, Bosonic particles trapped in a periodic potential
, Energy bands for different lattice depths
,
, Numerical values computed for J and U as a function of the lattice depth V 0, p.13
, Sketch of the Superfluid and the Mott insulating phases
,
31 2.2 Evolution of the momentum distribution across the Mott transition, p.38 ,
,
,
Loading of the BEC from the ODT to optical lattice potential, p.48 ,
,
54 3.10 Sketch of the electronic detector assembly ,
Transfer of the atoms from the m J = 1 to the m J = 0 state, p.59 ,
, Electronic detection of lattice superfluid
Effect of the MCP channel angle on the detector resolution, p.62 ,
, Local saturation of the electronic detector
, Harmonic approximation of Wannier functions
, Atomic density as a function of the time of flight
, Effect of the interactions during the time of flight
,
, Three-dimensional atom distribution of a lattice gas
, Effect of saturation
, 76 3.24 3D collisions happening during the time-of-flight of a lattice gas, p.77
, Adiabatic ramping of the lattice potential
, 2 QMC profiles at U/J = 9, vol.5
,
, 1D momentum cuts calculated with the QMC algorithm for different temperatures, vol.86
Temperature measurement across the SF-MI transition, vol.87 ,
, Temperature of the lattice gases produced to explore the Mott transition, p.88
, Comparison between the experimental and the QMC cuts
89 4.9 Temperature of the lattice gas clouds used to investigate the SF-NF and the SF-MI transition ,
, Method to distinguish the condensate distribution from the depletion, p.93
,
, RMS and HWHM sizes of the central diffraction peak across the Mott transition calculated using the QMC data
, Evolution of the momentum distribution across the Mott transition, p.98
, Determination of the presence of a condensate fraction
, Measured values of P (k r )
, Condensate fraction across the Mott transition
, Finite-temperature phase diagram for a homogeneous system at filling n = 1, p.104
, Height of the central peaks across the Mott transition
, Measurement of the condensate mode fluctuations
, Variance of the condensate mode atom number in the superfluid phase and across the Mott transition
, Measurement of the lowest-energy single-particle state population fluctuations across the Mott transition
, 26 1D cuts of the data used for the calculation of the fidelity susceptibility, p.112
, Measurement of the 1D susceptbility
, Signatures of the particle-holes excitation revealed in other experiments, p.115
, Strong coupling momentum distributions
Measured momentum distribution in the Mott insulating phase, p.121 ,
, Contrast of the momentum distribution modulation for the data at U/J ? 35, p.122
, Contrast of the momentum distribution computed with the QMC profiles, p.123
, Difference between the experimental data and the strong coupling theory, p.124
, Spectral weight of the quasi-particles in the Mott state
,
Measured ?k = k d correlation peak amplitude as a function of ?, p.133 ,
, , p.135
,
, ?k) far a Mott insulator
, In-situ density profile of a Mott insulator at s = 18 and N = 15 000 atoms, p.138
139 6.10 Coherence length l c as a function of, Effect of the Mott in-situ profile on the bunching peak shape ,
Comparison between the central and the lateral bunching peaks, p.142 ,
) for a perfect Mott insulator, p.146 ,
Profiles extracted from the third-order correlation g (3) (?k 1 , ?k 2 ), p.147 ,
) (?k 1 , ?k 2 = 0.5 k d ), p.148 ,
,
Spatially-resolved measurement of the second-order correlation, p.151 ,
Coherence length l c and amplitude ? across the SF-NF transition, p.152 ,
157 2 He energy level used for the cooling, Phase-space density for the different cooling steps ,
, 16 3.1 Far-field regime for He and Rb, p.122
, 136 6.2 Parameters used to compute the data of Fig. 6.10 and Fig. 6.11. In order to measure the correlation length with a good precision, we use ?k ? ? l c
? 1 < 1. The measured value of of l c and ? are also reported, p.140 ,
, Investigation of the shape of the lateral bunching peaks
,
Reflection of electrons by a crystal of nickel, Proceedings of the National Academy of Sciences, vol.14, issue.4, pp.317-322, 1928. ,
A test of a new type of stellar interferometer on Sirius, Nature, vol.178, pp.1046-1048, 1956. ,
Theory for a Hanbury Brown Twiss experiment with a ballistically expanding cloud of cold atoms, Phys. Rev. A, vol.74, p.53607, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00080649
Measurement of subpicosecond time intervals between two photons by interference, Phys. Rev. Lett, vol.59, pp.2044-2046, 1987. ,
Atomic Hong-Ou-Mandel experiment, Nature, vol.520, pp.66-68, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01102786
, Bose-Einstein Condensation in Dilute Gases, 2008.
