  Hopf-link semimetals exhibit exotic gapless band structures with fascinating
topological properties, which have never been observed in nature. Here we
demonstrate nodal lines with topological form of Hopf-link chains in artificial
semimetal-bands. Driving superconducting quantum circuits with elaborately
designed microwave fields, we mapped the momentum space of a lattice to a
parameter space of the Hamiltonian for a Hopf-link semimetal. By measuring the
energy spectrum, we directly imaged nodal lines in cubic lattices. By tuning
the driving fields, we adjusted various parameters of Hamiltonian. Important
topological features, such as link-unlink topological transitions and the
robustness of the Hopf-link chain structure were investigated. Moreover, we
extracted the linking number by detecting the Berry phase associated with
different loops encircling nodal lines. This topological invariant clearly
reveals the nontrivial topology of the Hopf-link semimetal. Our results provide
knowledge for developing new materials and quantum devices.
