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We show that resonant dipole-dipole interactions between Rydberg atoms in a triangular lattice can give rise to artificial magnetic fields for spin excitations. We consider the coherent dipole-dipole coupling between $np$ and $ns$ Rydberg states and derive an effective spin-1/2 Hamiltonian for the $np$ excitations. By breaking time-reversal symmetry via external fields we engineer complex hopping amplitudes for transitions between two rectangular sub-lattices. The phase of these hopping amplitudes depends on the direction of the hop. This gives rise to a staggered, artificial magnetic field which induces non-trivial topological effects. We calculate the single-particle band structure and investigate its Chern numbers as a function of the lattice parameters and the detuning between the two sub-lattices. We identify extended parameter regimes where the Chern number of the lowest band is $C=1$ or $C=2$.
We develop a formalism for photoionization (PI) and potential energy curves (PECs) of Rydberg atoms in ponderomotive optical lattices and apply it to examples covering several regimes of the optical-lattice depth. The effect of lattice-induced PI on
The dynamics of excitons in a one-dimensional ensemble with partial spatial order are studied. During optical excitation, cold Rydberg atoms spontaneously organize into regular spatial arrangements due to their mutual interactions. This emergent latt
Long-range dipole-dipole and quadrupole-quadrupole interactions between pairs of Rydberg atoms are calculated perturbatively for calcium, strontium and ytterbium within the Coulomb approximation. Quantum defects, obtained by fitting existing laser sp
We present quantum mechanical calculations of Auger decay rates for two Rubidium Rydberg atoms with weakly overlapping electron clouds. We neglect exchange effects and consider tensor products of independent atom states forming an approximate basis o
We experimentally realize Rydberg excitations in Bose-Einstein condensates of rubidium atoms loaded into quasi one-dimensional traps and in optical lattices. Our results for condensates expanded to different sizes in the one-dimensional trap agree we