Quantum multimode model of elastic scattering from Bose-Einstein condensates, Phys. Rev. Lett, vol.94, p.200401, 2005. ,
Observation of Bose-Einstein condensation in a dilute atomic vapor, Science, vol.269, issue.5221, pp.198-201, 1995. ,
Evaporative cooling of Sodium atoms, Phys. Rev. Lett, vol.74, pp.5202-5205, 1995. ,
Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature, vol.415, pp.39-44, 2002. ,
, Brown et Twiss pour les atomes froids, 2007.
URL : https://hal.archives-ouvertes.fr/tel-00168946
Semi-conductors with partially and with completely filled 3d-lattice bands, Proceedings of the Physical Society, vol.49, pp.59-71, 1937. ,
Discussion of the paper by de Boer and Verwey, Proceedings of the Physical Society, vol.49, pp.72-73, 1937. ,
Boson localization and the superfluid-insulator transition, Phys. Rev. B, vol.40, pp.546-570, 1989. ,
Cours du collège de France, 2013. ,
, Solid State Physics. Cengage Learning, 1976.
,
Interaction effects on Wannier functions for bosons in an optical lattice, Phys. Rev. A, vol.92, p.63637, 2015. ,
Quantum cell model for Bosons, Phys. Rev, vol.129, pp.959-967, 1963. ,
Bose-Einstein condensation and liquid Helium, Phys. Rev, vol.104, pp.576-584, 1956. ,
Cold atoms: A field enabled by light, Europhysics Letters), vol.110, p.53001, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01166054
Quantum phases in an optical lattice, Phys. Rev. A, vol.63, p.53601, 2001. ,
Phase diagram of the Bose-Hubbard model, Europhysics Letters (EPL), vol.26, pp.545-550, 1994. ,
Phase diagram and thermodynamics of the three-dimensional Bose-Hubbard model, Phys. Rev. B, vol.75, p.134302, 2007. ,
, Quantum Phase Transitions, 2011.
High-precision measurement of the thermal exponent for the three-dimensional XY universality class, Phys. Rev. B, vol.74, p.132502, 2006. ,
Superfluid and insulating phases in an interacting-Boson model: Mean-Field theory and the RPA, Europhysics Letters (EPL), vol.22, pp.257-263, 1993. ,
Dynamics and thermodynamics of the Bose-Hubbard model, Phys. Rev. B, vol.59, pp.12184-12187, 1999. ,
Mott-insulator-to-superfluid transition in the Bose-Hubbard model: A strong-coupling approach, Phys. Rev. A, vol.71, p.33629, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00117529
Gutzwiller projection for bosons, Phys. Rev. B, vol.44, pp.10328-10332, 1991. ,
The Monte Carlo method, Journal of the American Statistical Association, vol.44, issue.247, pp.335-341, 1949. ,
, Rombouts Journal of Computational Physics, vol.225, pp.2249-2266, 2017.
Noise correlations in low-dimensional systems of ultracold atoms, Phys. Rev. A, vol.79, p.13609, 2009. ,
Interference pattern and visibility of a Mott insulator, Phys. Rev. A, vol.72, p.53606, 2005. ,
Simulating physics with computers, International Journal of Theoretical Physics, vol.21, pp.467-488, 1982. ,
Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect, Phys. Rev. Lett, vol.56, pp.827-830, 1986. ,
The reflection of electrons from standing light waves, Mathematical Proceedings of the Cambridge Philosophical Society, vol.29, issue.2, pp.297-300, 1933. ,
Bragg scattering of atoms from a standing light wave, Phys. Rev. Lett, vol.60, pp.515-518, 1988. ,
Transition from a strongly interacting 1D Superfluid to a Mott Insulator, Phys. Rev. Lett, vol.92, p.130403, 2004. ,
Bloch oscillations of atoms in an optical potential, Phys. Rev. Lett, vol.76, pp.4508-4511, 1996. ,
Cold bosonic atoms in optical lattices, Phys. Rev. Lett, vol.81, pp.3108-3111, 1998. ,
CO 2 -laser optical lattice with cold Rubidium atoms, Phys. Rev. A, vol.57, pp.20-23, 1998. ,
Phases of a two-dimensional Bose gas in an optical lattice, Phys. Rev. Lett, vol.105, p.110401, 2010. ,
Ultracold quantum gases in triangular optical lattices, New Journal of Physics, vol.12, p.65025, 2010. ,
Mean-field scaling of the Superfluid to Mott insulator transition in a 2D optical superlattice, Phys. Rev. Lett, vol.119, p.100402, 2017. ,
A Mott insulator of fermionic atoms in an optical lattice, Nature, vol.455, pp.204-207, 2008. ,
Optical dipole traps for neutral atoms, Advances In Atomic, Molecular, and Optical Physics, vol.42, pp.95-170, 2000. ,
Probing the superfluid-to-Mott insulator transition at the single-atom level, Science, vol.329, issue.5991, pp.547-550, 2010. ,
