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Trapping, cooling and controlling neutral atoms have advanced experimental exploration on multiple fronts. On the one hand, atoms trapped in spatially extended optical lattices with a few atoms confined per site have enabled an extensive exploration of Fermi-Hubbard, Bose-Hubbard models and their variants which are the quintessential examples used to understand the microscopic theory of materials. On the other hand, 1000s of atoms trapped in spatially confined dipole traps and cooled to a Bose-Einstein Condensate (BEC) have been useful to explore the limits and applications of quantum sensing including magnetometry and gravimetry. It is important to note that the former has a microscopic per-site occupancy (n = O(1)) revealing deep quantum mechanical phenomena, the latter is essentially macroscopic (n = O(10^3)), revealing mostly mean-field and semi-classical phenomena. This leaves the mesoscopic intermediate regime, i.e., the meeting point of classical and quantum phenomena open. Here, we propose to build a system of bosons in a 1D lattice, with a mesoscopic number of bosons per site, i.e., n = O(10).
The idea is to make a cylindrical trapping region with a single weakly focused dipole trap and divide it into trapping sites with a set of painted blue-detuned ultrathin ``walls", at normal incidence. Unlike standard optical lattices, painted lattices can trap several bosonic atoms per lattice site paving the way to simulating Bose-Hubbard models with higher local occupancies, $n \sim 10$. This opens the avenue to study transport phenomena, phase transitions and many other fundamental aspects of quantum materials in mesoscopic Hubbard models. Moreover, this system can also be viewed as a connected BEC array with applications in quantum sensing, e.g., lattice gravimetry
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