routes to Vortex Nucleation, Physical Review Letters, vol.86, issue.20, p.4443, 2001. ,
DOI : 10.1103/PhysRevLett.86.4443
URL : https://hal.archives-ouvertes.fr/hal-00002550
Vortex Nucleation in Bose-Einstein Condensates in an Oblate, Purely Magnetic Potential, Physical Review Letters, vol.88, issue.1, p.10405, 2002. ,
DOI : 10.1103/PhysRevLett.88.010405
P h y s .R e v .L e t t, p.564, 2001. ,
C a s t i n ,P h y s .R e v .L e t t, p.20403, 2004. ,
Bose-Einstein Condensation in Quasi-2D Trapped Gases, Physical Review Letters, vol.84, issue.12, pp.2551-012706, 2000. ,
DOI : 10.1103/PhysRevLett.84.2551
URL : https://hal.archives-ouvertes.fr/hal-00001658
Superconductivity in a two-dimensional Fermi gas: Evolution from Cooper pairing to Bose condensation, Physical Review B, vol.41, issue.1, p.327, 1990. ,
DOI : 10.1103/PhysRevB.41.327
Extension of Bogoliubov theory to quasicondensates, Physical Review A, vol.67, issue.5, p.53615, 2003. ,
DOI : 10.1103/PhysRevA.67.053615
URL : https://hal.archives-ouvertes.fr/hal-00157445
Study of Ultracold Fermi gases: crystalline LOFF phase and nucleation of vortices, Phys. Rev. A, vol.72, 2005. ,
magnetic moment of the closed channel with respect to the two-atom open channel. For K-Rb in their ground state, J. Phys. B, vol.39, issue.6, 2006. ,
In the other regimes attractively and repulsively interacting atoms, we have 1 / k typ a rel In the harmonic approximation for the experimental lattice depth a rel = 103 nm. Thus, the above inequality is fairly well satisfied. 15 Y. Castin, e-print arXiv:cond-mat/0612613 17 A. Simoni private communication Hecker Denschlag, e-print arXiv:cond-mat/ 0608721v2. 19 We note that we neglect many low-energy basis states N , L ,0,0,0,0 with 2N + L max when the scattering length is small and positive a s 0. These molecule states with highly excited center-of-mass energy have nevertheless low total energy since the energy of the relative motion is large and negative . We have included the states max to allow for the flattening of the center of mass wave function due to the anharmonicity of the lattice site potential. However, we have neglected the states with 2N + L max since they are only weakly coupled to the states 0 repulsively interacting atoms of the decoupled problem, nm 16. Using E res ?4.6 nm. It remains to estimate k typ . In the molecule regime These matrix elements become even zero if 2N + L p p =1,...,8 since in this case the matrix elements 0 are exactly zero. 20 C. Ospelkaus, S. Ospelkaus, K. Sengstock, and K. Bongs, 2001. ,
27 For the scattering length in the initial 87 Rb1, Rev. Mod. Phys, vol.4931, issue.2 2, pp.11977-12017 ,
Long-Lived Feshbach Molecules in a Three-Dimensional Optical Lattice, Physical Review Letters, vol.96, issue.5, p.50402, 2006. ,
DOI : 10.1103/PhysRevLett.96.050402
92007, and references therein. 47 For an equivalent energy-independent formulation of such a model, see L. Pricoupenko, Phys. Rev. Lett. New J. Phys. Phys. Rev. A, vol.931, issue.73, 2006. ,
51 F. Werner and Y. Castin 52 VFG-150, a FPGA-driven fast versatile frequency generator, controlled via an USB2.0 interface and developed by Th, Phys. Rev. A Phys. Rev. Lett, vol.72, issue.97, 2006. ,
Cold Bosonic Atoms in Optical Lattices, Physical Review Letters, vol.81, issue.15, p.3108, 1998. ,
DOI : 10.1103/PhysRevLett.81.3108
Bose-Einstein Condensation of Molecules, Science, vol.302, issue.5653, p.2101, 2003. ,
DOI : 10.1126/science.1093280