Singleatom imaging of fermions in a quantum-gas microscope, Nat. Phys, vol.11, pp.738-741, 2015. ,
High-resolution scanning electron microscopy of an ultracold quantum gas, Nature Physics, vol.4, pp.949-953, 2008. ,
Single-particle-sensitive imaging of freely propagating ultracold atoms, New Journal of Physics, vol.11, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00746758
Signatures of the superfluid to Mott-insulator transition in the excitation spectrum of ultracold atoms, New Journal of Physics, vol.8, pp.160-160, 2006. ,
The Higgs amplitude mode at the two-dimensional superfluid/Mott insulator transition, Nature, vol.487, pp.454-458, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-01397828
Dynamical structure factor of one-dimensional bose gases: Experimental signatures of beyond-Luttingerliquid physics, Phys. Rev. A, vol.91, p.43617, 2015. ,
Singleatom-resolved probing of lattice gases in momentum space, Phys. Rev. A, vol.97, p.61609, 2018. ,
An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays, Science, vol.354, issue.6315, pp.1021-1023, 2016. ,
Boson Mott insulators at finite temperatures, Phys. Rev. Lett, vol.99, p.120405, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00149582
Local-density approximation for confined bosons in an optical lattice, Phys. Rev. A, vol.70, p.53601, 2004. ,
Recent developments in quantum Monte Carlo simulations with applications for cold gases, Rep. Prog. Phys, vol.75, p.94501, 2012. ,
Critical behavior at the spatial boundary of a trapped inhomogeneous Bose-Einstein condensate, Phys. Rev. A, vol.95, p.53606, 2017. ,
Critical behavior of a trapped interacting Bose gas, Science, vol.315, issue.5818, pp.1556-1558, 2007. ,
Influence of the trap shape on the detection of the superfluid-Mott-insulator transition, Phys. Rev. A, vol.78, p.23605, 2008. ,
Critical behavior and scaling in trapped systems, Phys. Rev. Lett, vol.102, p.240601, 2009. ,
Criticality in trapped atomic systems, Phys. Rev. Lett, vol.104, p.245705, 2010. ,
Reconstructing the quantum critical fan of strongly correlated systems using quantum correlations, Nature Communications, vol.10, 2019. ,
The quantum theory of optical coherence, Phys. Rev, vol.130, pp.2529-2539, 1963. ,
Imaging with amplitude and intensity interferometers, 2004. ,
, Quantum Optics, 2010.
Fluctuations of photon beams: The distribution of the photo-electrons, Proceedings of the Physical Society, vol.74, pp.233-243, 1959. ,
, Statistical Optics. A Wiley-Interscience publication, 1985.
, , 2000.
The evaluation of the collision matrix, Phys. Rev, vol.80, pp.268-272, 1950. ,
Une démonstration simplifiée du théorème de Wick en mécanique statistique, Nuclear Physics, vol.15, 1960. ,
Condensate fraction in a 2D Bose gas measured across the Mott-Insulator transition, Phys. Rev. Lett, vol.100, p.120402, 2008. ,
Phase coherence of an atomic Mott Insulator, Phys. Rev. Lett, vol.95, p.50404, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00116291
Solving the quantum many-body problem via correlations measured with a momentum microscope, Phys. Rev. Lett, vol.118, p.240402, 2017. ,
Theory of correlations between ultracold bosons released from an optical lattice, Phys. Rev. A, vol.78, p.13627, 2008. ,
Measuring the momentum distribution of a lattice gas at the single-atom level, 2018. ,
URL : https://hal.archives-ouvertes.fr/tel-02012074
Etude miscroscopique de la distibution en impulsion de condensats de Bose-Eintein d'Hélium métastable, 2018. ,
A New Metastable Helium Machine : An Investigation into the Attributes of Trapping, Cooling and Detecting Metastable Helium, 2015. ,
URL : https://hal.archives-ouvertes.fr/tel-01124010
A Bose-Einstein condensate of metastable atoms, vol.292, pp.461-464, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00568654
Bose-Einstein condensation of metastable Helium, Phys. Rev. Lett, vol.86, pp.3459-3462, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00002127
Penning collisions of laser-cooled metastable helium atoms, The European Physical Journal D -Atomic, Molecular, Optical and Plasma Physics, vol.14, pp.15-22, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00002126
, Quantum Mechanics. Dunod, 2003.
