Figure 1

Spatially resolved atom-number fluctuations in an approximately symmetric six-site optical lattice after slow ramp up of the lattice potential. (a) Single-shot absorption image of the atomic cloud with typical mean atom numbers indicated. The experimentally observed normalized on-site fluctuations ${\zeta }^2$ (dark) are compared to TWA numerics (light). (b) Experimental (dark colors) and numerical (light colors) results for the relative atom-number fluctuations ${\xi }_N^2$ between all site pairs that increase with pair separation (different colors/darkness). Representative one-standard-deviation statistical error bars [transparent boxes in (b)] show increased experimental uncertainty for the outer wells. For this summarizing figure we average all measurements taken for final lattice heights larger than $900\hspace{0.5em}$Hz.Reuse & Permissions

Figure 2

Evolution of the on-site fluctuations during the lattice ramp. Experiment (red filled circles), eight-site discrete model at $T\simeq 16\hspace{0.5em}$nK (blue diamonds), advanced model (TWA) at $T\simeq 5.5\hspace{0.5em}$nK (black open circles) and $T=0$ (inset). (a)-(c) show ${\zeta }^2$ in sites 4-6, respectively. Temperatures are chosen for the best agreement in all experimental observables shown in this manuscript.Reuse & Permissions

Figure 3

Normalized relative atom-number fluctuations ${\xi }_N^2$ vs lattice height for experiment (red filled circles), TWA numerics at $T\simeq 5.5$ nK (black open circles), the local two-mode model at $T\simeq 10$ nK (green solid line), and the eight-site discrete model at $T\simeq 16$ nK (blue diamonds). (a)–(c) correspond to the well pairs (34), (45), and (56). On the bottom row, ${\xi }_N^2$ between larger subsystems of adjacent sites binned together: (d) sites ({23}{45}), (e) sites ({123}{456}), (f) the cumulative contribution of the number of continuum Hartree-Fock-Bogoliubov phonon modes to the correct value of ${\xi }_N^2$ for the pairs (34) (dashed line) and ({123}{456}) (solid line) at $T\simeq 5.5$ nK (red or higher pair of lines) and $T=0$ (black or lower pair of lines).Reuse & Permissions