One- and two-atom states in a rotating ring lattice

We study the states of one and two atoms in a rotating ring lattice in a Hubbard-type tight-binding model. The model is developed carefully from basic principles in order to properly identify the physical observables. The one-particle ground state may be degenerate and represent a finite flow velocity depending on the parity of the number of lattice sites, the sign of the tunneling matrix element, and the rotation speed of the lattice. Variation of the rotation speed may be used to control one-atom states and leads to peculiar behaviors such as wildly different phase and group velocities for an atom. Adiabatic variation of the rotation speed of the lattice may also be used to control the state of a two-atom lattice dimer. For instance, at a suitably chosen rotation speed both atoms are confined to the same lattice site.

Figure 1

Energies of the lattice eigenstates for $N=3$ (upper panel) and $N=4$ (lower panel) sites as a function of the site-to-site rotation phase $\phi$. The graphs are for lattice momenta $q=0$ (solid black line), $q=2\pi /N$ (red dotted line), $q=4\pi /N$ (green dashed line), and $q=6\pi /N$ (blue dash-dotted line).