Adiabatic loading of a Bose-Einstein condensate in a 3D optical lattice, Journal of Modern Optics, vol.54, issue.5, pp.735-743, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00116297
Exploring phase coherence in a 2D lattice of Bose-Einstein condensates, Phys. Rev. Lett, vol.87, p.160405, 2001. ,
The direct detection of thermal neutrons by imaging microchannelplate detectors, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.293, issue.3, pp.569-574, 1990. ,
Lifetimes of metastable states of noble gases, Phys. Rev, vol.89, pp.1202-1208, 1953. ,
Characterization of a detector chain using a FPGA-based time-to-digital converter to reconstruct the three-dimensional coordinates of single particles at high flux, Review of Scientific Instruments, vol.86, issue.11, p.113105, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01179601
Second-order coherence of superradiance from a Bose-Einstein condensate, Phys. Rev. A, vol.90, p.13615, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00922184
The spatial extent of gain depression for MCPbased photon detectors, Review of Scientific Instruments, vol.63, issue.1, pp.816-819, 1992. ,
Expansion of a quantum gas released from an optical lattice, Phys. Rev. Lett, vol.101, p.155303, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00330438
Role of interactions in time-of-flight expansion of atomic clouds from optical lattices, Phys. Rev. A, vol.82, p.23618, 2010. ,
Quantum fluctuations and condensate fraction during time-of-flight expansion, Phys. Rev. A, vol.82, p.31601, 2010. ,
Ghost imaging with atoms, Nature, vol.540, pp.100-113, 2016. ,
Elastic scattering losses from colliding Bose-Einstein condensates, Phys. Rev. A, vol.73, p.33602, 2006. ,
Matter-wave Fourier optics with a strongly interacting two-dimensional Fermi gas, Phys. Rev. A, vol.90, p.43611, 2014. ,
Suppression of the critical temperature for superfluidity near the Mott transition, Nature Physics, vol.6, pp.998-1004, 2010. ,
Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms, Nature, vol.519, pp.211-214, 2015. ,
Bosonizing one-dimensional cold atomic gases, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.37, pp.1-47, 2004. ,
Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys, vol.71, pp.463-512, 1999. ,
Exploring the thermodynamics of a universal Fermi gas, Nature, vol.463, pp.1057-1060, 2010. ,
Intrinsic heating and cooling in adiabatic processes for Bosons in optical lattices, Phys. Rev. Lett, vol.99, p.120404, 2007. ,
Single-atomresolved fluorescence imaging of an atomic Mott insulator, Nature, vol.467, pp.68-72, 2010. ,
A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice, Nature, vol.462, pp.74-77, 2009. ,
Observation of quantum criticality with ultracold atoms in optical lattices, Science, vol.335, issue.6072, pp.1070-1072, 2012. ,
Revealing the condensate and noncondensate distributions in the inhomogeneous Bose-Hubbard model, Phys. Rev. A, vol.87, p.51603, 2013. ,
Quantum depletion of a homogeneous Bose-Einstein condensate, Phys. Rev. Lett, vol.119, p.190404, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01637897
Precision measurements on a tunable Mott insulator of ultracold atoms, Phys. Rev. Lett, vol.107, p.175301, 2011. ,
Phase diagram for a Bose-Einstein condensate moving in an optical lattice, Phys. Rev. Lett, vol.99, p.150604, 2007. ,
State diagrams for harmonically trapped bosons in optical lattices, Phys. Rev. A, vol.79, p.53605, 2009. ,
Observation of atom number fluctuations in a Bose-Einstein condensate, Phys. Rev. Lett, vol.122, p.163601, 2019. ,
Microcanonical fluctuations of a Bose system's ground state occupation number, Phys. Rev. E, vol.54, pp.3495-3498, 1996. ,
Condensate fluctuations of a trapped, ideal Bose gas, Phys. Rev. A, vol.54, pp.5048-5054, 1996. ,
Quantum phase transitions and vortex dynamics in superconducting networks, Physics Reports, vol.355, issue.4, pp.235-334, 2001. ,
Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations, Scientific Reports, vol.9, 2019. ,
Quantum information and computation, Nature, vol.404, pp.247-255, 2000. ,
Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys, vol.90, p.35005, 2018. ,
Ground state overlap and quantum phase transitions, Phys. Rev. E, vol.74, p.31123, 2006. ,
Fisher information and entanglement of non-Gaussian spin states, Science, vol.345, issue.6195, pp.424-427, 2014. ,