Observation of Bose-Einstein Condensation of Molecules, Physical Review Letters, vol.91, issue.25, p.250401, 2003. ,
DOI : 10.1103/PhysRevLett.91.250401
Experimental Study of the BEC-BCS Crossover Region in Lithium 6, Physical Review Letters, vol.93, issue.5, p.50401, 2004. ,
DOI : 10.1103/PhysRevLett.93.050401
URL : https://hal.archives-ouvertes.fr/hal-00001237
Adiabatic cooling of fermions in an optical lattice, Physical Review A, vol.71, issue.3, p.33616, 2005. ,
DOI : 10.1103/PhysRevA.71.033616
High-Temperature Superfluidity of Fermionic Atoms in Optical Lattices, Physical Review Letters, vol.89, issue.22, p.220407, 2002. ,
DOI : 10.1103/PhysRevLett.89.220407
Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Reviews of Modern Physics, vol.68, issue.1, p.13, 1996. ,
DOI : 10.1103/RevModPhys.68.13
Phase diagram of the three-dimensional Hubbard model at half filling, The European Physical Journal B, vol.17, issue.3, p.411, 2000. ,
DOI : 10.1007/s100510070120
=??? Hubbard model: Evidence for a Mott transition, Physical Review Letters, vol.69, issue.8, p.1240, 1992. ,
DOI : 10.1103/PhysRevLett.69.1240
Physical properties of the half-filled Hubbard model in infinite dimensions, Physical Review B, vol.48, issue.10, p.7167, 1993. ,
DOI : 10.1103/PhysRevB.48.7167
Finite Temperature Mott Transition in the Hubbard Model in Infinite Dimensions, Physical Review Letters, vol.83, issue.17, p.3498, 1999. ,
DOI : 10.1103/PhysRevLett.83.3498
Magnetic properties of the three-dimensional Hubbard model at half filling, Physical Review B, vol.61, issue.7, p.4567, 2000. ,
DOI : 10.1103/PhysRevB.61.4567
Functional integral theories of low-dimensional quantum Heisenberg models, Physical Review B, vol.38, issue.1, p.316, 1988. ,
DOI : 10.1103/PhysRevB.38.316
Probing many-body states of ultracold atoms via noise correlations, Physical Review A, vol.70, issue.1, p.13603, 2004. ,
DOI : 10.1103/PhysRevA.70.013603
Spatial quantum noise interferometry in expanding ultracold atom clouds, Nature, vol.22, issue.7032, p.481, 2005. ,
DOI : 10.1103/PhysRevA.59.4595
Nous comptons également généraliser l'étude des résonances à N corps présentée ici Une autre voie est l'étude du problème à N corps unitaire dans un réseau optique profond ,
Production of three-body Efimov molecules in an optical lattice, Phys. Rev. A, vol.72, p.22714, 2005. ,
Evidence for Efimov quantum states in an ultracold gas of caesium atoms, Nature, vol.440, p.315, 2006. ,
Energetics and structural properties of trapped two-component Fermi gases, Physical Review A, vol.77, issue.4, p.43619, 2008. ,
DOI : 10.1103/PhysRevA.77.043619
Specific heat and high-temperature series of lattice models: Interpolation scheme and examples on quantum spin systems in one and two dimensions, Physical Review B, vol.63, issue.13, p.134409, 2001. ,
DOI : 10.1103/PhysRevB.63.134409
Threshold and resonance phenomena in ultracold ground-state collisions, Physical Review A, vol.47, issue.5, pp.4114-4122, 1993. ,
DOI : 10.1103/PhysRevA.47.4114
Observation of Feshbach resonances in a Bose???Einstein condensate, Nature, vol.77, issue.6672, p.151, 1998. ,
DOI : 10.1038/32354
Observation of a Strongly Interacting Degenerate Fermi Gas of Atoms, Science, vol.298, issue.5601, p.2179, 2002. ,
DOI : 10.1126/science.1079107
Measurement of Positive and Negative Scattering Lengths in a Fermi Gas of Atoms, Physical Review Letters, vol.90, issue.23, p.230404, 2003. ,
DOI : 10.1103/PhysRevLett.90.230404
Fermi Gas, Physical Review Letters, vol.91, issue.2, p.20402, 2003. ,
