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Physical Realization of von Neumann Lattices in Rotating Dipole-blockaded Bose Gases

A mathematical lattice, called the von Neumann lattice, is a subset of coherent states and exists periodically in the phase space. It is unlike solids or Abrikosov lattices that are observable in physical systems. Abrikosov lattices are vortices closely packed into a lattice with a flux quantum through a unit cell. Although Abrikosov lattices appear generally in various physical systems, vortex lattices with multiple-flux quantums through a unit cell are more stable than Abrikosov lattices in some physical regimes of the systems with non-local interactions between particles. No theory is able to describe these vortex lattices today. Here, we develop a theory for these vortex lattices by extending von Neumann lattices to the coordinate space with a unit cell of area that is proportional to flux quantums through a unit cell. The von Neumann lattices not only show the same physical properties as the Abrikosov lattice, but also describe vortex lattices with multiple-flux quantums through a unit cell. From numerical simulations of a rapidly rotating dipole-blockaded gas, we confirm that vortex lattices showed in our simulations are the representation of von Neumann lattices in the coordinate space. We anticipate our theory to be a starting point for developing more sophisticated vortex-lattice models. For example, the effect of Landau-level mixing on vortex lattice structures, vortices formed inside superfluid droplets and structural phase transitions of vortex matter in two-component Bose-Einstein condensates will be relevant for such developments.