# Time of flight images of Bose-Hubbard model

on the website of Immanuel Bloch, you can find time of flight images of bosonic particles inside an optical lattice for different values of the depth of the lattice.

Can someone precisely explain this picture? To what does the distance between the interference peaks refer to?

This is a time-of-flight image, and it therefore refers to the momentum distribution of the atoms. As explained in the original Nature paper (10.1038/415039a), the distance between the peaks (in the picture, i.e., in the momentum space) is $2\hbar k$, where $k = 2\pi/\lambda$ is the wavenumber corresponding to the periodicity of the lattice with $\lambda$ being the laser wavelength.