DOI : 10.1103/PhysRevLett.91.020402
URL : https://hal.archives-ouvertes.fr/hal-00001552
Many-body physics with ultracold gases, Reviews of Modern Physics, vol.80, issue.3, p.885, 2008. ,
DOI : 10.1103/RevModPhys.80.885
URL : https://hal.archives-ouvertes.fr/hal-00195515
Theory of ultracold atomic Fermi gases, Reviews of Modern Physics, vol.80, issue.4, p.1215, 2008. ,
DOI : 10.1103/RevModPhys.80.1215
???ber die Streuung von Neutronen an Protonen, Zeitschrift f???r Physik, vol.83, issue.3-4, p.253, 1933. ,
DOI : 10.1007/BF01331145
Quantum Theory of the Diplon, Proc. R. Soc, p.146, 1935. ,
Universality in few-body systems with large scattering length, Physics Reports, vol.428, issue.5-6, p.259, 2006. ,
DOI : 10.1016/j.physrep.2006.03.001
Weakly-bound states of three resonantly interating particles, Yad. Fiz.Sov. J. Nucl. Phys, vol.12, issue.12, pp.1080-589, 1970. ,
Strongly Enhanced Inelastic Collisions in a Bose-Einstein Condensate near Feshbach Resonances, Physical Review Letters, vol.82, issue.12, pp.2422-2425, 1999. ,
DOI : 10.1103/PhysRevLett.82.2422
Magnetic Field Dependence of Ultracold Inelastic Collisions near a Feshbach Resonance, Physical Review Letters, vol.85, issue.4, pp.728-731, 2000. ,
DOI : 10.1103/PhysRevLett.85.728
Precision Measurement and Analysis, Feshbach Resonances in Rubidium Phys. Rev. Lett, vol.87, issue.89, p.283202, 2002. ,
Three-Body Recombination at Large Scattering Lengths in an Ultracold Atomic Gas, Physical Review Letters, vol.91, issue.12, p.123201, 2003. ,
DOI : 10.1103/PhysRevLett.91.123201
Weakly Bound Dimers of Fermionic Atoms, Physical Review Letters, vol.93, issue.9, p.90404, 2004. ,
DOI : 10.1103/PhysRevLett.93.090404
URL : https://hal.archives-ouvertes.fr/hal-00002933
Diatomic molecules in ultracold Fermi gases???novel composite bosons, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.38, issue.9, p.645, 2005. ,
DOI : 10.1088/0953-4075/38/9/014
URL : https://hal.archives-ouvertes.fr/hal-00004896
Bose-Einstein Condensate, Physical Review Letters, vol.101, issue.13, p.135301, 2008. ,
DOI : 10.1103/PhysRevLett.101.135301
Efimov physics in cold atoms, Annals of Physics, vol.322, issue.1, p.120, 2007. ,
DOI : 10.1016/j.aop.2006.10.011
Dilute Bose-Einstein Condensate with Large Scattering Length, Physical Review Letters, vol.88, issue.4, p.40401, 2002. ,
DOI : 10.1103/PhysRevLett.88.040401
Universal Properties of a Trapped Two-Component Fermi Gas at Unitarity, Physical Review Letters, vol.99, issue.23, p.233201, 2007. ,
DOI : 10.1103/PhysRevLett.99.233201
Molecules of Fermionic Atoms in an Optical Lattice, Physical Review Letters, vol.96, issue.3, p.30401, 2006. ,
DOI : 10.1103/PhysRevLett.96.030401
Ultracold Heteronuclear Molecules in a 3D Optical Lattice, Physical Review Letters, vol.97, issue.12, p.120402, 2006. ,
DOI : 10.1103/PhysRevLett.97.120402
Exact scaling transform for a unitary quantum gas in a time dependent harmonic potential, Comptes Rendus Physique, vol.5, issue.3, p.407, 2004. ,
DOI : 10.1016/j.crhy.2004.03.017
URL : https://hal.archives-ouvertes.fr/hal-00001653
Proceedings of the International School of Physics "Enrico Fermi" on Ultra- Cold Fermi gases, 2007. ,
Two Cold Atoms in a Harmonic Trap, Foundations of Physics, vol.28, issue.4, p.549, 1998. ,
DOI : 10.1023/A:1018705520999
Solvable models in quantum mechanics, 1988. ,
-wave Feshbach resonance, Physical Review A, vol.77, issue.4, p.43611, 2008. ,
DOI : 10.1103/PhysRevA.77.043611