Quantum phase transitions and bipartite entanglement, Phys. Rev. Lett, vol.93, p.250404, 2004. ,
Entanglement, quantum phase transitions, and density matrix renormalization, Quantum Information Processing, vol.1, pp.45-53, 2002. ,
Entanglement entropy across the superfluid-insulator transition: A signature of Bosonic criticality, Phys. Rev. Lett, vol.116, p.190401, 2016. ,
Mott-Insulator transition in a two-dimensional atomic bose gas, Phys. Rev. Lett, vol.98, p.80404, 2007. ,
Observation of correlated particle-hole pairs and string order in low-dimensional Mott insulators, Science, vol.334, issue.6053, pp.200-203, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-01397834
Strongcoupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results, Phys. Rev. A, vol.79, p.53631, 2009. ,
Green's function approach to the Bose-Hubbard model, Arxiv, 2009. ,
Complex methods for the sciences ,
Vers uneétude spectroscopique de la transition d'Anderson, 2018. ,
Mesoscopic Physics of Electrons and Photons, 2007. ,
Quantum Material's Theory, from perturbation theory to dynamical-mean Oeld theory ,
Probing many-body states of ultracold atoms via noise correlations, Phys. Rev. A, vol.70, p.13603, 2004. ,
Ideal n-body correlations with massive particles, Nature Physics, vol.9, pp.341-344, 2013. ,
Spatial coherence and density correlations of trapped Bose gases, Phys. Rev. A, vol.59, pp.4595-4607, 1999. ,
Spatial quantum noise interferometry in expanding ultracold atom clouds, Nature Physics, vol.434, pp.481-484, 2005. ,
Noise correlation spectroscopy of the broken order of a Mott Insulating phase, Phys. Rev. Lett, vol.100, p.250403, 2008. ,
Correlations and counting statistics of an atom laser, Phys. Rev. Lett, vol.95, p.90404, 2005. ,
Position sensitive anodes for MCP read-out using induced charge measurement, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.477, issue.1, pp.256-261, 2002. ,
High accuracy position response calibration method for a micro-channel plate ion detector, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.835, pp.42-50, 2016. ,
URL : https://hal.archives-ouvertes.fr/in2p3-01323815
The physic of Hanbury-Brown and Twiss intensity interferometry: from stars to nuclear collisions, Acta. Phys. Pol. B, vol.29, pp.1839-1884, 1998. ,
Hanbury Brown and Twiss-type experiment with electrons, Science, vol.284, issue.5412, pp.299-301, 1999. ,
Hanbury Brown and Twiss interferometry with interacting photons, Nature Photonics, vol.4, pp.721-726, 2010. ,
Hanbury Brown Twiss effect for ultracold quantum gases, Science, vol.310, pp.648-651, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00091259
Experimental characterization of a quantum many-body system via higherorder correlations, Nature, vol.545, pp.323-326, 2017. ,
Energetics of a strongly correlated Fermi gas, Annals of Physics, vol.323, issue.12, pp.2952-2970, 2008. ,
Tan's contact for trapped Lieb-Liniger Bosons at finite temperature, Phys. Rev. Lett, vol.121, p.220402, 2018. ,
Contact and sum rules in a near-uniform Fermi gas at unitarity, Phys. Rev. Lett, vol.122, p.203401, 2019. ,
An oscillator circuit to produce a radio-frequency discharge and application to metastable helium saturated absorption spectroscopy, Review of Scientific Instruments, vol.83, issue.4, p.44705, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00672488
Three-dimensional laser cooling at the Doppler limit, Phys. Rev. A, vol.90, p.63407, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01068704
Efficient all-optical production of large 6 Li quantum gases using D 1 gray-molasses cooling, Phys. Rev. A, vol.90, p.43408, 2014. ,
Sub-Doppler laser cooling of fermionic 40K atoms in three-dimensional gray optical molasses, EPL, vol.100, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00738260
Cold bosonic atoms in optical lattices, Phys. Rev. Lett, vol.81, pp.3108-3111, 1998. ,
Single atom-resolved probing of lattice gases in momentum space, Phys. Rev. A, vol.97, p.61609, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01826115
, Two-body collisions in the time-of-flight dynamics of lattice Bose superfluids, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02318623
Momentum-space atom correlations in a Mott insulator, Phys. Rev. X, vol.9, p.41028, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02113175