Extreme fragmentation of a Bose gas

Fragmentation of an interacting Bose gas refers to the macroscopic occupation of a finite set of single-particle eigenstates. This phenomenon is related to the notion of particle-number squeezing in quantum optics, an exquisite property of quantum states that can offer metrological gain. So far, fragmentation has only been partially achieved in experiments involving a large number $N$ of bosons in few modes. Here, we introduce a practical and efficient scheme to prepare fragmented states in systems realizing the $L$-mode Bose-Hubbard model. We demonstrate how a large energy detuning between the modes can be used as a practical control parameter to successfully fragment a Bose gas over an extremely short preparation time. Applying an optimal-control approach within realistic experimental constraints, we obtain total fragmentation at a high filling factor, realizing $\mathrm{\mid }N\mathrm{/}L,\mathrm{.}\mathrm{.}\mathrm{.},N\mathrm{/}L⟩$ Fock states with hundreds of bosons in very few modes over a few tunneling times.