URL : https://hal.archives-ouvertes.fr/hal-00623276
Methods of modern mathematical physics 1 : functional analysis, 1980. ,
Unitary Fermi gas in a harmonic trap, Physical Review A, vol.76, issue.2, p.21603, 2007. ,
DOI : 10.1103/PhysRevA.76.021603
Production of cold molecules via magnetically tunable Feshbach resonances, Reviews of Modern Physics, vol.78, issue.4, p.1311, 2006. ,
DOI : 10.1103/RevModPhys.78.1311
Superfluid Fermi Gases with Large Scattering Length, Physical Review Letters, vol.91, issue.5, p.50401, 2003. ,
DOI : 10.1103/PhysRevLett.91.050401
Equation of State of a Fermi Gas in the BEC-BCS Crossover: A Quantum Monte Carlo Study, Physical Review Letters, vol.93, issue.20, p.200404, 2004. ,
DOI : 10.1103/PhysRevLett.93.200404
BCS to Bose crossover: Broken-symmetry state, Physical Review B, vol.55, issue.22, pp.15153-15156, 1997. ,
DOI : 10.1103/PhysRevB.55.15153
Sign-free stochastic mean-field approach to strongly correlated phases of ultracold fermions, New Journal of Physics, vol.9, issue.6, p.163, 2007. ,
DOI : 10.1088/1367-2630/9/6/163
URL : https://hal.archives-ouvertes.fr/hal-00090944
Expansion of an ultra-cold lithium gas in the BEC-BCS crossover, Proceedings of the International School of Physics "Enrico Fermi" on Ultra-Cold Fermi gases, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00123470
Heat Capacity of a Strongly Interacting Fermi Gas, Science, vol.307, issue.5713, p.1296, 2005. ,
DOI : 10.1126/science.1109220
Pairing and Phase Separation in a Polarized Fermi Gas, Science, vol.311, issue.5760, p.503, 2006. ,
DOI : 10.1126/science.1122876
Fermi Gas in the BCS-BEC Crossover, Physical Review Letters, vol.97, issue.22, p.220406, 2006. ,
DOI : 10.1103/PhysRevLett.97.220406
Quantum Monte Carlo studies of superfluid Fermi gases, Physical Review A, vol.70, issue.4, p.43602, 2004. ,
DOI : 10.1103/PhysRevA.70.043602
Stability of trapped fermionic gases with attractive interactions, Physical Review A, vol.73, issue.4, p.43616, 2006. ,
DOI : 10.1103/PhysRevA.73.043616
Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity, Physical Review Letters, vol.96, issue.16, p.160402, 2006. ,
DOI : 10.1103/PhysRevLett.96.160402
Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity, Physical Review Letters, vol.96, issue.16, pp.160402-239902, 2006. ,
DOI : 10.1103/PhysRevLett.96.160402
The Fermi???Hubbard model at unitarity, New Journal of Physics, vol.8, issue.8, p.153, 2006. ,
DOI : 10.1088/1367-2630/8/8/153
Fermions in the Unitary Regime: A Superfluid of a New Type, Physical Review Letters, vol.96, issue.9, p.90404, 2006. ,
DOI : 10.1103/PhysRevLett.96.090404
Simple theoretical tools for low dimension Bose gases, Journal de Physique IV (Proceedings), vol.116, 2003. ,
DOI : 10.1051/jp4:2004116004
URL : https://hal.archives-ouvertes.fr/hal-00002178
Quantum Gases in Low Dimensions, J. Phys. IV France, vol.116, pp.89-132, 2004. ,
Extension of Bogoliubov theory to quasicondensates, Physical Review A, vol.67, issue.5, p.53615, 2003. ,
DOI : 10.1103/PhysRevA.67.053615
URL : https://hal.archives-ouvertes.fr/hal-00157445
Three fermions in a box at the unitary limit: universality in a lattice model, Journal of Physics A: Mathematical and Theoretical, vol.40, issue.43, p.12863, 2007. ,
DOI : 10.1088/1751-8113/40/43/003
URL : https://hal.archives-ouvertes.fr/hal-00145589
Short Range Scaling Laws of Quantum Gases With Contact Interactions ,
Binding Energy of the Triton, Physical Review, vol.81, issue.1, pp.142-143, 1951. ,
DOI : 10.1103/PhysRev.81.142
