Atoms in electronically high-lying (Rydberg) states exhibit long-range and strong van der Waals or dipole-dipole interactions. Recent experimental and theoretical investigations have shown that Rydberg gases can map to the Ising and Heisenberg model in optical lattices. In this work, we will show how we can control the landscape of the interaction potential from a power-law dependence on inter-particle distances to a soft-core shape, which is realized by coupling an electronically ground state to a Rydberg state by a detuned laser. With this soft-core interaction, we study a two-component many-body setting, where the Rydberg-dressed bosonic atom is described by an extended Bose-Hubbard model, while the bare bosonic state exhibits only on-site interactions (the Bose-Hubbard model). Using the real-space bosonic dynamical mean-field theory, we obtain the ground state phases of the system, including a Mott-insulator, a superfluid and two supersolid phases. Starting from a Mott insulator phase, we find that the bare state first enters the supersolid phase when the inter-site tunneling is increased. Keeping increasing the tunneling, both the dressed and bare state can form supersolid phases. But their order parameters and density patterns can differ significantly. The two states become superfluid phases when the tunneling is further increased.

Weibin Li obtained his Bachelor degree from Huazhong University of Science and Technology in 2002. He got his PhD at Wuhan Institute of Physics and Mathematics, CAS in 2007. Immediately after his PhD, he started his first postdoc at Max-Planck-Institute for the Physics of Complex Systems, Dresden, Germany. In 2010, he was awarded an EU Marie-Curie fellowship and moved to the University of Nottingham, UK. In 2015, he was promoted to an assistant professor at the University of Nottingham.