, Bosonic particles trapped in a periodic potential

, Energy bands for different lattice depths

. Wannier and .. .. Bloch's-functions,

, 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

. .. Numerical-values-of-u/j,

. .. , 31 2.2 Evolution of the momentum distribution across the Mott transition, p.38

.. .. He,

A. He and *. Bec,

. .. , Loading of the BEC from the ODT to optical lattice potential, p.48

.. .. Tunneling-time,

. .. Band-mapping-technique, 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

.. .. Far-field-regime,

, 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

.. .. Thermometry,

, 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

. .. Experiment, 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

.. .. Mott-crossover,

, 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

. .. Mott-insulator, , p.135

.. .. Periodicity,

, ?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

.. .. Three-body-bunching-peak,

. .. , 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

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