On the three-body problem with short-range forces, JETPSov. Phys. JETP, vol.40, issue.13, p.349, 1961. ,
Comment on the problem of three particles with point interactions, JETPSov. Phys. JETP, vol.41, issue.14, pp.1850-1315, 1961. ,
On the point interaction for a three-particle system in quantum mechanics, Sov. Phys. Dokl, vol.6, pp.1335-1072, 1961. ,
A class of exactly solvable three-body quantum mechanical problems and the universal low energy behavior, Physics Letters A, vol.83, issue.3, p.105, 1981. ,
DOI : 10.1016/0375-9601(81)90507-7
Universal Behavior of the Energy of Trapped Few-Boson Systems with Large Scattering Length, Physical Review Letters, vol.89, issue.25, p.250401, 2002. ,
DOI : 10.1103/PhysRevLett.89.250401
Three-Boson Problem near a Narrow Feshbach Resonance, Physical Review Letters, vol.93, issue.14, p.143201, 2004. ,
DOI : 10.1103/PhysRevLett.93.143201
Pseudopotential in resonant regimes, Physical Review A, vol.73, issue.1, p.12701, 2006. ,
DOI : 10.1103/PhysRevA.73.012701
URL : https://hal.archives-ouvertes.fr/hal-00007776
Analytical Solution of the Bosonic Three-Body Problem, Physical Review Letters, vol.100, issue.14, p.140404, 2008. ,
DOI : 10.1103/PhysRevLett.100.140404
URL : https://hal.archives-ouvertes.fr/hal-00272446
-Wave Scattering, Physical Review Letters, vol.96, issue.5, p.50401, 2006. ,
DOI : 10.1103/PhysRevLett.96.050401
URL : https://hal.archives-ouvertes.fr/hal-01355490
Energy levels of three resonantly interacting particles, Nuclear Physics A, vol.210, issue.1, p.157, 1973. ,
DOI : 10.1016/0375-9474(73)90510-1
Tables of integrals, series, and products, 1994. ,
A unitary quantum gas in a harmonic trap : exact mapping to free space zero energy eigenstates and application to the three-body problem ,
Singular Potentials, Physical Review, vol.80, issue.5, p.797, 1950. ,
DOI : 10.1103/PhysRev.80.797
Methods of Theoretical Physics, tome II, p.1665, 1953. ,
Excited Thomas-Efimov levels in ultracold gases, Physical Review A, vol.76, issue.1, p.12720, 2007. ,
DOI : 10.1103/PhysRevA.76.012720
Three Body Problem for Short Range Forces. I. Scattering of Low Energy Neutrons dy Deuterons, JETPSov. Phys. JETP, vol.31, issue.4, p.648, 1956. ,
Collisional properties of weakly bound heteronuclear dimers, Physical Review A, vol.77, issue.3, p.32707, 2008. ,
DOI : 10.1103/PhysRevA.77.032707
URL : https://hal.archives-ouvertes.fr/hal-00266160
Effective theory for trapped few-fermion systems, Physical Review A, vol.76, issue.6, p.63613, 2007. ,
DOI : 10.1103/PhysRevA.76.063613
Hyperspherical adiabatic eigenvalues for zero-range potentials, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.35, issue.10, p.2239, 2002. ,
DOI : 10.1088/0953-4075/35/10/304
Renormalization-group analysis of repulsive three-body systems, Journal of Physics A: Mathematical and General, vol.39, issue.2, p.49, 2006. ,
DOI : 10.1088/0305-4470/39/2/L01
Three-body problem in Fermi gases with short-range interparticle interaction, Physical Review A, vol.67, issue.1, p.10703, 2003. ,
DOI : 10.1103/PhysRevA.67.010703
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations, Physical Review Letters, vol.50, issue.18, p.1395, 1983. ,
DOI : 10.1103/PhysRevLett.50.1395
Effective interaction of three resonantly interacting particles and the force range, Physical Review C, vol.47, issue.5, p.1876, 1993. ,
DOI : 10.1103/PhysRevC.47.1876
Level Density of a Bose Gas and Extreme Value Statistics, Physical Review Letters, vol.98, issue.7, p.70404, 2007. ,
DOI : 10.1103/PhysRevLett.98.070404
URL : https://hal.archives-ouvertes.fr/hal-00134522
Large momentum part of a strongly correlated Fermi gas, Annals of Physics, vol.323, issue.12, p.2971, 2008. ,
DOI : 10.1016/j.aop.2008.03.005
Energetics of a strongly correlated Fermi gas, Annals of Physics, vol.323, issue.12, p.2952, 2008. ,
DOI : 10.1016/j.aop.2008.03.004
Tables of integral transforms, 1954. ,
Fermi pseudopotential approximation: Two particles under external confinement, Physical Review A, vol.65, issue.4, p.43613, 2002. ,
DOI : 10.1103/PhysRevA.65.043613
Interacting atoms under strong quantum confinement, Physical Review A, vol.61, issue.6, p.63416, 2002. ,
DOI : 10.1103/PhysRevA.61.063416
Scattering models for ultracold atoms, Annals of Physics, vol.323, issue.7, p.1770, 2008. ,
DOI : 10.1016/j.aop.2007.12.004
Collisional relaxation of Feshbach molecules and three-body recombination, Phys. Rev. A, vol.87, issue.75, p.20702, 2007. ,
Role of three-body correlations in recombination of spin-polarized atomic hydrogen, Physical Review B, vol.38, issue.1, pp.646-658, 1988. ,
DOI : 10.1103/PhysRevB.38.646
molecular states, Physical Review B, vol.40, issue.13, pp.9176-9182, 1989. ,
DOI : 10.1103/PhysRevB.40.9176
Universal equation for Efimov states, Physical Review A, vol.67, issue.2, p.22505, 2003. ,
DOI : 10.1103/PhysRevA.67.022505
Enhanced dimer relaxation in an atomic and molecular Bose-Einstein condensate, Physical Review A, vol.70, issue.4, p.42706, 2004. ,
DOI : 10.1103/PhysRevA.70.042706
Scattering properties of weakly bound dimers of fermionic atoms, Physical Review A, vol.71, issue.1, p.12708, 2005. ,
DOI : 10.1103/PhysRevA.71.012708
URL : https://hal.archives-ouvertes.fr/hal-00003932
Effect of Bose condensation on inelastic processes in gases, JETP Lett, vol.42, p.209, 1985. ,
Scattering Length Scaling Laws for Ultracold Three-Body Collisions, Phys. Rev. Lett, vol.94, p.213201, 2005. ,
Three-Body Recombination into Deep Bound States in a Bose Gas with Large Scattering Length, Physical Review Letters, vol.87, issue.16, p.160407, 2001. ,
DOI : 10.1103/PhysRevLett.87.160407
Atom-Photon Interactions, C I .3b, 1992. ,
Interference of a variable number of coherent atomic sources, Physical Review A, vol.72, issue.5, p.51601, 2005. ,
DOI : 10.1103/PhysRevA.72.051601
Radio-frequency transitions on weakly bound ultracold molecules, Physical Review A, vol.71, issue.1, p.12713, 2005. ,
DOI : 10.1103/PhysRevA.71.012713
Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments, Physical Review Letters, vol.88, issue.9, p.93201, 2002. ,
DOI : 10.1103/PhysRevLett.88.093201
Atoms, Physical Review Letters, vol.85, issue.13, pp.2721-2724, 2000. ,
DOI : 10.1103/PhysRevLett.85.2721
Total Control over Ultracold Interactions via Electric and Magnetic Fields, Physical Review Letters, vol.100, issue.15, p.153201, 2008. ,
DOI : 10.1103/PhysRevLett.100.153201
URL : http://arxiv.org/abs/0710.0733
Imaging the Mott Insulator Shells by Using Atomic Clock Shifts, Imaging the Mott Insulator Shells By Using Atmoic Clock Shifts, p.649, 2006. ,
DOI : 10.1126/science.1130365
Strongly interacting atoms and molecules in a 3D optical lattice, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.39, issue.10, p.47, 2006. ,
DOI : 10.1088/0953-4075/39/10/S05
State Preparation and Dynamics of Ultracold Atoms in Higher Lattice Orbitals, Physical Review Letters, vol.99, issue.20, p.200405, 2007. ,
DOI : 10.1103/PhysRevLett.99.200405
Controlled exchange interaction between pairs of neutral atoms in an optical lattice, Nature, vol.83, issue.7152, p.452, 2007. ,
DOI : 10.1038/nature06011
BCS theory for trapped ultracold fermions, The European Physical Journal D, vol.7, issue.3, p.433, 1999. ,
DOI : 10.1007/s100530050587
Proceedings of the International School of Physics "Enrico Fermi" on Ultra-Cold Fermi gases, 2007. ,
Energy-dependent effective interactions for dilute many-body systems, Physical Review A, vol.75, issue.1, p.13615, 2007. ,
DOI : 10.1103/PhysRevA.75.013615
High-precision calculations of van der Waals coefficients for heteronuclear alkali-metal dimers, Physical Review A, vol.63, issue.5, p.52704, 2001. ,
DOI : 10.1103/PhysRevA.63.052704
Effective-scattering-length model of ultracold atomic collisions and Feshbach resonances in tight harmonic traps, Physical Review A, vol.66, issue.1, p.13403, 2002. ,
DOI : 10.1103/PhysRevA.66.013403
Analytical solutions for the dynamics of two trapped interacting ultracold atoms, Physical Review A, vol.74, issue.2, p.22712, 2006. ,
DOI : 10.1103/PhysRevA.74.022712
Fermions in Optical Lattices Swept across Feshbach Resonances, Physical Review Letters, vol.96, issue.1, p.10402, 2006. ,
DOI : 10.1103/PhysRevLett.96.010402
Experimental determinations of the hyperfine structure in the alkali atoms, Reviews of Modern Physics, vol.49, issue.1, p.31, 1977. ,
DOI : 10.1103/RevModPhys.49.31
Phase diagram of two-component bosons on an optical lattice, New Journal of Physics, vol.5, p.113, 2003. ,
DOI : 10.1088/1367-2630/5/1/113
Time-Resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices, Science, vol.319, issue.5861, p.295, 2008. ,
DOI : 10.1126/science.1150841
Achieving a BCS Transition in an Atomic Fermi Gas, Physical Review Letters, vol.92, issue.15, p.150404, 2004. ,
DOI : 10.1103/PhysRevLett.92.150404
URL : https://hal.archives-ouvertes.fr/hal-00002433
Measurement of the Entropy and Critical Temperature of a Strongly Interacting Fermi Gas, Physical Review Letters, vol.98, issue.8, p.80402, 2007. ,
DOI : 10.1103/PhysRevLett.98.080402
Adiabatic loading of a Bose???Einstein condensate in a 3D optical lattice, Journal of Modern Optics, vol.54, issue.5, p.735, 2007. ,
DOI : 10.1103/PhysRevLett.89.250404
URL : https://hal.archives-ouvertes.fr/hal-00116297
Probing many-body states of ultracold atoms via noise correlations, Physical Review A, vol.70, issue.1, p.13603, 2004. ,
DOI : 10.1103/PhysRevA.70.013603
Spatial quantum noise interferometry in expanding ultracold atom clouds, Nature, vol.22, issue.7032, p.481, 2005. ,
DOI : 10.1103/PhysRevA.59.4595
Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice, Nature, vol.73, issue.7120, p.733, 2006. ,
DOI : 10.1038/nature05319
Bragg scattering and the spin structure factor of two-component atomic gases, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.39, issue.10, p.211, 2006. ,
DOI : 10.1088/0953-4075/39/10/S20
Bose-Einstein Condensation in Quasi-2D Trapped Gases, Physical Review Letters, vol.84, issue.12, pp.2551-2555, 2000. ,
DOI : 10.1103/PhysRevLett.84.2551
URL : https://hal.archives-ouvertes.fr/hal-00001658
Two-dimensional spin-1/2 Heisenberg antiferromagnet: A quantum Monte Carlo study, Physical Review B, vol.43, issue.4, p.3562, 1991. ,
DOI : 10.1103/PhysRevB.43.3562
Low Temperature Behavior and Crossovers of the Square Lattice Quantum Heisenberg Antiferromagnet, Physical Review Letters, vol.80, issue.12, p.2705, 1998. ,
DOI : 10.1103/PhysRevLett.80.2705